Algebra II Chemistry
How many carbon atoms are in 1-pentene?
5
What inequality describes the graph? (Evernote)
x ≤ -5
Which of the following is an example of a chemical reaction?
Lighting a match
Use a graph to solve the system of equations. {x + y = -4 {y = 3x - 8
(1, -5)
Determine which ordered pair (x, y) is a solution of 3x - y ≤ 15.
(5, 4) Solution Substitute 3(5) - 4 ≤ 15 11 ≤ 15 True
Express 0.7312 as a geometric series, and write its sum as the ratio of two integers.
(Evernote)
Evaluate the radical expression: (-1/7)(³√-64)⁴
-256/7
Which of the following is a balanced chemical equation? 1. 2Na(s) + 2 H2O(l) → 2 NaOH(aq) + H2(g) 2. 2Na(s) + H2O(l) → 2 NaOH(aq) + H2(g) 3. 2Na(s) + 2 H2O(l) → NaOH(aq) + H2(g) 4. None of the listed answers are correct 5. Na(s) + 2 H2O(l) → NaOH(aq) + 2 H2(g)
1. 2Na(s) + 2 H2O(l) → 2 NaOH(aq) + H2(g)
Which of the following chemical formulas represents an alkane? 1. C5H12 2. C4H8 3. C3H6 4. None of the listed answers are correct 5. C6H6
1. C5H12
What is the most likely value for the neutron-proton ratio of a small, stable atom?
1.5
What is the change in enthalpy when 45.7 g water is heated from 15.4°C to 85.6°C? The specific heat of water is 4.18 J/g°C.
13,400 J
Teesha is in the bowling club. There are 33 students in the club. Five of them will be picked at random to attend an awards banquet. What is the probability that Teesha will not be randomly chosen to attend the banquet?
28/33 Solution Probability of getting chosen is 5/33, so the the probability of not getting chosen is 33 - 5 = 28
Given the equation 3 O2(g)→2 O3(g) ∆H = +285.4 kJ, calculate ∆H for the following reaction. 3/2 O2(g) → O3(g). 1. +109.8kJ 2. +212.4kJ Correct! 3. +142.7kJ 4. +181.3kJ 5. None of the listed answers are correct
3. +142.7kJ
Which of the following is an example of a compound? 1. Co 2. Na 3. H2O 4. Cl2 5. None of the listed answers are correct
3. H2O
What is the pH of an acid with a pOH of 10?
4
Which is the equation of the line with slope -4 and y-intercept 5?
4x + y -5 = 0 y = -4x + 5
Use the quadratic formula to solve the equation. 6x² - 24x - 30 = 0
5, -1
Determine the probability that you will roll a number greater than 1 on a number cube.
5/6
Evaluate the expression. (3/8)⁻²
64/9
Simplify 3x² - 4x - 5 + 4x² + 8x - 7
7x² + 4x - 12
Find: ₇P₄
840
Isotope A contains 56 protons and 80 neutrons. Isotope B contains 55 protons and 81 neutrons. Isotope C contains 57 protons and 80 neutrons. Isotope D contains 56 protons and 74 neutrons. Which isotopes have the same mass number?
A and B
What occurs during nuclear fission?
A large nucleus splits into two smaller nuclei.
CH 1
CH 1
CH 10
CH 10
CH 2
CH 2
CH 3
CH 3
CH 4
CH 4
CH 5
CH 5
CH 6
CH 6
CH 7
CH 7
CH 8
CH 8
CH 9
CH 9
Which of the following atoms is most able to attract electrons?
F
Which of the following ions has the largest ionic radius?
I
Find all solutions of cos(x) - √(1 - 3cos²(x)) = 0
Incorrect: None of the listed answers are correct Correct: No Solution
In May, Victor bought 24 styrofoam balls and decorated them as toy figurines. In June, he sold 17 figurines. In May, Wanda bought 28 styrofoam balls to decorate and in June, she sold 12 figurines. Which matrix represents all of their May purchases and their June sales?
May June Victor [24 -17] Wanda [28 -12]
Which must occur for the atom of an element to be transformed into an atom of an element whose atomic number is less by two?
The atom must lose two protons.
Why are gamma rays dangerous to humans while radio waves are not?
The high levels of energy in gamma rays indirectly cause more ionization.
What are alkali metals often used for?
batteries
What is true of the orbitals in the 4f energy level?
Together, the seven 4f orbitals can hold 14 electrons.
Which statement accurately relates the octet rule to the reactivity of xenon, a noble gas?
Xenon is very inert because it has eight electrons in its valence shell.
Find AC - CB (Evernote)
[-13 19] [-12 -44]
A student is given a mixture that he is told consists of two pure substances. The mixture is a clear liquid. The student is able to separate the mixture only through distillation. Which were most likely the states of matter of the two substances in the mixture?
a liquid dissolved in another liquid
Which of the following is a quadratic function?
f(x) = -1 + 9x² + 7x
In water solution, hydrogen ions exist in the form of
hydronium ions
The sublimation and deposition point for carbon dioxide (CO2) is -78.5°C. A student wants to transform a sample of solid CO2 into a gas. What is the simplest method?
leave the solid carbon dioxide at room temperature
Which system of equations can be classified as independent?
none of these
Which metal would you expect to have the weakest metallic bonds?
potassium
Classify the polynomial by degree and number of terms. Describe the shape of its graph. 7x² + 7x + 7
quadratic trinomial; parabola
Describe how the graph of the function y = 15(x + 2) + 4 can be obtained from the graph of y = 3(x + 2).
shift up 4 units, and vertically stretch by a factor of 5
What solid forms during the reaction of silver nitrate with sodium chloride?
silver chloride
Find the variance and the standard deviation for the following data. 7, 20, 7, 15, 21, 4, 22, 17, 13
variance ≈ 39.78; standard deviation ≈ 6.31 https://www.easycalculation.com/statistics/standard-deviation.php Take the Variance (Population Standard deviation) and Population Standard deviation
Which set of characteristics matches the given standard equation and parabola graph? (Evernote) x = 1/24 y²
vertex: (0, 0) directrix: x=-6
A closed system of water and water vapor at equilibrium is at a temperature of 30°C. If the temperature of the system is reduced to 15°C, then
water will change from water vapor to liquid
Solve the quadratic inequality, and graph the solution on a number line. x² - 2x ≥ 24
x ≤ -4 or x ≥ 6
Write an equation in slope-intercept form for a line that passes through the given pair of points. (-6,5), (-9,0)
y = 5x/3 + 15
Write the pair of parametric equations as a single equation in x and y. {x = 8t - 4 {y = 6t² - 2
y = 6((x+4)/8)² - 2 Solution x = 8t - 4 Add 4 to both sides x + 4 = 8t Divide by 8 on both sides t = (x + 4)/8 Substitute y = 6((x+4)/8)² - 2
The two hyperbolas in the graph are conjugates, meaning they share the same asymptotes. Given the following equation of the hyperbola represented by the thin curve, find the equation of its conjugate, which is represented by the thick curve. (Evernote) x²/9 - y²/25 = 1
y²/25 - x²/9 = 1
Find the three positive geometric means between 6 and 1875/8.
15, 75/2, 375/4 Solution t₁=6 and t₅=1875/8 t(n) = t₁r^(n-1) t₅ = 6r⁴ 1875/8 = 6r⁴ r = 2.5 t₂ = 6(2.5)¹ 15 t₃ = 6(2.5)² 37.5 or 75/2 t₄ = 6(2.5)³ 9375 or 375/4
Which of the following pressures of gas over one liter of water will result in the greatest quantity of dissolved oxygen at 25°C?
2.0 atm
The turnstiles at the entrance to the State Fair kept track of the number of people entering the fairgrounds, for the first seven hours following the openning of the fair. Find a quadratic equation that models the data shown. (Evernote)
0.083x² - 0.197x + 7.62 Graphing Calculator STAT→Edit Put x values into L1 and y values into L2. 2ND→MODE→STAT→CALC →5:QuadReg
How much heat is lost when a 64 g piece of copper cools from 375 °C, to 26 °C? (The specific heat of copper is 0.38452 J/g x °C). Place your answer in kJ.
-8588.63 J = -8.6 kJ
Find the determinant, and tell whether the matrix has an inverse. det [10 -7] [-5 -6 ]
-95; Yes
Determine the quantity (in moles) of cadmium metal that is produced in a solution of cadmium sulfate, CdSO4, when a current of 1.50 amperes passes through the solution for 200 minutes. Cadmium ions are Cd2+. F = 96,485 C/mol.
0.0933 mol Cd
Solve the system of equations by substitution. {4y = 4 {x + 2y + z = 10 {y - 2z = -5
Incorrect: None of the listed answers are correct Correct: x=5 y=1 z=3
The mass of a proton is closest to the mass of which particle?
a neutron
Which of the following describes the arrangement of electrons in the Bohr model of the atom?
arranged in circular orbits
During which physical changes does a substance absorb energy from its surroundings?
as it melts, vaporizes, and increases in temperature
The periodic table organizes elements based on _____.
atomic number
Which of the following determines where an element is placed on the periodic table?
atomic number
Which set of characteristics matches the given parabola graph and standard equation? (Evernote) x = -1/4 y²
axis of symmetry: y=0 focus: (-1, 0) vertex: (0, 0) Mathway: Graph
Which set of characteristics matches the given standard equation and parabola graph? (Evernote)
focus: (-1, -4) vertex: (-1, 2)
Solve the nonlinear system of equations. {x² + y² = 144 {x² - 4y² = 64
four solutions: (±8√2, ±4)
Thermal energy would naturally flow between objects at which temperatures?
from 5°C to -5°C
Show that the function is a quadratic function by writing it in the form f(x) = ax² + bx + c and indentifying a, b and c. f(x) = (5x - 4) (5x + 3)
f(x) = 25x² - 5x - 12 a = 25, b =5, c = -12
Find the inverse of the function and determine whether the inverse is a function. f(x) = 19x²
f⁻¹(x) = ±√(x/19), f⁻¹(x) is not a function.
Given the graph of y = 3(x + 1), what function would be obtained by moving the graph up 4 and moving it 6 to the right?
f(x) = 3(x - 5) + 4
A student is given an unknown mixture and asked to determine whether it is a solution, suspension, or emulsion. How would the student eliminate a suspension?
filter the mixture
The graph of f(x) = x² is stretched vertically by a factor of 3, translated 4 units to the right, and translated 8 units downward. Determine the equation of the transformed function, g(x).
g(x) = 3(x - 4)² - 8
The boiling point of water at sea level under normal atmospheric conditions is 100°C. At what temperature would you predict water will boil on the top floor of a high-rise apartment house?
slightly less than 100°C
A student wants to transform a sample of gaseous carbon dioxide into solid carbon dioxide. What must she do to accomplish this feat?
remove energy from the sample
Determine the end behavior of the graph of the function f(x) = 3x⁴ - 2x³ + 2x + 2
rises to the left; rises to the right
Find the exact value of the sine, cosine, and tangent of -210°.
sin = 1/2 cos = -√3/2 tan = -√3/3 Mathway (Trigonometry) Find the Exact Value
Matter consists of a variety of particles of different sizes with different properties. When comparing protons, molecules, and atoms, which describes a molecule?
the largest of the three particles; has no charge
The Group I metals are highly reactive because
the lone electron in their valance shells is easily lost
What information is left out of a balanced equation showing the reactants and products of an esterification reaction?
the mechanism showing the series of steps involved in the reaction
What is the benefit of writing a net ionic equation instead of a formula equation?
the net ionic equation shows only the substances that change in the reaction
A cook adds sugar and soluble citric acid (for a lemon flavor) to a cup of tea. Which are the solutes in the drink?
the tea, sugar, and citric acid
In an elastic collision,
the total energy of all molecules in the collision remains constant
In a hot air balloon, the balloon fills because
the volume of the air increases as the temperature increases
Evaluate x⁴ - 10x² + 24 when x=3
15
Which of the following is formed during the reaction of hydrochloric acid and ammonia? 1. ammonium ions and water 2. ammonium chloride 3. chloride ions and water 4. None of the listed answers are correct 5. ammonium chloride and water
2. ammonium chloride
Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: In 10
2.303
Evaluate the expression. (2/5)⁵
32/3125
Simplify: (2 + 5i)/(5 + 4i)
(30/41) + (17/41)i
Find the exact value of cos(345°).
(√6 + √2)/4 Mathway (Trigonometry) Find the Exact Value
What is the oxidation number of hydrogen in a molecule of NH3?
+1
Which of the following will produce the same change in the boiling point of water?
0.20 molal methanol and 0.10 molal KF
Calculate the molarity of 16.4 g CaCl2 in 0.614 L solution.
0.241 M CaCl2
As one goes down vertically in a group in the periodic table, which of the following is true? 1. Both answers are true 2. Neither answer is true 3. the number of protons in each element increases 4. the atomic mass increases
1. Both answers are true
Write the first five terms of the sequence defined by the given recursive or explicit formula. (Evernote)
4, -3, 31, -167, 959
2SO3(g)⇄⇄⇄ 2SO2(g) + O2(g) The conventional equilibrium constant expression (Kc) for the system as described by the above equation is: 1. None of the listed answers are correct 2. [SO3]2/[SO3]2[O2] 3. [SO2][O2] 4. [SO2]2/[SO3] 5. [SO2]2[O2]/[SO3]2
5. [SO2]2[O2]/[SO3]2
What volume of 2 N base is needed to neutralize 34 mL of 3 N acid?
51 mL
What is the final temperature when 42.3 grams of water at 0.0 °C and 255.8 grams of water at 76.78 °C are mixed?
65.9 °C
Which equation describes a parabola?
6y² + 11x - 13y = -1
Evaluate the radical expression: 8(⁴√(81)²
72
Solution A is 0.44 M and reacts with 0.11 M of solution B. Assume that the value of x is 0, the value of y is 1, and r is 1.07 × 10-1 /s. Find the rate constant for this reaction.
9.73 × 10-1 /s
Evaluate the expression. (-3/8)²
9/64
How many different ways can 6 people be seated around a circular table?
120 Solution (n-1)! (6-1)! 5! = 5 × 4 × 3 × 2 × 1 = 120
When chemical bonding occurs, which of the following elements would be most likely to gain valence electrons?
Cl
What happens in a solution where the [Mg2+] is 0.005M and the [CO32-] is 0.05M if the Ksp for MgCO3 is 2.6 × 10-5?
The solution is saturated, so a precipitate will be present.
√((6x + 2)² - 4(9)(x²+1))/(2(9))
X≈1.3333333 or X≈133/100
Is it possible to increase the wavelength of light by varying frequency? Explain.
Yes, to increase wavelength, frequency is decreased.
Find [1 17 14][11 3] [19 7] [9 5]
[460 192]
A chemist remotely measures the temperature of a substance as it progresses from a solid to a liquid to a gas. Unfortunately, the chemist is unable to directly observe the behavior of the substance as it is heated. Nevertheless, she is able to describe the period during which the substance melts. What evidence allows the chemist to do this?
a period of constant temperature near the beginning of the experiment
csc(2x) + cot(2x) forms an identity with which of the following?
cot x Use Mathway to "Verify the Identity" csc(2x) + cot(2x) = cot(x)
Transition of an electron between which of the following results in absorption of light at the greatest frequency?
from n=1 to n=5
How does a coordinate covalent bond differ from a standard covalent bond?
in the source of the electrons shared
How does a catalyst affect reaction rate?
it increases reaction rate
Which inequality has the solution shown in the graph? (Evernote)
m + 7 ≥ 9
A single-displacement reaction can also be classified as what other type of chemical reaction?
oxidation-reduction
Fireworks are created through a chemical reaction of certain color-producing compounds and _____.
oxygen
Which pair of elements will form bonds with the lowest degree of polarity?
phosphorus (2.19 Paulings) and hydrogen (2.20 Paulings)
Which particle is mostly likely to carry electromagnetic force?
photon
Liquid nitrogen is used in medicine to freeze and destroy precancerous skin cells. This liquid is stored in a cylinder-shaped container. If the cylinder is left open, the liquid nitrogen will become a gas and escape from the container into a rectangular room. Which of the following will be the shape of the volume of gas?
rectangular
What happens when an inhibitor is added to a chemical reaction in progress?
the rate of the chemical reaction decreases
What happens when a catalyst is added to a chemical reaction that is already in progress?
the reaction with the lower activation energy occurs
A mineralogist discovers a new substance in a volcanic rock. When the mineralogist searches for more samples of the same substance in rocks from different locations, she should expect the new samples of the substance to have
the same chemical properties and the same physical properties
Solve the equation for x. Write the exact solution and the approximate solution to the nearest hundredth, when appropriate. In(8x - 6) = 3
x = (3/4) + (e³/8) x ≈ 3.26 Exponential form e³= 8x - 6
solve for x. 3x - 3 = x - 9
x = -3
Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (−2, 0) asymptote: y = 3x
x²/4 - y²/36 = 1
Find the standard equation for the ellipse, using the given characteristics. vertices: (0, ±8) foci: (0, ±√55)
x²/9 + y²/64 = 1
Write an equation in slope-intercept form of the line that passes through (- 5, 4) and is parallel to the graph of y = -4x + 1.
y = -4x -16
If $1500 is invested at an interest rate of 10%, compounded continuously, determine the balance in the account after 2 years. Use the formula A = Pe^rt.
$1832.10
A T-shirt company estimates that the average cost per shirt can be approximated by the function A(x) = (3.75x + 200)/x, where x is the number of T-shirts made. Find the average cost per T-shirt when the company makes 10 shirts.
$23.75
The inflation rate of the U.S. dollar is 3.1 percent. What this means is that every year, prices increase by 3.1 percent. If a pound of meat cost $2.37 nine years ago, what does it cost now?
$3.12 Solution 2.37(1+0.031)⁹
Rationalize the denominator. (√11) ÷ (9 + √5)
( 9√11 - √55) / 76
Use elimination to solve the system of equations. {4x + 2y = -12 {3x - 2y = 5
(-1, -4)
Use elimination to solve the system of equations. {2x - 5y = 1 {5x -2y = -4
(-22/21, -13/21)
Which of the given ordered pairs are NOT solutions to the system of inequalities? {2x + 3y < 1 {x -3y > 2 (3, 1), (-3, -2), (5, -5), (-2, 4), (-4, 5)
(-4, 5), (3, 1), (-2, 4)
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {4x + y = -24 {2x + 2y = -18
(-5, -4) You can just solve by using Elimination or Substitution
Use a graph to solve the system of equations. {x + y = -1 {y = 3x + 19
(-5, 4)
Convert 279° to radians.
(31/20)π Mathway (Trigonometry) Convert from Degrees to Radians
Solve the system of equations by substitution. {3x + 4y = 32 {3x + y = 17
(4, 5)
For a circle of radius 8 feet, find the arc length of a central angle of 30°.
(4/3)π feet Solution r = 8 and θ = π/6 (change 30° to radians) s = rθ s = 8(π/6) s = (4/3)π or 4π/3
Factor the quadratic expression. x² - 11x + 30
(x - 5) (x - 6)
Simplify the rational expression. ( (x² + 14x + 49)/8x ) ÷ ( (x+7)/4x )
(x+7)/2
Find the exact value of sin(- 450° + 300°).
-1/2 Solution Use Sum and Diffrence Identities: sin(A + B) = sinAcosB + cosAsinB sin(450°)cos(300°) + cos(450°)sin(300°) = -1/2 Mathway (Trigonometry) Find the Exact Value
Evaluate the trigonometric expression. Sin⁻¹(-½)
-30° Solution π = 180° -π/6 -180°/6 = 30° Mathway Evaluate (Do not use Find the Exact Value)
Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - x² - 14x + 24 = 0
-4, 2, 3
Solve the equation by completing the square. Give exact solutions. x² - 2x - 24 = 0
-4, 6
Evaluate the expression. 3 - 14 × 6 ÷ 7 + 3
-6
Simplify the expression. ((-u)³(-u⁹)⁸)/(u⁵)³
-u⁶⁰ Solution (-u³ × u⁷²)/u¹⁵ -u⁷⁵/u¹⁵ = -u⁶⁰
If the equilibrium constant for the reaction A + 2B ⇄ C + 5/2 D has a value of 4.0, what is the value of the equilibrium constant for the reaction 2C + 5D ⇄ 2A + 4B at the same temperature?
0.063
A hat contains 22 names, 10 of which are female. If five names are randomly drawn from the hat, what is the probability that at least four female names are drawn?
0.105 ((₁₀C₄ × ₁₂C₁)+(₁₀C₅ × ₁₂C₀))÷(₂₂C₅) ((210 × 12)+(252 × 1))÷(26334) 2772÷26334 = 0.105
Nitrosyl chloride, NOCl, dissociates on heating as shown below. When a 1.50 gram sample of pure NOCl is heated at 350oC in a volume of 1.00 liter, the percent dissociation is found to be 57.2%. Calculate Kc for the reaction as written. NOCl(g) ⇄ NO(g) + 1/2 Cl2(g)
0.107
A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?
0.21617 Solution (₆C₃)(0.67)³(1-0.67)³ = 0.21617
Compound A and compound B react according to the following chemical equation: In which of the following cases will compound A be the limiting reagent? A + 2B → 2C + D
0.3 mol A is combined with 0.8 mol B
Calculate the molality of 2.89 g of NaCl dissolved in 0.159 L of water (density of water is 1.00 g/mL).
0.311 molal NaCl
The Statue of Liberty was damaged by corrosion and had to be repaired. Before making repairs, scientists investigated which of the following? 1. All of the listed answers are correct 2. the materials used to build the statue 3. the environment around the statue 4. the interactions of the building materials with each other and the environment
1. All of the listed answers are correct
Which of the following must be true of a compound with the molecular formula C6H12 if this compound contains only single bonds? 1. It is a monocyclic hydrocarbon. 2. It is a polycyclic hydrocarbon. 3. It is a linear hydrocarbon. 4. There is not enough information to tell.
1. It is a monocyclic hydrocarbon.
If a compound falls into the class of compounds with the general formula CnH2n+2, what must be true? 1. It must contain single bonds only. 2. It must contain at least one double bond. 3. It must contain triple bonds only. 4. It must contain double bonds only.
1. It must contain single bonds only.
Which of the following is true about rows of the periodic table? 1. atomic mass increases from left to right 2. periods contain whole groups 3. atomic number increases from right to left 4. None of the listed answers are true 5. periods contain whole families
1. atomic mass increases from left to right
Solve the equation for x: 10^x = 18
1.26
Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: e^¼
1.284
In a bag there are 3 green jelly beans, 2 black jelly beans, and 8 yellow jelly beans. Once a jelly bean is drawn, it is not replaced. Find the probability of randomly drawing a green jelly bean and then a black jelly bean in two consecutive draws.
1/26
The bowling scores of all of the bowlers in 12 bowling leagues are normally distributed. Their mean score is 201 points, with a standard deviation of 33 points. If one league has 120 bowlers, how many of them are likely to score more than 168 points?
101 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(168, 10⁹⁹, 201, 33)→Enter = 0.84 .84 or 84% 84% of 120 is 100.8 rounded to the nearest whole number equals 101
If the number of molecules, temperature, and volume are equal, at which pressure measurement would molecules experience the fewest intermolecular interactions?
101,325 Pa
Which of the following temperatures of gas over one liter of water will result in the greatest quantity of dissolved oxygen at 25°C?
10°C
In Sean's school there are 96 families which have 4 children. The circle graph shows the probability of each combination of girls and boys in a family with four children. Use the circle graph to predict the probability that one of these 96 families, chosen at random, will only have children of the same sex. (Evernote)
12.5%
If 50 mL of 0.12 M HCl is used to titrate 0.45 M KOH, what is the volume of the base?
13.3 mL
Kozinski played in 16 basketball games this season, Hussein played in 32 games, and Johnson played in 55 games. Kozinski averaged 6 points and 2 rebounds per game, Hussein averaged 8 points and 11 rebounds, and Johnson averaged 18 points and 16 rebounds. Multiply the following matrices to get the total number of points scored and the total number of rebounds made, by all three players combined. [ 6 2 ] [16 32 55] [ 8 11] [18 16]
1342 points, 1264 rebounds
For ∆ ABC, find the measure of ∠A to the nearest degree. (Evernote)
19° Solution Use Law of Cosines for "c" c = √(a² + b² - 2ab cos C) c = 37 a = 12, b = 35, and c = 37 Use Law of Sines sin A/a = sin C/c sin A/12 = sin(90°)/37 sin A = 12sin(90°)/37 sin A ≈ 12/37 Convert from radians to degrees ∠A = 18.58° → 19°
Find the sum of the infinite geometric series, if it exists. (Evernote) ∑3(-½)^(k-1)
2 Solution ∑3(-½)^(k-1) t₁ = 3(-½)⁰ 3 t₂ = 3(-½)¹ -1.5 r = t₂/t₁ r = -1.5 ÷ 3 r = -½ S = t₁/(1 - r) S = 3/(1 - (-½)) S = 3/1.5 S = 2
Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - 7x² + 14x - 8 = 0
2, 1, 4
Which of the following elements has the largest atomic radius? 1. P 2. Ba 3. F 4. Ga
2. Ba
Which of the following chemical formulas represents an alcohol? 1. None of the listed answers are correct 2. C6H13OH 3. HCOOH 4. COH2 5. C5H11NH2
2. C6H13OH
Calcium's valence shell holds two electrons. Chlorine's valence shell holds seven electrons. Which represents the ions that are bonded in calcium chloride? 1. Ca2- + 2Cl+ 2. Ca2+ + 2Cl- 3. None of the listed answers are correct 4. Ca2+ + Cl2- 5. 2Ca+ + 2Cl-
2. Ca2+ + 2Cl-
Identify the species being oxidized and reduced in this reaction: Cr+ + Sn4+ → Cr3+ + Sn2+ 1. Cr3+: reduced, Sn2+: oxidized 2. Cr+: oxidized, Sn4+: reduced 3. None of the listed answers are correct 4. Cr3+: oxidized, Sn2+: reduced 5. Cr+: reduced, Sn4+: oxidized
2. Cr+: oxidized, Sn4+: reduced
Determine the oxidation number of the elements in this compound: LiH 1. Li: -1, H: +1 2. Li: +1, H: -1 3. Li: -1, H: -1 4. None of the listed answers are correct 5. Li: +1, H: +1
2. Li: +1, H: -1
Which of the following is true? 1. More ionization energy is required to release an electron from a lead atom than from a carbon atom. 2. More ionization energy is required to release an electron from a carbon atom than from a lithium atom. 3. None of the listed answers are true. 4. More ionization energy is required to release an electron from a lead atom than from a radon atom.
2. More ionization energy is required to release an electron from a carbon atom than from a lithium atom.
A change occurs that cools the container in which it happens. What is the best term to describe the change? 1. genetic 2. None of the listed answers are correct 3. exothermic 4. chemical 5. physical
2. None of the listed answers are correct
Three cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of three cards are possible?
22,100 Solution 52 choose 3 ₅₂C₃ = 22,100
A circular, rotating, serving tray has 5 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the circular tray?
24 Solution (n-1)! (5-1)! 4! = 4 × 3 × 2 × 1 = 24
How many different arrangements can be made using all of the letters in the word GAME?
24 Solution ₄P₄
At 685 mmHg pressure and 50°C, a gas has a volume of 5.35 L. If the volume of the container decreases to 1.25 L, what is the amount of the pressure change?
2930 mmHg
Solve the equation. Round your answers to the nearest hundredth. 5^x-1 = 25
3
Which of the following will produce the same change in the freezing point of water? 1. None of the listed answers are correct 2. 0.15 molal ethanol and 0.30 molal NaBr 3. 0.30 molal ethanol and 0.15 molal NaBr 4. 0.15 molal ethanol and 0.15 molal NaBr
3. 0.30 molal ethanol and 0.15 molal NaBr
The ratio of elements in the molecular compound ethyl alcohol is: carbon, 2; hydrogen, 6; oxygen, 1. Which is the formula for this compound? 1. None of the listed answers are correct 2. CHO 3. C2H6O 4. CH3O 5. C2H3O
3. C2H6O
Which of the following groups of elements is ranked from least reactive to most reactive? 1. K, Ca, Sc, Ti 2. None of the listed answers are correct 3. Li, Na, K, Rb 4. Sr, Ca, Mg, Be 5. K, Na, Li, H
3. Li, Na, K, Rb
Evaluate: ₇C₄
35
If the mole fraction of glucose in water is 0.050 for a particular solution, what is the mass percent of glucose in this solution?
35%
Use the Law of Cosines to solve for "A" to the nearest tenth of a degree. (Evernote)
35.3° Law of Cosines cos A = (b² + c² - a²)/(2bc) cos A = (43² + 50² - 29²)/(2 × 43 × 50) cos A = 0.8158 cos⁻¹(0.8158) = 35.3° Just do this ↓ ∠A = cos⁻¹((b² + c² - a²)/(2 × 43 × 50)) ∠A = 35.3°
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - 9x³ + 10x² + 90x - 200
4, 5, ±3.16
What is the enthalpy change when 12.8g H2(g) reacts with excess Cl2(g) to form HCl(g)?H2(g) + Cl2(g) → 2HCl(g) ∆H = -184.6kJ 1. -4.73 x 103kJ 2. -2.41 x 103kJ 3. None of the listed answers are correct 4. -1.17 x 103kJ 5. -3.39 x 103kJ
4. -1.17 x 103kJ
Suppose you mix-up the cards below and choose one without looking. What is the probability of selecting neither "E" nor "G"? H E H E G W I
4/7 Solution Probability of selecting "E" or "G" is 3/7. 7/7 - 3/7 = 4/7
What mass of solute is needed to prepare the following solution? 500 mL of 0.350 M C6H12O6 1. None of the listed answers are correct 2. 30.2 g C6H12O6 3. 33.8 g C6H12O6 4. 36.1 g C6H12O6 5. 31.5 g C6H12O6
5. 31.5 g C6H12O6
Which of the following is true about halogens? 1. they have eight valence electrons 2. they have one valence electron 3. None of the listed answers are correct 4. they have two valence electrons 5. they have seven valence electrons
5. they have seven valence electrons
Solve triangle ABC given that a = 11, b = 13, and c = 15.
A = 45.6° , B = 57.6° , C = 76.9° Solution Use Law of Cosines cos A = (b² + c² - a²)/2bc cos A = (13² + 15² - 11²)/(2 × 13 ×15) cos A = 7/10 cos⁻¹(7/10) = 45.6° cos B = (c² + a² - b²)/2ca cos B = (15² + 11² - 13²)/(2 × 15 × 11) cos B = 59/110 cos⁻¹(59/110) = 57.6° cos C = (a² + b² - c²)/2ab cos C = (11² + 13² - 15²)/(2 × 11 × 13) cos C = 5/22 cos⁻¹(5/22) = 76.9°
Which of the following best describes a compound?
A compound can be separated into its elements.
Evaporating water produces gaseous water. What has occurred during this process?
A physical change has not resulted in a new substance.
Which best describes the basis of VSEPR theory?
All valence electrons repel each other.
The following statement is false: An absorption spectrum illustrates the size of the photon absorbed by an electron. Why is this false?
An absorption spectrum illustrates the wavelength, not the size, of the photon absorbed by an electron.
Which of the following statements provides information about the magnetic orbital quantum number of an electron?
An electron is one of two found in the same orbital.
Identify the species being oxidized and reduced in this reaction: 2 As (s) + 3 Cl2 (g) → 2 AsCl3
As: oxidized, Cl2: reduced
Which statement best describes covalent bond formation?
Atoms share electrons to have eight valence electrons.
Given that F = 32°, G = 55°, and f = 10, solve the triangle. If no such triangles exist, write none. Round to the nearest tenth. (Evernote)
E = 93° , g = 15.5, e = 18.8 Solution F = 32°, G = 55° , E = ?° f = 10, g = ?, e = ? 32° + 55° + ∠E = 180° ∠E = 93° Use Law of Sines 10/sin(32) = g/sin(55) g = 10sin(55)/sin(32) g = 15.5 10/sin(32) = e/sin(93) e = 10sin(93)/sin(32) e = 18.8
Write the expression csc(2x) + cot(2x) in terms of tan x or cot x.
Incorrect: None of the listed answers are correct Correct: cot(x)
A chemist adds 3.0 g sodium nitrate to 1.0 L water and stirs. The resulting solution is clear and colorless. He adds another 1.0 g sodium nitrate and stirs. The solution remains clear and colorless. What was true of the original solution he made?
It contained less solute than the maximum amount that can be dissolved in 1.0 L water.
Which statement correctly describes the second law of thermodynamics in relation to chemical and physical changes?
It limits the direction in which energy flows.
If the frequency of a wave is doubled, how will the energy of the wave change?
It will increase by a factor of two.
The depth of snow at seven different mountain lodges is 13 in., 15 in., 21 in., 17 in., 90 in., 13 in., and 19 in. Find the mean, median, and mode. Tell which measure is the most useful for predicting how deep the snow will be at an eighth lodge.
Mean = 26.9 in Median = 17 in Mode = 13 The median is the most useful.
Find the mean, the median, and mode of the data set: 14, 6, 21, 16, 16, 7, 20, 19, 7
Mean: 14 Median: 16 Mode: 7, 16
Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 27, 8, 9, 48, 19, 10, 29, 42, 2, 50, 44
Minimum = 2 Maximum = 50 Q₁=9; Q₂=27; Q₃=44 Range = 48 IQR = 35 Mathway Find the Five Number Summary, range, and Find the Interquartile Range (H-Spread)
Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 29, 14, 40, 12, 16, 46, 22, 23, 19, 31, 7, 9
Minimum = 7 Maximum = 46 Q₁=13; Q₂=20.5; Q₃=30 Range = 39 IQR = 17 Q₂ = mean
A student is naming ionic compounds and names a compound nitrogen baride. Is this the proper name for this compound? Why or why not?
No, the cation is named first and the anion second in an ionic compound.
What would happen in a nuclear reactor with no control rods?
Nuclear reactions would proceed too quickly, making it impossible to regulate the chain reaction.
Which best explains the surface tension of water?
Surface molecules are attracted only downward and sideways.
Si and Ge have which properties in common?
They are semiconductors, have four valence electrons, and are generally stable.
Ivan Bogdanovich plans to decorate stuffed animals to sell at a crafts fair. The decorations cost $44.00 and the stuffed animals cost $5.25 each. a. Write a function expressing the cost, C(x), of the project in terms of the number of stuffed animals decorated, x. b. Determine the cost of decorating 25 stuffed animals. c. How many stuffed animals can be decorated with a budget of $227.75?
a. C(x) = 5.25x + 44.00 b. $175.25 c. 35
Solve the equation or formula for the variable specified. B = 7a²b, for b.
b = B/(7a²)
When a chemical reaction occurs, atoms _____.
join together
How is the periodic table of elements arranged?
top to bottom and left to right
Solve for x. x-7=1
x=8
Which equation best describes the graph below? (Evernote)
y = -2x + 5
Write the equation of the line, in slope-intercept form, that contains the point (-1, - 5) and is perpendicular to the line -8x - 4y = 3.
y = -2x -7
Write the slope-intercept form of an equation of the line that passes through the point (3, - 6) and has the slope m = -4.
y = -4x + 6
How many distinct committees of 14 people can be formed if the people are drawn from a pool of 23 people? Use factorials to express the answer.
₂₃C₁₄ = 23!/(9! 14!) Solution nCr = n!/(r!(n-r)!) 23!/(14!(23-14)!) 23!/(14!(9)!) 23!/ (9! 14!)
Rationalize the denominator. 2 ÷ √5
(2√5)/5
The Student Government secretary, and two teacher's aides are ordering supplies. The supplies they need are listed in the table. (Evernote)
(Evernote)
Write an explicit formula for the nth term of the geometric sequence. 7/4, 49/24, 343/144, 2401/864, ...
(Evernote) Solution explicit formula for nth term in a geometric sequence is t(n) = t₁r^(n-1) t₁ = 7/4 and r = 7/6 t(n) = 7/4(7/6)^(n-1)
Which of the following is an identity?
(cos(x))/(1 + sin(x)) = (1 - sin(x))/(cos(x)) Mathway Verify the Identity
For the pair of functions, f and g, find (g o f)(x) and (f o g)(x). f(x) = 6 - x, g(x) = x² - 2
(g o f)(x) = x² - 12x + 34 Solution (6-x)² - 2 36 - 6x - 6x + x² - 2 x² - 6x - 6x + 36 - 2 x² - 12x + 34 (f o g)(x) = -x² + 8 Solution -x(x² - 2) + 6 -(x² - 2) + 6 -x² + 2 + 6 -x² + 8
Which function is the correct match with the the given graph and vertex (Evernote)
f(x) = -3(x + 1)²
Find the standard equation of a circle with the given radius and center. radius: 7 center: (1, 1)
(x - 1)² + (y - 1)² = 49
Evaluate the expression. 64 × 4² - 2 × 2²
1016
Find the standard equation of a circle with the given radius and center. radius: 4 center: (3, - 5)
(x - 3)² + (y + 5)² = 16 Mathway: Find the Equation (put coordinate points comma r=4)
Find the standard equation for the ellipse, using the given characteristics taken from the graph. (Evernote)
(x+4)²/16 + (y+3)²/9 = 1
Find all the zeros of the polynomial function. f(x) = x³ + 4x² + 6x + 9
-3, (-1 ±i√11)/2
Evaluate the sum. (Evernote)
-3003
Solve the equation or inequality. (2x-2)/(x²-36) ≥ 1/(x+6)
-6 ≤ x ≤ -4 or x ≥ 6
If a principal of $1250 is invested at an annual interest rate of 4% compounded annually, what is the account balance at the end of 6 years?
$1581.648
NCUse the frequency table below, with the a total of 18 catalog items sold at four different prices, to find the average price per item. (Evernote)
$16.50
Mr. Reaich, the ticket agent for a small commuter airline, has developed a model to forecast the total monthly revenue from the airline's passenger service. Under this model, the total revenue, R, is equal to $368 times the number of first-class, F, plus $324 times the number of coach passengers, C. Their flight schedule and overall aircraft capacity limit the total number of passengers carried during a single month to a maximum of 30,775. The number of coach class passengers is at least seven times the number of first-class passengers, and logically, the number of airline passengers in either class cannot be negative. Express the model in mathematical form.
$368F + $324C = R F + C ≤ 30,775 C ≥ 7F F ≥ 0; C ≥ 0
Find the final amount of the investment: $3000 at 8% interest compounded quarterly for 4 years.
$4118.36
Simplify. ( (x - 2)/(2x²) ) - ( (2x + 1)/(9x) ) + ( (7x)/(12) )
( 21x³ - 8x² + 14x - 36 ) / 36x²
Simplify the rational expression. (Evernote) ( 3/(x² + 7x + 12) + 1/(x² + 11x + 28) ) ÷ ( 2/(x² + 10x + 21) + 1/x² + 13x + 36) )
( 4(x + 9)(x + 6) ) / ( 3(x² + 12x + 31) )
Find the image of (5, -6) after a counterclockwise rotation of 270° about the origin. (Evernote)
(-6, -5)
Use elimination to solve the system of equations. {7x - 3y = -43 {5x + 6y = -47
(-7, -2)
If f(x) = 3x + 4 and g(x) = 2 + x, which is the rule of function 3g(x) - 3f(x)?
-6x - 6
Find the standard equation for the hyperbola with the given characteristics. center: (5, 4) one focus: (-25, 4) one vertex: (23, 4)
(x-5)²/324 - (y-4)²/576 = 1
Write the equation in standard form and classify the conic section it defines. 2x² + 2y² - 28x + 24y + 162 = 0
(x-7)² + (y+6)² = 4; circle
Evaluate the logarithmic expression to the nearest thousandth. log₈ 1/2
-0.333
Simplify. (-3x + 8)/(x² - 49) - (-2x + 1)/(x² - 49)
-1/(x+7)
Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 205 cm and a standard deviation of 13 cm. What is the probability that a randomly selected high jumper has a personal best between 218 and 244 cm? (Evernote)
0.1574 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(→Enter→75, 90, 85, 7) Between, mean, then standard deviation
Which of the following would be expected to dissolve most rapidly in 100 mL water?
0.2 g powdered sugar
The personal savings of the Young Saver Club were normally distributed with a mean of $525 and a standard deviation of $64. What is the probability that a randomly selected saver has an account total between $525 and $589?
0.3413 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(525, 589, 525, 64)→Enter = 0.3413
Find cot (-290°).
0.364 Mathway (Trigonometry) Find the Exact Value
Find tan 382°.
0.404 Mathway (Trigonometry) Find the Exact Value
Determine the specific heat of a certain metal if a 450 gram sample of it loses 34,500 Joules of heat as its temperature drops by 97 °C.
0.79 J/g x °C
A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of the purchases are returned. What is the probability that no more than 1 of the next 6 purchases will be returned?
0.954 Solution ((₆C₁)(0.06)¹(1 - 0.06)⁵) + ((₆C₀)(0.06)⁰(1 - 0.06)⁶) = 0.954
Solve the quadratic inequality, and graph the solution on a number line. (Evernote) x² - 4x + 3 < 0
1 < x < 3
Iodine is in Group 17 of the periodic table. Which number of electrons must be gained or lost for iodine to form a complete valence shell?
1 gained
Which of the following would be reduced if plants could be used to produce polymers and plastics instead of fossil fuels? 1. All of the listed answers are correct 2. CO2 production 3. polymers and plastics going into landfills 4. environmental damage due to drilling for oil
1. All of the listed answers are correct
Which property of lignin is beneficial to plants but detrimental to the manufacture of paper? 1. Lignin binds cellulose fibers. 2. Lignin aids in photosynthesis. 3. Lignin contributes to plant reproduction. 4. Lignin transports fluids. 5. None of the listed answers are correct
1. Lignin binds cellulose fibers.
Find the sum of the first 7 terms of the geometric series 8 + 8/3 + 8/9 + 8/27 + ...
11.99 Solution r ≠ 1 r = 8/3 ÷ 8 r = 1/3 & t₁ = 8 S(n) = t₁[(1 - r^n) ÷ (1 - r)] S₇ = 8[(1 - (1/3)⁷) ÷ (1 - 1/3)] S₇ = 11.99
If the order of the reaction with respect to the first reactant is 1 and the order of the reaction with respect to the second reactions is 2, what is the overall order of the reaction? 1. None of the listed answers are correct 2. 4 3. 2 4. 0 5. 1
1. None of the listed answers are correct
Which of the following pairs include molecules that both belong in the class known as lipids? 1. diglycerides and sterols 2. fats and proteins 3. None of the listed answers are correct 4. waxes and RNA
1. diglycerides and sterols
Which of the following is not a way to reduce air pollution from burning coal? 1. use more electricity for light and heat 2, use nuclear power to produce electricity 3. use coal that has been cleaned of sulfur, which gives off pollutants when burned 4. use natural gas and renewable energy sources, such as wind power 5. None of the listed answers are correct
1. use more electricity for light and heat
In a certain normal distribution of scores, the mean is 30 and the standard deviation is 5.5. Find the z-score corresponding to a score of 37 and find the percentage of the scores that are below 37.
1.27; 89.80% Solution z-score z = (x - x̅) ÷ σ z = (37 - 30) ÷ 5.5 = 1.27 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 37, 30, 5.5)→Enter = 0.8984 or 89.80%
Find tan 421°.
1.804 Mathway (Trigonometry) Find the Exact Value
Consider the following reversible reaction. In a 3.00 liter container, the following amounts are found in equilibrium at 400 oC: 0.0420 mole N2, 0.516 mole H2 and 0.0357 mole NH3. Evaluate Kc. N2(g) + 3H2(g) ⇄ 2NH3(g)
1.99
Use factoring and the Zero-Product Property to solve the quadratic equation 2x² + 5x -3 = 0
1/2, -3 Use Quadratic equation: (-b ± √((b² - 4ac))/2a
Two cards are randomly drawn in succession from a deck of 52 playing cards. Find the probability that the king of spades and any ace are drawn, in that order, without replacement.
1/663 or 0.0015082 Solution 1/52 × 4/51 = 0.0015082
Write a proportion that models the statement 10 is to 5 as 16 is to 8.
10/5 = 16/8
Find the sum of the infinite geometric series, if it exists. 3 - 9/5 + 27/25 - 81/125 + 243/625 - ...
15/8 Solution (9/5) ÷ 3 = 0.6 r = 0.6 (common ration) t₁ = 3 S = t₁ ÷ (1 - r) S = 3 ÷ (1 - 0.6) S = 3 ÷ 0.4 S = 7.5 or 15/8
Find the reference angle for 525°.
15° Mathway (Trigonometry) Find the Reference Angle
Find the value of x to the nearest hundredth.
17.2
What volume does 15.6 g of H2O(g) occupy at 36.2°C and 1.25 atm?
17.6 L
Evaluate 2x² + 3x + 4 when x=2
18
Find the four arithmetic means between -3 and 102.
18, 39, 60, 81 Solution t(n) = t(1) + (n - 1)d 102 = -3 + (6 -1)d 102 = -3 + 5d 105 = 5d d = 21 Substitute t(2) = -3 + (2 - 1)21 -3 + (1)21 -3 + 21 18 t(3) = -3 + (3 - 1)21 -3 + (2)21 -3 + 42 39 And so on
For the electron configuration 3p2, which of the following describes the number of electrons in the given orbital?
2
Which of the following chemical formulas represents an amide? 1. C2H6O 2. C2H5NO 3. None of the listed answers are correct 4. C2H7N 5. C2H7NO
2. C2H5NO
Hydrogen bonding occurs in all of these materials EXCEPT 1. NH3 2. LiH 3. H2S 4. HCl
2. LiH
Which statement describes the strength of London dispersion forces? 1. London dispersion forces are equal to the force between atoms within the molecule. 2. London dispersion forces are the weakest intermolecular force. 3. London dispersion forces are medium-strength intermolecular forces. 4. London dispersion forces are the strongest intermolecular force.
2. London dispersion forces are the weakest intermolecular force
What is the oxidation number of hydrogen in a molecule of CaH2? 1. 0 2. None of the listed answers are correct 3. +2 4. +1 5. -2
2. None of the listed answers are correct
For the reaction 3 ClO- (aq) → ClO3- (aq) + 2 Cl- (aq) doubling the concentration of ClO- quadruples the initial rate of formation of ClO3-. What is the rate expression for the reaction? None of the listed answers are correct 1. Rate = k[ClO3]-2 2. Rate = k[ClO-]2 3. Rate = k[ClO-2] 4. Rate = k[ClO3]2
2. Rate = k[ClO-]2
What are the oxidation numbers of nitrogen in the following compounds: (i) Li3N, (ii) LiNO3, and (iii) NO2? 1. The oxidation number for nitrogen is +3 in all three compounds. 2. The oxidation numbers for nitrogen are: (i) -3, (ii) +5, and (iii) +4. 3. The oxidation numbers for nitrogen are: (i) -1/3, (ii) +5, and (iii) +4. 4. None of the listed answers are correct
2. The oxidation numbers for nitrogen are: (i) -3, (ii) +5, and (iii) +4.
For the equilibrium reaction 2NH3(g) + 22 kJ ↔ N2(g) + 3H2(g), which of the following changes would result in the formation of more N2 and H2 at equilibrium? 1. adding N2 2. increasing temperature 3. removing NH3 4. None of the listed answers are correct 5. increasing pressure
2. increasing temperature
Which of the following is an organic substance? 1. iron 2. petroleum 3. None of the listed answers are correct 4. water
2. petroleum
A solution of 0.17 M acetone (C3H6O) reacts with a solution of 0.29 M bromide (Br2). Assume that the value of x is 1, the value of y is 0, and k is 1.32 × 10-6/s. Find the rate for this reaction.
2.24 × 10 − 7 mol / L ⋅ s
An airplane, flying at an altitude of 3.21 miles above the ground, has a horizontal speed of 350 miles per hour and is descending at a rate of 14 miles per hour. Use parametric equations to find the airplane's altitude above ground after it has traveled 11 miles, as measured along the ground.
2.77 mi Solution x(t)=350t y(t)=3.21-14t Solve either equation for "t" x=350t t=x/350 Substitute y=3.21-14(x/350) Substitute for "x", x=11 y=3.21-14(11/350) y=2.77
If the mole fraction of glucose in water is 0.050 for a particular solution, what is the molality of this solution?
2.9 m
Find the sum of the geometric series 0.2 + 0.02 + 0.002 + . . . given the formula S=a/(1 - r), where "a" is the first term, "r" is the common ratio, and "S" is the sum.
2/9 Solution S = 0.2/(1 - 0.1) S = 0.222... or 2/9
Using the given information, which data set is the correct choice? (Evernote)
20, 12, 27, 14, 16, 13, 12, 13, 26, 27, 21, 28, 20, 22, 20
Expand the binomial raised to a power. (3a - b)⁵
243a⁵ - 405a⁴b + 270a³b² - 90a²b³ + 15ab⁴ - b⁵ Mathway: Expand Using the Binomial Theorem
What is the reference angle for 516° ?
24° Mathway (Trigonometry) Find the Reference Angle
A 50-row theater has 30 seats in the front row. The second row has 31 seats. If each row has one more than the row in front of it, how many seats are there in the theater?
2725 Solution t₁ = 30 and d = 1 t(n) = t₁ + (n-1)d t₅₀ = 30 + (49)1 t₅₀ = 79 S = n/2[2t₁ + (n - 1)d] S = 50/2[2(30) + 49] S = 25(60 + 49) S = 25(109) S = 2725
Use either the Law of Sines or the Law of Cosines to solve for "a" to the nearest tenth. (Evernote)
28.8 Solution ∠A + 61° + 76° = 180° ∠A = 43° Use Law of Sines a/sin(43°) = 41/sin(76°) a = 41sin(43°)/sin(76°) a = 28.8
The formula for estimating the number, N, of a certain product sold is N = 7400 In(7t + 3), where t is the number of years after the product is introduced. What is the expected number of sales 7 years after the product is introduced? Round to the nearest whole number.
29,239
Use the Law of Sines to solve for m∠A to the nearest tenth. (Evernote)
29.8 Solution sin B/b = sin C/c sin B/43 = sin(80°)/45 sin B = 43sin(80°)/45 sin B = 0.94103 sin⁻¹(sin B) = ∠B sin⁻¹((43sin¹(80°)/45)) sin⁻¹(0.94103) = 70.2° (rounded to the nearest tenth) ∠B = 70.2° ∠A + 70.2° + 80° = 180° ∠A = 29.8° Use graphing calculator on degree mode or use Mathway and change answer to degrees.
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - x³ - 16x² + 10x + 60
3, -2, ±3.16
Write the balanced half reactions of this reaction: 2 H+ + H2O2 + 2 Fe2+ → 2 Fe3+ + 2 H2O in acidic solution 1. 2 H2O2 + 4 e- + 4 H+ → 4 H2 O 2 Fe2+ → 2 Fe3+ + e- 2. 4 H2O2 + e- + H+ → 4 H2 O Fe2+ → 2 Fe3+ + e- 3. H2O2 + 2 e- + 2 H+ → 2 H2 O Fe2+ → Fe3+ + e- 4. None of the listed answers are correct 5. 2 H2O2 + e- + H+ → 6 H2 O 4 Fe2+ → Fe3+ + 4 e-
3. H2O2 + 2 e- + 2 H+ → 2 H2 O Fe2+ → Fe3+ + e-
If a compound falls into the class of compounds with the general formula CnH2n+2, what must be true? 1. It must contain at least one double bond. 2. It must contain double bonds only. 3. It must contain single bonds only. 4. It must contain triple bonds only.
3. It must contain single bonds only.
The following equation shows the net reaction taking place in a voltaic cell. Identify the substance that is oxidized and the substance that is reduced. Zn + Br 2 → Zn 2 + + 2Br − E ∘ = + 1.85 V 1. Zn2+ is oxidized and Br− is reduced 2. Zn2+ is reduced and Br2 is oxidized 3. Zn is oxidized and Br2 is reduced 4. None of the listed answers are correct 5. Zn is reduced and Br− is oxidized
3. Zn is oxidized and Br2 is reduced
When chemical bonds form, the valence electrons in an atom can undergo all of the following in relation to other atoms EXCEPT _____. 1. be given away 2. be shared 3. be decomposed 4. be gained
3. be decomposed
A box contains 2 green, 6 yellow, and 3 purple balls. Find the probability of obtaining a purple ball in a single random draw.
3/11
What is the overall order of reaction for Rate = k[H2][Br2]1/2
3/2 order
Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. Find tan x (Evernote)
3/4 or 0.75 Solution tan x = opp./adj. 24/32 = 0.75
Find the amplitude, the period, and the frequency of the graph. Then write an equation for the sine function for the graph.
3/4, 180°, 2, y = 3/4 sin 2x Graph all multiple choices and pick the one that fits
A spinner is evenly divided into 8 equal areas and numbered from 1 through 8. What is the probability of spinning a number less than 4 in a single spin?
3/8
How many grams of water would require 92.048 kJ of heat to raise its temperature from 34.0 °C to 100.0°C? (Remember to change units first)
333 grams
Abbiville is a small town that has been steadily growing since 1960. Use the table below to create a linear equation that estimates Abbiville's population over time. What will the population be in 2014 if the growth remains constant? (Evernote)
364 people
When Spheres-R-Us ships bags of golf balls, each bag must be within 5 balls of 370. Identify the inequality which results in an acceptable number of golf balls in each bag.
365 ≥ 375
How many degrees would the temperature of a 450 g piece of iron increase if 7600 J of energy are applied to it? (The specific heat of iron is 0.4494 J/g x °C)
37.6 °C
Write the balanced half reactions of this reaction: NiO2 + 2 H2O + Fe → Ni(OH)2 + Fe(OH)2 in basic solution 1. H2O + NiO2 + e- → Ni(OH)2 + OH- OH- + Fe → Fe(OH)2 + e- 2. 6 H2O + NiO2 + 6 e- → Ni(OH)2 + 6 OH- 6 OH- + Fe → Fe(OH)2 + 6 e- 3. 4 H2O + NiO2 + 4 e- → Ni(OH)2 + 4 OH- 4 OH- + Fe → Fe(OH)2 + 4 e- 4. 2 H2O + NiO2 + 2 e- → Ni(OH)2 + 2 OH- 2 OH- + Fe → Fe(OH)2 + 2 e-
4. 2 H2O + NiO2 + 2 e- → Ni(OH)2 + 2 OH- 2 OH- + Fe → Fe(OH)2 + 2 e-
What mass of solute is needed to prepare the following solution? 1.00 L of 0.125 M K2SO4 1. 18.3 g K2SO4 2. None of the listed answers are correct 3. 14.4 g K2SO4 4. 21.8 g K2SO4 5. 16.7 g K2SO4
4. 21.8 g K2SO4
Which of the following will have the same boiling point as 0.1 molal NaCl? 1. 0.1 molal KCl 2. 0.2 molal glucose 3. 0.2 molal sucrose 4. All of the listed answers are correct
4. All of the listed answers are correct
For the reaction H3PO4 (aq)+3 I-(aq) + 2 H+ (aq) → H3PO3 (aq)3 + I- (aq) + H2O (l), the rate expression under certain conditions is given by Rate = k[H3PO4][I-][H+]2. What method(s) could be used if you want to double the reaction rate? 1. Half the concentration of H3PO4 or double the concentration of I-. 2. Half the concentration of H3PO4 or triple the concentration of I-. 3. Double the concentration of H3PO4 or half the concentration of I-. 4. Double the concentration of H3PO4 or double the concentration of I-.
4. Double the concentration of H3PO4 or double the concentration of I-.
Determine the oxidation number of the elements in this compound: H2CO3 1. H: +2, O: +3, C: 0 2. H: +4, O: +1, C: -2 3. H: -2, O: +4, C: +1 4. H: +1, O: -2, C: +4 5. None of the listed answers are correct
4. H: +1, O: -2, C: +4
Which statement best describes the dipoles that cause London dispersion forces? 1. The dipoles are caused by a difference in electronegativity. 2. The dipoles contain a hydrogen atom. 3. The dipoles are permanent separations of charges. 4. The dipoles are instantaneous and temporary.
4. The dipoles are instantaneous and temporary.
What is the oxidizing agent in the following reaction: Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)? 1. None of the listed answers are correct 2. Cl 3. H 4. Zn
4. Zn
Determine the oxidation number of the elements in this compound: Zn(OH)42- 1. Zn: +1, H: +2, O: -2 2. Zn: -2, H: +2, O: +1 3. None of the listed answers are correct 4. Zn: +2, H: +1, O: -2 5. Zn: +1, H: -2, O: +2
4. Zn: +2, H: +1, O: -2
Which of the following would be of most interest to an electrochemist? 1. determining the contents of living cells 2. designing a new type of nuclear power plant 3. comparing the reactivities of several metals 4. comparing three kinds of batteries to power electric cars 5. None of the listed answers are correct
4. comparing three kinds of batteries to power electric cars
A piece of metal with a mass of 15.3 grams has a temperature of 50.0 °C. When the metal is placed in 80.2 grams of water at 21.0 °C, the temperature rises by 4.3 °C. What is the specific heat capacity of the metal?
4.15 J/g x °C
A lunch menu consists of 4 different kinds of sandwiches, 2 different kinds of soup, and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
40 4 × 2 × 5 = 40
Which of the following is an example of the Commutative Property of Addition?
5 + 2 = 2 + 5
Write a balanced equation for this reaction: Cr(OH)3 + Br2 → CrO42- + Br- in basic solution 1. 8 OH- + 2 Cr(OH)3 + 3 Br2 → 2 CrO42- + 6 H2O + 4 Br- 2. 8 OH- + 4 Cr(OH)3 + 5 Br2 → 4 CrO42- + 6 H2O + 2 Br- 3. 6 OH- + 6 Cr(OH)3 + 7 Br2 → 4 CrO42- + 6 H2O + 4 Br- 4. None of the listed answers are correct 5. 10 OH- + 2 Cr(OH)3 + 3 Br2 → 2 CrO42- + 8 H2O + 6 Br-
5. 10 OH- + 2 Cr(OH)3 + 3 Br2 → 2 CrO42- + 8 H2O + 6 Br-
What is the balanced redox equation for the following reaction in acid: Cr3+(aq) + Cl2(g) → Cr2O72-(aq) + Cl-(aq) 1. None of the listed answers are correct 2. 2Cr3+(aq) + Cl2(g) +H+(aq) → Cr2O72-(aq) +2Cl-(aq) 3. 2Cr3+(aq) + 3Cl2(g) + H2O(l) → Cr2O72-(aq) + 6Cl-(aq) +2H+(aq) 4. Cr3+(aq) + Cl2(g) +7H2O(l) → Cr2O72-(aq) + Cl-(aq) +14H+(aq) 5. 2Cr3+(aq) + 3Cl2(g) + 7H2O(l) → Cr2O72-(aq) + 6Cl-(aq) +14H+(aq)
5. 2Cr3+(aq) + 3Cl2(g) + 7H2O(l) → Cr2O72-(aq) + 6Cl-(aq) +14H+(aq)
Write a balanced equation for this reaction: HCOOH + MnO4- → CO2 + Mn2+ in acidic solution 1. 4 H+ + MnO4- + HCOOH → 6 Mn2+ + 6 H2O + 7 CO2 2. None of the listed answers are correct 3. 10 H+ + 6 MnO4- +7 HCOOH → 6 Mn2+ + 2 H2O + 3 CO2 4. 8 H+ + 4 MnO4- + 3 HCOOH → 4 Mn2+ + 4 H2O + 5 CO2 5. 6 H+ + 2 MnO4- + 5 HCOOH → 2 Mn2+ + 8 H2O + 5 CO2
5. 6 H+ + 2 MnO4- + 5 HCOOH → 2 Mn2+ + 8 H2O + 5 CO2
Carbon dioxide can react with hydrogen according to the following equation:CO2(g) + H2(g) ↔ CO(g) + H2O(g). The equilibrium constant for this reaction is 4.9 × 10-3. Which of the following is true about this system? 1. None of the listed answers are correct 2. At equilibrium, the concentrations of products will be higher than the concentrations of reactants. 3. At equilibrium, the concentrations of all four substances will be equal. 4. At equilibrium, the concentrations of all four substances will fluctuate randomly. 5. At equilibrium, the concentrations of reactants will be higher than the concentrations of products.
5. At equilibrium, the concentrations of reactants will be higher than the concentrations of products.
Which of the following molecular formulas can be represented by two or more isomers? (Assume no ring structures.) 1. C2H4 2. C2H6 3. None of the listed answers are correct 4. C3H8 5. C4H10
5. C4H10
Which of the following chemical formulas could represent a carboxylic acid? 1. C2H5NO 2. COH2 3. None of the listed answers are correct 4. C2H6O 5. CH2O2
5. CH2O2
Which statement correctly describes why a chemical change does not change the identity of an atom? 1. It occurs at the electron level and does not change the number of neutrons in the atom. 2. It occurs at the level of the nucleus but only affects neutrons. 3. It occurs at the level of the nucleus but only affects protons. 4. None of the listed answers are correct 5. It occurs at the electron level and does not change the nuclei of atoms.
5. It occurs at the electron level and does not change the nuclei of atoms.
How does the oxidation number of barium change in the following compounds: BaCO3, Ba(NO3)2, and BaSO4? 1. The oxidation number of barium is +1 in all compounds. 2. None of the listed answers are correct 3. The oxidation number of barium is +2 in BaCO3 and BaSO4 and +1 in Ba(NO3)2. 4. The oxidation number of barium is +1 in BaCO3 and BaSO4 and +2 in Ba(NO3)2. 5. The oxidation number of barium is +2 in all compounds.
5. The oxidation number of barium is +2 in all compounds.
Which statement best describes the relationship between the system and the surroundings? 1. The system is found around the surroundings and includes the surroundings. 2. The system is found in the surroundings and is part of the surroundings. 3. The system is found around the surroundings but does not include the surroundings. 4. None of the listed answers are correct 5. The system is found in the surroundings but is not included as part of the surroundings.
5. The system is found in the surroundings but is not included as part of the surroundings.
Which of the following challenges would be of most interest to a thermochemist? 1. comparing three kinds of batteries to power electric cars 2. None of the listed answers are correct 3. determining the contents of living cells 4. comparing the reactivities of several metals 5. designing a new type of air conditioner
5. designing a new type of air conditioner
Which of the following is true about alkaline earth metals? 1. they have three valence electrons 2. they have four valence electrons 3. None of the listed answers are correct 4. they have one valence electron 5. they have two valence electrons
5. they have two valence electrons
If 2 blocks are randomly taken from a bag containing 10 blue blocks, 10 red blocks, and 7 yellow blocks, what is the probability of drawing a blue block and a red block?
50/351 or 0.1424501 Solution 10/27 × 10/26 = 0.1424501
Write the product as a polynomial in standard form. (5x² - 2x + 5)(x² - 8x - 2)
5x⁴ - 42x³ + 11x² - 36x - 10
Solve log₃(x+4) - log₃(x-4) = log₃5 for x
6
Simplify the sum, difference, product, or quotient. Assume that the value of any variable is positive ³√(-27x) - 4 ³√(x⁴) + 9 ³√(x) + 9x ³√(x)
6 ³√(x) + 5x ³√(x)
Evaluate: (₁₂C₇ × ₁₄C₁₀)/₁₃C₅
616 Solution ₁₂C₇ = 792 ₁₄C₁₀ = 1001 ₁₃C₅ = 1287 (792 × 1001)/1287 = 616
Using the given stem and leaf plot and and it's median and mode, select the data set on which it was created. (Evernote)
7, 6.9, 8.2, 7.6, 6, 7.2, 8.4, 7.6, 7.3, 7.8, 6.2, 9.5, 8.9, 6.5, 9
Find the 6th and 8th entries in the row 12 of Pascal's triangle.
792;792 Solution Use nCk-₁ to love for nth entry ₁₂C₆-₁ = ₁₂C₅ = 792 ₁₂C₈-₁ = ₁₂C₇ = 792
Use factoring and the Zero-Product Property to find the zeros of the quadratic function. f(x) = x² -7x - 8
8, -1
Whitney starts the engine on her small private airplane. The engine drives a propeller with a radius of 7.5 feet and its centerline 12.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 850 revolutions per minute. The height of one propeller tip as a function of time is given by h = 12.5 + 7.5 sin(850t), where h is the height in feet and t is the time in minutes. Find h when t = 2.5
8.2 ft Solution h = 12.5 + 7.5 sin(850t) h = 12.5 + 7.5 sin(850 × 2.5) h = 8.2
Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. (Evernote)
8/17 or 0.4706 sinθ = opp./hyp.
Jamila spins a spinner with 3 sections of equal area, like the one below, 25 times. It lands on the 1eight times. What is the experimental probability of spinning a 1?
8/25
A student isolated 15.6 g of product from a chemical reaction. He calculated that the reaction should have produced 18.4 g of product. What was the student's percent yield?
84.8%
Since 1993, Daphne Hamilton has owned a franchise of take-out restaurants called The Burger Barn. The number of customers, C, in thousands, that The Burger Barn has served each year can be modeled by the function C(t) = t² + 38t + 600, where t is the number of years from 1993. Using this model, estimate the number of customers served in 1999.
864,000
A 1.28-g sample of gas occupies 345 cm3 at 58.2°C and 1.15 atm. What is the molecular weight of the gas?
87.7 g/mol
Evaluate 8^log₈ 9
9
The function d = 9 cos 2t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the maximum displacement of the object from its resting position?
9 m Solution A = displacement d = A cos wt d = 9 cos 2t A = 9 or 9m
Use the given formula to find the first four terms of the arithmetic sequence. t(n) = 12 - 3n
9, 6, 3, 0 Solution t(1) = 12 - 3(1) 9 t(2) = 12 - 3(2) 6 ...
A quantity of HI was sealed in a tube, heated to 425oC and held at this temperature until equilibrium was reached. The concentration of HI in the tube at equilibrium was found to be 0.0706 mol/L. Calculate the equilibirum concentration of H2 (and I2). For the gas-phase reaction, H2 + I2⇄ 2HI Kc = 54.6 at 425oC
9.55 x 10-3 M
Calculate the molality of 13.0 g benzene, C6H6 in 17.0 g CCl4.
9.80 molal C6H6
Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 8400 dolls when $84,000 was spent on advertising and the price of a doll was set at $70. Determine the number of dolls sold when the amount spent on advertising is increased to $98,000.
9800
How did Mendeleev organize the elements? atomic mass All of the listed answers are correct physical properties chemical properties
All of the listed answers are correct
Subatomic particles such as protons and neutrons are similar to fundamental particles because they display which of the following properties? charge electromagnetism mass All of the listed answers are correct
All of the listed answers are correct
Based on VSEPR theory, which of these molecules would be linear?
CO2
If the density of oxygen gas is 1.4 g/L, the density of carbon dioxide is 2.0 g/L, and the density of nitrogen gas is 1.3 g/L, which of the following statements is true?
Carbon dioxide has the slowest rate of effusion.
Which of the following atoms is least able to attract electrons?
Cs
Which of the following ideas are included in the quantum mechanical model of the atom? I. Electrons are likely to be located in s, p, d, and f orbitals; II. The differences between energy levels are quantized amounts; III. The positive charge of the nucleus eventually pulls electrons into the center of the atom.
I and II
Find the reduced row-echelon form of the augmented matrix that represents the following system of equations: (Evernote) {-6x + 9y = -5 {-8x - 4y = 0
Incorrect: [1 0| 5/24 ] [0 1|-5/12] Correct: [1 0| -5/24] [0 1| 5/12
Find cos((1/2)A) and sin((1/2)A) if sin(A)=4/5 and Ais a first-quadrant angle. (Evernote)
Incorrect: cos(A/2) = √3/5 sin(A/2) = 2/5 Correct: cos(A/2) = (2√5)/5 sin(A/2) = √5/5 Solution Pathagorean Identities sin A = 4/5 cos²A = 1 - sin²A cos A = 1 - (4/5)² cos A = 3/5 Use Half-Angle Identities sin(A/2) = √((1 - cos A)/2) sin(A/2) = √((1 - 3/5)/2) sin(A/2) = √5/5 cos(A/2) = √((1 + cos A)/2) cos(A/2) = √((1 + 3/5)/2) cos(A/2) = (2√5)/5 A = θ and the cos((1/2)A) is the same as cos(A/2)
Determine whether the function is a rational function. If so, find the domain and identify the horizontal and vertical asymptotes, and any holes in the graph. If the function is not rational, state why not. f(x) = (x - 1)/((x - 7)(x + 3))
Incorrect: rational; x≠1, 7 or -3; asymptotes at y=0, x=1, x=7 and x=-3 Correct: rational; x≠-3,7 asymptotes at y=0, x=-3, and x=7
Write the system of inequalities whose solution is graphed as the shaded region.
Incorrect: y < 3x - 2 y > -2x + 5 Use mathway; Graph the intersection (and)
Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = -6x² - 24x - 31
Incorrect: y = 6(x + 2)² - 7 x = -2; (2,-7) Correct: y = -6(x + 2)² - 7 x = -2; (-2, -7) Mathway: Find the Vertex Form Find the Axis of Symmetry Find the Vertex (Coordinates)
Which inequality has (1, 7) as a solution?
Incorrect: -2x - 5y ≥ -32 Solution Substitute -2(1) - 5(7) ≥ -32 -2 - 35 ≥ -32 -37 ≥ -32 False, not a solution of the inequality
Given sinθ = 5/9, where π/2 < θ < π, find the exact values of sin 2θ and cos 2θ.
Incorrect: -31/81, (20√14)/81 Correct: 10/9, -(4√14)/9
Two cards are randomly selected from a standard 52-card deck. What is the probability of getting 2 diamonds or 2 face cards?
Incorrect: 0.108 Correct: 0.106 or 47/442 Solution (13/52 × 12/51) + (12/52 × 11/51) - (3/52 × 2/51)
Erosion gradually reduces the size of a small Pacific island that has a current area of just 460 acres. If the island's area decreases at an annual rate of 0.05%. Find the multiplier for the rate of exponential decay.
Incorrect: 0.95 Correct: 0.9995 Solution 100 - 0.05 = 99.95 99.95/100 = 0.9995
Use Pascal's triangle to solve for the value of n: 2(n C 3) = n+4 C ₇ (Evernote)
Incorrect: 2 Correct: 4
Use Pascal's triangle to find the number of ways to choose 3 boxes from 7 boxes.
Incorrect: 21 Correct: 35 Solution ₇C₃ = 35
The function d = - 6 cos 3t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the frequency?
Incorrect: 3π/2 cycles/seconds Correct: 3/2π Solution d = A cos wt d = -6 cos 3t w = 3 f (frequency) = w/2π f = 3/2π
Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 2(x + 4)² - 48 = 0
Incorrect: 4 ± 2√6; 5.8 or -13.9 Correct: -4 ± 2√6; 0.9 or -8.9
Find all the zeros of the polynomial function. f(x) = x² - 10x + 34
Incorrect: 5 ± 6i Correct: 5 ± 3i
Find the two geometric means between 7 and 3584.
Incorrect: 63, 567 Correct: 56, 448 Solution t₁=7 and t₄=3584 Formula t(n) = t₁r^(n - 1) Substitute t(4) = 7r⁴⁻¹ 3584 = 7r³ divide both sides by 7 r³ = 512 Take cube root of both sides r = 8 t(2)=7 × 8 56 t(3)=7 × 8² 448 7, 56, 448, 3584
Use Pascal's Triangle to determine the probability that you will get three green lights in a row of five lights. Assume red and green are equally likely occurrences.
Incorrect: 7/32 Correct: 5/16 (10/32) Solution (n C k)(p∧k)(1 - p)∧(n-k) (₅C₃)(½)³(1 - ½)⁵⁻³ (₅C₃)(½)³(1 - ½)² 10 × 1/8 × 1/4 = 5/16
Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°
Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°
Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°.
Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°
A server at a restaurant kept track of the number of requests for the daily special, and the time of day the request was made. The data is displayed below. (Evernote)
Incorrect: It is a linear model with a positive correlation.
Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = x² + 14x + 4
Incorrect: None of the listed answers are correct Correct: y = (x+7)² - 45 x = -7; (-7, -45)
Describe the value of b for the function y(x) = 1/3(1/b)^x to represent exponential growth.
Incorrect: None of the listed answers are correct Correct: "b" has to be greater than 0 and less than 1. (0 < b < 1)
Which of the following is equal to sin²(x)/(1 - cos(x))
Incorrect: None of the listed answers are correct Correct: 1 + cos(x) or 1 + cosθ Mathway Rationalize the Denominator Mathway Verify the Identity+
The relative frequency histogram below represents the age in years of the first 100 children to have their portraits taken at the "See What Develops" photography studio. What is the probability that the next child to have portraits taken will be between 1 and 2 years old?
Incorrect: None of the listed answers are correct Correct: 31/100 or 31% (maybe 0.315 or 32%) Solution .11 + .20 + .31 + 30 + .15 + 24 = 1 (or 100%) Age 1= .20 Age 2= .11 .20 + .11 = .31 (or 31%) 31/100 or 31% Probability
Wilfred is checking his bicycle's wheel. The wheel has a radius of 25 cm, and its center is 54 cm above the ground. Wilfred is rotating the wheel at a constant speed of 230° /s. The height of a point on the tire as a function of time is given by h = 54 + 25 sin(230t), where h is the height in centimeters and t is the time in seconds. Find h when t = 5.5 s. Round your answer to the nearest tenth of a centimeter.
Incorrect: None of the listed answers are correct Correct: 51.8 Solution h = 54 + 25 sin(230t) h = 54 + 25 sin(230 × 5.5) h = 51.8
The magnitude of an earthquake is found by the equation M = 2/3 log E/10^11.8 , where M is the magnitude and E is the energy released. Find the magnitude of an earthquake that released 10^24.4 ergs of energy.
Incorrect: None of the listed answers are correct Correct: M = 8.4 Solution M = 2/3 log₁₀ (10^24.4/10^11.8)
The wattage rating of an appliance is given as "W", in watts, and varies jointly as the resistance, "R", in ohms, and as the square of the current, "I", in amperes. If the wattage is 2 watts when the resistance is 200 ohms and the current is 0.1 amperes, find the wattage when the resistance is 150 ohms and the current is 0.4 amperes.
Incorrect: None of the listed answers are correct Correct: W (wattage) = 24
Solve log₇ 8 - log₇ (x + 3) = log₇ 3, for x
Incorrect: None of the listed answers are correct Correct: x=-1/3 Solution log(x) - log(y) = log(x/y) log₇ 8 - log₇ (x+3) = log₇ (8/(x+3)) log₇ (8/(x+3)) = log₇ 3 (Mathway can solve once the left terms are combined)
For the data given, find the equation of the line of best fit. (Evernote)
Incorrect: None of the listed answers are correct Correct: y = 0.63x + 1.90
Is the flow of energy during vaporizing more like the flow of energy during melting or during freezing?
It is more like the flow of energy during melting because both processes absorb energy.
Use the set of constraints to find the maximum and minimum values of the objective function C = 5x + 11y Constraints: {x + y ≥ 2 {6x - 6y ≤ 12 {8y ≤ 4x + 16
Incorrect: The maximum value of C is 139 at (8, 9) and the minimum value is 10 at (0, 2). Correct: The maximum value of C is 106 at (8,6) and the minimum value is 10 at (2,0).
Make a conjecture about the pattern of the given data. Find the sum of the 7th row. 3 3 + 6 + 3 3 + 6 + 9 + 6 + 3 3 + 6 + . . . + ( 3n − 3) + ( 3n ) + ( 3n − 3) + . . . + 3
Incorrect: The sums of the rows are 3, 12, 27, . . . . The sum of the nth row is n(2n +3). The sum of the 7th row is 119. Correct: The sum of the rows are 3, 12, 27, . . . . The sum of the nth row is 3(n²). The sum of the 7th row is 147.
An English class was taken by 28 students. Their final scores were: three As, five Bs, nine Cs, six Ds, and five Fs. Using the given frequency table, find the mean grade point score, using A = 4, for the entire group of 28 students. Give the answer to the nearest hundredth, if necessary. (Evernote)
Incorrect: [none] Correct: 1.82 (Close to a "C")
Suppose the depth of the tide in a certain harbor can be modeled by y = 25 - 4 cos(π/6t), where "y" is the water depth in feet and "t" is the time in hours. Consider a day in which t = 0 represents 12:00 midnight. For that day, when are high tide and low tide and what is the depth of each?
Incorrect: high tide at 12:00 noon and 12:00 midnight, depth 29 ft low tide at 6:00 a.m. and 6:00 p.m., depth 21 ft Correct: high tide at 12:00 noon and 12:00 midnight, depth 21 ft low tide at 6:00 a.m. and 6:00 p.m., depth 29 ft
Use elimination to solve the system of equations. {-16x - 6y = 170 {8x + 3y = -85
Incorrect: no solutions Correct: Infinitely Many Solutions
Solve: (Evernote) det[x+3 2] [3 x-2] =0
Incorrect: x =-4 Correct: x = 0 Mathway: Find the Determinant
There are 8 cars in a parking lot on a very cold day. Suppose the probability of any one of them not starting is 0.14. What is the probability that exactly 3 of the cars will not start?
Incorrect: ≈ 0.003 Correct: ≈ 0.072 Solution (nCk) × (p)^n × (1 - p)^(n - k) (₈C₃) × (0.14)³ × (1 - 0.14)⁵ = 0.072
Graph and classify the system of equations as independent, inconsistent, or dependent. If the system is independent, find the solution from the graph. {3x + 3y = 2 {3x - y = 8
Independent (2, -2)
A way to prevent rust from forming is to mix in other metals such as zinc or magnesium. Why do you think this would help?
Iron is lower on the reactivity series than zinc or magnesium, so zinc or magnesium will react with oxygen and water first.
How does an inhibitor affect reaction rate?
It decreases reaction rate.
The graph represents the energy change of a chemical reaction. (its a picture where the reactants are high up on the graph and the product down at the bottom) Which must be true about the entropy of the reaction in order for the reaction to be spontaneous at all temperatures?
It must be positive so that the change in Gibbs free energy will be negative.
Calculate the mole fractions of 35.7 g of KBr in 16.2 g of water
KBr: 0.250, H2O: 0.750
A student must prepare a poster display that describes three criteria that must be met for a sample of a liquid to change state to a solid. Which are these three criteria?
Kinetic energy must be removed from the sample. The temperature of the sample must reach its freezing point. The molecules in the sample must lose sufficient energy so the attraction of the molecules in the sample for one another exceeds the force that tends to separate them.
Element Xx reacts with chlorine to form a common compound with the formula XxCl. Element Xx is very reactive. What is element Xx?
Na
A student was assigning oxidation numbers for different elements in the compound Fe3O4. The student assigned Fe an oxidation number of +2. Is this correct? Why or why not?
No, Fe has an oxidation number of +2 2/3.
A scientist is considering formaldehyde (HCHO) for use in an experiment. She is studying the strength of triple bonds in molecules. Is formaldehyde a good choice for her to use? Why?
No, HCHO has a double bond but no triple bonds.
A student was assigning oxidation numbers for different elements in the compounds OF2 and NaF. The student assigned F an oxidation number of +1 in OF2 and -1 in NaF. Is this correct? Why or why not?
No, fluorine is always assigned an oxidation number of -1.
A formulation scientist is creating a formula for a new product that requires the following compounds: barium chloride, silicon oxide, and calcium carbonate. Are these chemicals named properly? If not, why?
No, the prefixes for the molecular compound silicon oxide are omitted.
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x³ - 4x² + 7x - 12
None of the listed answers are correct
How many sets of quantum numbers must be used to describe the electrons in a neutral beryllium atom? None of the listed answers are correct 5 1 3 2
None of the listed answers are correct
For a circle of radius 4 feet, find the arc length "s" subtended by a central angle of π/30 radians. Round to the nearest hundredth.
None of the listed answers are correct Solution r = 4 and θ = π/30 s = rθ s = 4(π/30) s = 2π/15
A chemist heats four samples of the same substance to the following temperatures: Sample 1 to 30°C; Sample 2 to 15°C; Sample 3 to 45°C; Sample 4 to 35°C. The molecules of which sample will have the greatest motion?
Sample 3
A number cube is tossed 10 times with the following results. 5, 6, 1, 5, 5, 2, 6, 1, 2, 2 Find the range and the mean deviation of the data.
None of the listed answers are correct To find mean deviation minus the mean from each data value, add everything up, then divide by the number of data values. Example: 54, 49, 47, 48, 52 mean of data = 50 54 - 50 = | 4 | = 4 49 - 50 = |-1| = 1 47 - 50 = |-3| = 3 48 - 50 = |-2| = 2 52 - 50 = | 2 | = 2 4 + 1 + 3 + 2 + 2 = 12 12 ÷ 5 = 2.4 Mean deviation = 2.4
What happens when methane burns in the presence of oxygen, to form carbon dioxide and water?
Oxygen is reduced.
Ms. Kim, an analyst at Multi-Fastener Corp, has developed a model to forecast the company's total production of metal fasteners. Under this model, production, P, is equal to 4500 times the man-hours spent producing machine screws (S) plus 2900 times the man-hours spent producing nuts and bolts (P). Manpower constraints mean that total number of man-hours per year cannot exceed 44,000; logically, the number of man-hours assigned to either task cannot be negative. Express the model in mathematical form.
P = 4500S + 2900B {S + B ≤ 44,000 {S ≥ 0 {B ≥ 0
Which matrix represents the graph of polygon PQRS? (Evernote)
P Q R S [2 -3 -3 2] [6 2 -7 3]
Point P is located at the intersection of a circle with a radius of r and the terminal side of an angle θ. Find the coordinates of P to the nearest hundredth. θ = 120° , r = 13
P(- 6.5, 11.26) Solution 120° is in Quadrant II Coordinates: (cos θ = x/r, sin θ = y/r) θ = 120° and r = 13 cos(120°) = x/13 -½ = x/13 x = -13/2 or -6.5 sin(120°) = y/13 √3/2 = y/13 y = 13√3/2 or 11.26 P(-6.5, 11.26)
Write a polynomial equation in standard form by using the given information. P is of degree 3; P(0) = 24; zeros: 3, -4, 2
P(x) = x³ - x² - 14x + 24
A geologist wants to compare the percentage of different size particles in a sample of soil, which is a heterogeneous mixture. What should the geologist do?
Pass samples of the soil through increasingly smaller-holed sieves.
Consider the reaction A + 2B → C + D. The rate law for this reaction is first order in A and first order in B. If the rate constant at 25 °C is 3.01 x 102 s-1, find the rate of reaction when the concentration of A is 0.68 M and the concentration of B is 0.14M.
Rate = 18 M/s
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998. (Evernote)
T(x) = 0.2x³ + 0.3x² + 0.2x + 0.1; 304.8 thousand
Which two events will increase the rate of evaporation of a liquid?
Temperature will increase, and air pressure will decrease.
Which property is shown by the following statement? (13 + 3)+ 8 = 13 + (3 + 8)
The Associative Property of Addition
How does the activation energy of a forward reaction compare with the activation energy of the reverse reaction in the equation aA + bB ↔ cC + dD?
The activation energy of each reaction is positive.
Which statement is a valid conclusion about the activation energy of the reverse reaction if the forward reaction is exothermic?
The activation energy of the reverse reaction is greater than that of the forward reaction.
What observation would indicate that an endothermic reaction is occurring in a beaker?
The beaker feels cool.
A student is asked to identify evidence that supports the conclusion that paint is a colloid. Which set of evidence should the student cite?
The components of paint do not separate spontaneously nor can they be separated by passing the paint through ordinary filter paper.
Find the inverse of the following matrix (if it exists): [2 -13 -6] [0 5 0] [0 -24 0]
The matrix has no inverse.
Use the graph of the feasible region for the set of constraints to find the maximum and minimum values of the objective function C = 3x + 5y. Constraints: {x + y ≥ 1 {4x - 2y ≤ 4 {3y ≤ 3x + 3
The maximum value of C is 29 at (3, 4) and the minimum value is 3 at (1, 0) .
How does a chemical reaction obey the law of conservation of matter?
The number of atoms of each element is the same in the reactants as in the products.
How does the oxidation number of lithium change in the following compounds: LiClO, LiClO2, LiClO3, and LiClO4?
The oxidation number of lithium is +1 in all compounds.
Which statement best describes the interaction of the surroundings with a substance that is freezing?
The surroundings are cooler than the substance and absorb thermal energy from it.
A test tube containing a piece of wax is warmed in an oil bath until the wax melts. The test tube is removed from the bath and is allowed to cool until the wax freezes. Which of the following statements best describes the first law of thermodynamics as applied to this change?
The total energy lost by the wax and test tube is equal to the total energy absorbed by the surroundings.
How will the vapor pressure of a pure liquid change if enough solute is added to result in a mole fraction of 0.50?
The vapor pressure of the liquid will decrease by half.
Hans pays $205 in advance on his account at the athletic club. Each time he uses the club, $10 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 11 visits.
V = 205 - 10x; $95
How is metallic character related to ionization energy?
When positive nuclear charge increases, the energy needed to release electrons from the valence shell increases.
By comparing the electron configurations of two different atoms, which of the following questions can one answer?
Which atom has the highest electron number?
A student names the molecular compound that contains three fluorine atoms and one chlorine atom, chlorine trifluoride. Is this correct? Why or why not?
Yes, it is correct. If both elements are in the same group, the one with the higher atomic number is listed first in the name.
For the function, use synthetic division and substitution to determine whether the given value is a zero of the function. P(x) = 3x⁴ - 10x³ - 41x² + 68x + 60
Zeroes are 5, 2, -2/3, -3
Perform the indicated operations on the given matrices. [3 -6 -7] [-2 -1 7] [-3 -2 4] + [ 3 5 -7] [-4 -1 7] [4 -9 -3]
[ 1 -7 0 ] [ 0 3 -3 ] [0 -10 4]
Perform the indicated operations on the given matrices. (Evernote) [-8 -8] + [-2 3] [-6 4] + [3 -1] (2×2 matrice + 2×2 matrice)
[-10 -5] [-3 3]
Write the augmented matrix for the system of equations. {x - y = -9 {5x = 0
[1 -1| -9] [5 0| 0] Solution x=1, y=-1 5x=5
The band and the cheerleading squad at a local school are ordering supplies. The supplies they need are listed in the table. (Evernote)
[10 13 5] [ 5 ] [10 16 8] [12] [ 2 ] = [216] [258]
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {3x + 2y + z = -2 {3x -2y -z = -22 {3x + 2y -z = -10
[3 2 1] [x] [ -2 ] [3 -2 -1] [y] = [-22] [3 2 -1] [z] [-10] ;(-4, 3, 4)
Write the augmented matrix for the system of equations. {8x + 2y + 6z = -3 {3x - y + 10z = 3 {-9x -2y -4z = -7
[8 2 6| -3 ] [3 -1 10| 3 ] [-9 -2 -4 |-7 ]
A solution of magnesium nitrate in water freezes at a certain temperature. What could be done to lower the freezing point of this solution?
add more magnesium nitrate
A nuclear transmutation will happen during which type(s) of decay?
alpha and beta
Which atom has the greatest mass?
an atom with 8 protons, 8 neutrons, and 8 electrons
Use the following information to find the unknown sides and angles. m∠B = 28°; c=18
b = 8.5; a = 15.9; m∠A = 62°; m∠C = 90° Solution We have two angles m∠A + m∠B + m∠C = 180 m∠A + 28° + 90° = 180° m∠A = 62° Use Law of Sines to solve for side "a" or "b' a/sin A = c/sin C a/sin(62°) = 18/sin(90°) a = 18sin(62°)/sin(90°) a = 15.89 → 15.9 b/sin B = a/sin A b/sin(28°) = 15.9/sin(62°) b = 15.9sin(28°)/sin(62°) b = 8.45 → 8.5
Where are the other metals located on the periodic table?
between the transition metals and the metalloids
How is an s orbital similar to a p orbital?
both can hold two electrons
Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, C(-1, -4), D(5, 4)
center: (2, 0) radius: 5
Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, with endpoints C(- 1, 5), D(5, 9)
center: (2, 7) radius: √13; 3.61 Mathway: Find the Midpoint
Which of the following is evidence of a chemical change?
change of chemical composition
Identify the conic section produced by the intersection of the plane and the cones in the following diagram.
circle
A(n) _____ is a new substance that is formed by a chemical reaction.
compound
Given the quadrant of θ in standard position and a trigonometric function value of θ, find exact values for the remaining functions. Quadrant II, sinθ = 2/7
cosθ = -3√5/7 tanθ = -2√5/15 cotθ = -3√5/2 secθ = -7√5/15 cscθ = 7/2 Mathway (Trigonometry) Find the Other Trig Values in Quadrant II
A student wants to prepare a solution using a crystalline solid and ethanol. Which of the following will increase the rate at which the solid will dissolve in the ethanol?
crushing the crystalline solid before adding it to the ethanol
Classify the polynomial by degree and number of terms. Describe the shape of its graph. 3x³
cubic monomial; 'S' shaped with 2 turns
A student is given a solid piece of copper wire, and is asked to perform three separate experiments using the sample of the metal. The student plans to break the copper into three pieces by bending it. Indicate whether you agree or disagree with the student's plan and why.
disagree with the plan because the metal is both malleable and ductile and will bend, not break
Find the distance between points B(5, 7) and F(1, 2), and the coordinates of the midpoint of BF.
distance = √41; 6.4 midpoint = (3, 9/2) Mathway
Water is amphoteric because it can
donate or accept a proton
In both ionic and molecular bonds, the resulting compound is stabilized because _____.
each atom's outer electronic orbital is full
What was different about the atomic theory proposed by Niels Bohr?
electrons energy levels related to their orbits
An element that tends to give up its valence electrons during a chemical reaction is _____.
electropositive
In an endothermic reaction, the temperature decreases because_____.
energy is absorbed
A change occurs that raises the temperature of the container in which it happens. What is the best term to describe the change?
exothermic
Identify the conic section produced by the following diagram. (Evernote)
hyperbola
The molecular weight of an ionic compound is 118.9 g/mol. The ions in the unknown are sodium, oxygen, and bromine. What is the name of the unknown oxoanion?
hypobromite
If the temperature of a chemical reaction was reduced, how could the reaction rate most likely be increased?
increase the concentration of the reactants
Which of the following would increase the pressure acting on a closed-system chemical reaction?
increasing the temperature of the chemical reaction
Classify the following system of equations as inconsistent, dependent, or independent: {-3x -7y -2z = -25 {-6x +21y -6z = 57 {-3x +14y -4z = 40
independent, because there is an intersection
Ionic bonds are like covalent bonds because both type of bonds _____.
involve the valence electrons
An element that can oxidize easily__________.
is at the top of the reactivity series
The emission spectrum of an element
is different from any other element's absorption spectrum
Equal masses of four metals absorb the same amount of energy. Which substance would have the greatest increase in temperature?
lead (c = 0.159 J/g°C)
What is a common use for noble gases?
lighted signs
Write the equation in logarithmic form. 6^-4 = 1/1296
log₆ 1/1296 = -4
Identify the name of the ionic compound with the formula MgS.
magnesium sulfide
Carbon dioxide, sodium acetate, and water form when sodium bicarbonate and acetic acid react. Even though three products form from two reactants, it is wrong to conclude that _____.
matter is created
Which type of bond is best described as having electrons that are free to move about in the substance?
metallic bonds
Describe how the graph of the function y = f(x-3) can be obtained from the graph of y = f(x).
move it 3 to the right
What would you expect to happen if Cu(s) was placed in a beaker that contained a solution of MgCl2?
nothing
A chemist is selecting a radioactive element for use in cancer treatment. Which branch of chemistry best describes this chemist's work?
nuclear chemistry
An sample of gas is composed of molecules with a molecular weight x + 3y = 34. How many covalent x-y bonds appear in the Lewis structure for this gas?
three x-y bonds
Solve the nonlinear system of equations. {x² + y² = 256 {x + y = 16
two solutions: (0, 16) and (16, 0)
Which two factors would decrease reaction rate?
use of an inhibitor and decreased pressure on the system
Elements located in the same group in the periodic table have the same number of _____.
valence electrons
When are resonance structures the best representation of a molecule?
when electrons can occupy more than one possible location in the bonds
Under which circumstance would you be most certain that a reaction is a decomposition reaction?
when only one reactant is present
A sealed bottle is half full of water. The water undergoes condensation and evaporation. When will equilibrium be attained in the bottle?
when the rate of evaporation equals the rate of condensation
Use substitution to determine which of the given linear expressions is a not a factor of 3x⁴ - 16x³ - 15x² + 88x + 60
x + 5 Mathway (Algebra) Factor
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {x + 2y + z = -17 {3x + 7y + 2z = -56 {x - y + 2z = 0
x = -4, y = -6, z = -1
If x = 78 when y = 130 and x varies directly as y, then find x when y = 190.
x = 114 when y = 190 Formula: y = ky(solving for y) or x = ky(solving for x) Substitute 78 = k(130) Divide by 130 on both sides k = 0.6 x = 0.6(190) x = 114
Write the pair of parametric equations as a single equation in x and y. {x = 8t² -3 [y = 6t - 7
x = 8((y + 7)/6)² - 3
Solve the equation 3^4x = 27^x+3
x = 9
Find the domain of the radical function. f(x) - √(9-x)
x ≤ 9 Solution f(x) - √(9-x) = 0 Add √(9-x) to both sides f(x) = √(9-x) Mathway: Find the Domain
Solve the radical inequality. √(x + 14) ≤ x - 16
x ≥ 22
Solve the radical inequality. ³√(3x-6) + 6 ≥ 7
x ≥ 7/3
Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?
x/3 + x/9 = 1; 2.25 hr
Solve the equation or inequality. 4/(x-3) - 2/(x+4) = 0
x=-11
Solve the proportion (x−8)/8 = 4/5
x=14 or 72/5
Divide x³ + 5x² + 9x + 9 ÷ x + 3
x² + 2x + 3
Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (-2, 0) asymptote: y=1/2x
x²/4 - y² = 1 Put in each answer using Mathway: Find the Vertex Form, till the verices and asymptote matches up
If f(x) = 9 - x² and g(x) = 3 - x, which is the rule of function (f × g)(x)?
x³ - 3x² - 9x + 27
Write the product as a polynomial in standard form. (x - 6)(x + 5)(x - 4)
x³ - 5x² - 26x + 120
Gupta threw a baseball off a cliff into an open field 50 feet below. The chart gives the horizontal distance, x (in feet), the baseball traveled from Gupta and the height, y (in feet), of the baseball above the field. (Evernote) distance, x | 8 | 18 | 33 | 43 | height, y | 65 | 76 | 79 | 71 | Choose the quadratic equation that best fits the baseball's trajectory from Gupta to the open field below.
y = -0.0383x² + 2.143x + 50
Find a quadratic function that fits the set of data points exactly, in the form y = ax² + bx + c with values of a, b, and c to two decimal places. (1, 4.1), (5, 2.3), (11, 4.9)
y = 0.09x² - 0.98x + 4.99 Mathway: Find the Equation of the Parabola
Write an equation in slope-intercept form for a line that passes through the given pair of points. (4,-7), (-2,-10)
y = 1/2x - 9 Solution Slope Formula: slope(m) = (y2 - y1) / (x2 - x1) Substitute and Solve m = (-10 +7) / (-2 - 4) m = (-3) / (-6) m = 1/2 or 0.5 Slope intercept form: y = mx + b Pick one of the two points (4,-7) or (-2,-10), substitute and solve -7 = 1/2(4) + b -7 = 2 + b -7 - 2 = b -9 = b Final Answer y = 1/2x - 9
Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and z. y=98/3 when x=2 and z=7. Find y when x=8 and z=3
y = 7/3(x)(z); 56
Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and the inverse of z. y=-99.4 when x=-11 and z=4. Find y when x=2 and z=-8.
y = 9x/z; -9/4
Find the inverse of the function and determine whether the inverse is a function. y = 7x²
y = ±√(x/7), y is not a function.
Which inequality is best represented by the graph shown: (Evernote)
y ≤ -x² + 5x
Which function represents exponential decay?
y(x) = 5(0.44)^x
Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 4x² = 8
±√2; ±1.41
Evaluate the trigonometric expression. cos(Cot⁻¹1)
√2/2 Mathway (Trigonometry) Find the Exact Value
A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of all purchases are returned. What is the probability that no more than 1 of the next 7 purchases will be returned?
≈ 0.938 ((₇C₁)(0.06)¹(1 - 0.06)⁶) + ((₇C₀)(0.06)⁰(1 - 0.06)⁷) ≈ 0.938
The class average on a math test was 77.5 and the standard deviation was 5.8. Find the z-score for a test score of 83, and the percentage of the class who scored below 83.
≈ 0.95; 82.89% Solution z-score z = (x - x̅) ÷ σ z = (83 - 77.5) ÷ 5.8 = 0.948 → 0.95 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 83, 77.5, 5.8)→Enter = 0.83 or 83%
