Algebra 2 - lizzyag

Determine whether the following situation would require calculating a permutation or a combination. Selecting four teachers to attend a math seminar.

combination

Classify 2 by degree and by number of terms.

constant monomial

Which expression completes the equation to make it an identity? cos+ sin + cos / 1+ sin

cos θ

Simplify cot/cos

csc θ

Classify 2x3 - 2x by degree and by number of terms.

cubic binomial

Classify -4x3 - 2x2 - 2x by degree and by number of terms.

cubic trinomial

Write an explicit and a recursive formula for the sequence -7, -5.6, -4.2, -2.8, -1.4, ....

explicit: an = -8.4 + 1.4n; recursive: an = an - 1 + 1.4, where a1 = -7

Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.

explicit; 0, -8, -24, -48, -80

For f ( x ) = 5 - 3 x and g ( x ) = x 2 - 1, find f ( g ( x )) and g ( f ( x )).

f ( g ( x )) = -3 x 3 + 8, g ( f ( x )) = 9 x 2 - 30 x + 24

Solve |5x - 3| ≤ 3.

b

Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.

f ( x ) = 300(1.13) x

Solve

f = 0, g = -4, h = 9 or -9

Graph f ( x ) = 2 x + 1 + 3 as a translation of its parent function.

backwards L high

Graph y = 3 x + 1 as a translation of its parent function.

backwards L high

Graph y = 4x - 3 as a translation of its parent function.

backwards L low

A certain box of cereal should have a net weight that is within 1.5 grams of 510. After the first phase of production, the weight of the cereal is 308 grams. By how much should the weight of the cereal increase to remain within the specified weight?

between 200.5 and 203.5 grams

The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?

y = 1.25x + 1; y = 21

Find the equation of the graph.

y = 1.5x

A factory can produce two products, x and y, with a profit P approximated by P = 12x + 15y. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1000. What production levels yield maximum profit?

x = 1000; y = 0

Find the zeros of y = (x - 2)(x + 1)(x + 3).

x = 2, x = -1, x = -3

Find the zeros of y = (x - 2)(x + 9).

x = 2, x = -9

Solve 3(x - 5) - 15 = 48.

x = 26

Solve

x = 3

Find the zeros of the function. State the multiplicity of multiple zeros. y = (x - 4)2

x = 4 multiplicity 2

Solve 3x2 - 9x - 12 = 0 using the Quadratic Formula.

x = 4, x = -1

Solve

x = 6

Find only the rational roots of x4 - 9x3 + 16x2 + 18x - 36 = 0.

x = 6, x = 3

Refer to the question below.

x = 60

Solve x - x3 = 2x4 + 3x2 - 5.

x = ±1

State the excluded value(s) of

x cannot equal -4

State the excluded value(s) of

x cannot equal 5, -5

Solve |x + 4| ≥ 1.

x ≤ -5 or x ≥ -3

Simplify

x+3/2

Find

x+4 / x+2

Simplify

x-1 / 5(x-3) 1 and 3

Find the inverse of y = 3x2 + 4. Is the inverse a function?

x-4 / 3 no

Divide

x-4/x-3 3 4

Divide

x-5/x-3

Divide

x-6 / x-5

Simplify

x-7 /2

Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.

f(x) = 260(1.09)x

Find a quadratic model for the values in the table.

f(x) = 3x2 + 7x - 9

Find a polynomial function to model the data.

f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32

The expression | -2 | - |-7 | simplifies to 5.

false

The point-slope formula of a line that passes through the point (8,5) and has a slope of ¼ is y = 1/4x + 3.

false

Graph y = 5 cos x.

far apart 5 -5

In which quadrant does the terminal side of a 314° angle lie?

fourth quadrant

Determine whether the series -1024 + 256 -64 + 16 - ... is arithmetic or geometric. Then evaluate the series to the ninth term.

geometric; -819.203125

The graph below models the burning of a candle. At time t = 0, the candle was 8 inches tall. If the candle burns at a rate of 2 inches per hour, what equation models the height h of the candle after burning for t hours?

h = -2t + 8

Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0?

inconsistent

Classify the system.

independent

Solve the system of three equations by elimination: 5x + 2y - 3z = 10 2x - 2y + 4z = 6 x - y + 2z = 3

infinitely many solutions

Which set of numbers best describes the number -4?

integers

Which set of numbers best describes the number π (pi)?

irrationals

Expand

log b (1/2 -

Write 5 log x - 4 log (x - 4) as a single logarithm.

log x^5/x-4^4

What does the dot at 47 represent?

lower quartile

Solve |8 - m| + 4 = 21.

m = -9, m = 25

Which line, having the given slope and passing through the given point, represents a direct variation?

m= 2/3 ; (9, 6)

Multiply and simplify

m^2 sqr 12 m^2

The number of patients treated at Dr. Holman's dentist office each day was recorded for seven days. Using the data 3, 10, 18, 9, 22, 20, and 2, find the mean, median, and mode.

mean: 12, median: 10, no mode

The number of patients treated at Dr. Oster's dentist office each day was recorded for nine days. Using the data 7, 4, 18, 14, 14, 11, 13, 21, and 6, find the mean, median, and mode.

mean: 12, median: 13, mode: 14

Find the mean, the median, and mode of the set of values. 5, 20, 6, 5, 15, 18, 12, 13, 14

mean: 12, median: 13, mode: 5

Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15

mean: 15, standard deviation: 5.66

Find the mean and standard deviation for the set of values. 25, 19, 5, 21, 18, 22, 17, 10, 7

mean: 16, standard deviation: 6.62

If m varies directly as the square root of y, inversely as p2, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?

multiply 10/9

What is the GCF of 3n3 + 5np2 + n2p2?

n

Write an explicit formula for the sequence

n+1/n^2+3

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

x/3 + x/4 =1, 1.71 h

Is the sequence -9.9, -13, -16, -19.2, ... arithmetic? If so, identify the common difference.

no

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

no solution

Find the inverse of f(x) = 3x2. Is the inverse a function?

x/3 no

Solve

no solution

Solve the system of equations by using substitution. -2x + 3y = 7 4x - 6y = 8

no solution

Use substitution to solve the system of equations given below.

no solution

Write (x - 2)(x + 9) as a polynomial in standard form.

x2 + 7x - 18

Find the next two terms in the sequence -5, 8, -13, 20, -29, .... Write a formula for the nth term. Identify the formula as explicit or recursive.

none of these

The velocity of sound in air is given by the equation

none of these

Divide (5x3 - 6 - 5x) ÷ (10 + 5x) using synthetic division.

x2 - 2x + 3, R -36

Determine whether the following situation would require calculating a permutation or a combination. Assigning students to their seats on the first day of school.

permutation

Solve cot θ sin θ = 1/5 for 0 ≤ θ < 2π.

pi/3 5pi/3

What is the period of y = 3 tan 4x + 5?

pi/4

Which property was used to rewrite log

power property

Is y = (2x)2 + 5x - 7 + 1 linear or quadratic? Identify the quadratic, linear, and constant terms.

quadratic function quadratic term: 4x2 linear term: 5x constant term: -6

Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12

range: 32, interquartile range: 16.5

Find the range and the interquartile range of the set of values.37, 21, 44, 19, 22, 47, 26, 32, 25, 43, 11, 15

range: 36, interquartile range: 20

Use Pascal's Triangle to expand (s - v)5.

s5 - 5s4v + 10s3v2 - 10s2v3 + 5sv4 - v5

In which quadrant does the terminal side of a 117° angle lie?

second quadrant

Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.

sequence, finite

Simplify sin2 θ(1 - csc2 θ).

sin2 θ - 1

Find the slope and the y-intercept of the line. y = 5x - 7

slope: 5 y-intercept: (0, -7)

Let f(x) = 4 - x2 and g(x) = 2 - x. Find f(x) • g(x).

x3 - 2x2 - 4x + 8

Divide (x4 - 11x3 - 49x2 + 899x - 2506) ÷ (x - 8).

x3 - 3x2 - 73x + 315, R 14

Simplify sin θ sec θ.

tan θ

Multiply

x; x ≠ -6, -3, 0

Which polynomial function has the highest degree?

the quotient of f(x) and g(x), where f(x) = x9 - 3x and g(x) = 3x2 - 4

Given the set of axes y-axis: a car's velocity, x-axis: time, what does the area under the curve represent?

the total distance traveled by the car

Order does not matter when examining combinations, but order does matter in permutations.

true

Evaluate the discriminant of 25x2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.

two real solutions

Identify the graph of y = 2 x + 7 and its inverse.

up cross

Identify the graph of y = 2x2 - 5 and its inverse.

up right

Use Pascal's Triangle to expand (s - v)6.

v6 - 6v5s + 15v4s2 - 20v3s3 + 15v2s4 - 6vs5 + s6

Identify the vertex and the axis of symmetry of the parabola.

vertex: (1, -6); axis of symmetry: x = 1

Solve w + 12 = -6 - 2w.

w = -6

Match the given graph with its corresponding equation.

x + 4y = -4

Which polynomial is NOT a factor of 3x4 - 16x3 - 3x2 + 36x + 20?

x - 1

Which polynomial is NOT a factor of 3x4 - 10x3 - 29x2 + 16x + 20?

x - 2

Simplify

x -1/2 y 3/4

Multiply

x ; x ≠ -7, -4, 0

Solve x2 - 4x - 5 = 0 by factoring.

x = -1, x = 5

Solve |x + 9| = 8.

x = -17, x = -1

Solve x3 + 4x2 - x - 4 = 0.

x = -4, x = -1, x = 1

Solve x3 + 5x2 - 9x - 45 = 0.

x = -5, x = -3, x = 3

Find the zeros of y = x(x + 5)(x - 8).

x = 0, x = -5, x = 8

Solve x2 - 6x = 0 by graphing or by factoring.

x = 0, x = 6

Find the roots of x3 - x2 + 2 = 0.

x = 1 + i, x = 1 - i, x = -1

Find the zeros of y = (x - 1)(x + 2).

x = 1, x = -2

Multiply

xy/2 0 0

Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).

y + 3 = - 2(x - 4)

A line passes through the point (-6, 1) and has slope m = -4. Find the equation in point-slope form.

y - 1 = -4(x + 6)

Find the equation of the line that passes through the point (-7, 2) and has a slope m = -5 in point-slope form.

y - 2 = -5(x + 7)

What is an inequality for this graph?

y - 3x ≥ -5

Write the equation of the parabola in vertex form.

y = (x + 1)2 - 3

Rewrite y = x2 + 4x + 5 in vertex form. Then find the vertex.

y = (x + 2)2 + 1; (-2, 1)

Write the equation of the parabola in vertex form.T

y = (x - 1)2 - 3

Rewrite y = x2 - 10x + 3 in vertex form. Then find the vertex.

y = (x - 5)2 - 22; (5, -22)

Write y = -3x2 + 12x - 21 in vertex form.

y = -3(x - 2)2 - 9

Write y = -4x2 - 64x - 265 in vertex form.

y = -4(x + 8)2 - 9

The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?

y = 4x + 10

Which equation represents the line whose slope is 1 and whose y-intercept is (0, 0).

y = x

The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?

y = x + 6

What is the equation of the graph?

y = |x + 5|

Find the equation of the line that passes through the points (-6, 3), (5, -2) in point-slope form.

y-3=-5/11(x+6)

What is an equation for a direct variation whose graph passes through the point (-5, 3)?

y=-3/5x

Is the sequence -5.4, 5.1, 15.6, 26.1, ... arithmetic? If so, identify the common difference.

yes, 10.5

Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.

yes, 5.4

Write the specification 14.35 ≤ d ≤ 15.15 as an absolute value inequality.

|d - 14.75| ≤ 0.4

When 2251 voters were polled, 52% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

±2.1%; between 49.9% and 54.1%

When 876 voters were polled, 67% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

±3.4%; between 63.6% and 70.4%

The class average on a math test was 84.5 and the standard deviation was 4.4. Find the z-score for a test score of 94.

≈ 2.16

How much money invested at 5% compounded continuously for 2 years will yield $1150?

$1040.56

A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?

$13,616.61

You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?

$162.50

Jim's wages vary directly with the numbers of hours he works. For 7 hours, he makes $38.85. How much will he make in 37 hours?

$205.35

The cost of ten different portable MP3 players is shown in the table. What is the mean cost?

$90

Use substitution to solve the system of equations given below.

(-10, -12)

Use elimination to solve the system of equations. -x + 2y = 18 x + 8y = -38

(-22, -2)

Which ordered pair is the solution to the given system of equations?

(-3, -4)

Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)2 + 7.

(-3, 7), y-intercept -29

What is the vertex of the graph of y = |x| - 6?

(0, -6)

A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish. The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?

(0, 0), (0, 53), (71.76, 0), (28, 46); t = 28 and s = 46.

Determine the coordinates of the y-intercept of 2x + 4y = 8.

(0, 2)

Which point is in the solution set of this system of inequalities?

(0, 4)

Solve the system of equations. x = 3y + 2z 2x + 3y + 2z = 3 -x + y - z = 6

(1, 3, -4)

Find the values of x and y that maximize the objective function for this graph.

(1, 8)

The objective function for this graph is P = 5x + y. What values of x and y maximize this function?

(1000, 0): The maximum is 5000.

Use elimination to solve the system of equations given by 10x - 40y = 60 and 15x + 40y = -10.

(2, -1)

Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6.

(2, -2)

Solve the system of equations. 2x + y - z = 3 x + y + z = 5 x - 2y + z = 2

(2, 1, 2)

Factor 8ac + 12ad + 10bc + 15bd.

(2c + 3d)(4a + 5b)

Factor 4x2 - 49.

(2x + 7)(2x - 7)

A point (x, y, z) can be used to represent the location of a geographical point in space, where x represents the latitude in degrees, y represents the longitude in degrees, and z represents the elevation in feet above or below sea level. Jerimoth Hill is the highest point of elevation in Rhode Island. It is 812 feet above sea level and lies at about 42° north latitude and 72° west longitude. What ordered triple represents the location of Jerimoth Hill?

(42°, -72°, 812)

Factor 4x2 + 5x - 21.

(4x - 7)(x + 3)

Factor 4y2 - 3y - 1.

(4y + 1)(y - 1)

Solve the system of equations by using substitution. y = 2x + 1 3x - y = 4

(5, 11)

Factor 5r2 + 13r - 6.

(5r - 2)(r + 3)

The roots of a certain polynomial are -2/5, -6 and 4/3. What might the linear factors of the polynomial be?

(5x + 2)(x + 6)(3x - 4)

Which point lies in the plane represented by the equation 2x + 7y + 3z = 25?

(6, 4, -5)

Determine the coordinates of the x-intercept of 3x - 4y = 24.

(8, 0)

Factor 18ab + 9ax -4b - 2x.

(9a - 2)(2b + x)

The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.

False

The solution to this equation is x = 11.

False

The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.

False

The vertex of a parabola will never be on the axis of symmetry.

False

The vertex of f(x) = 2(x-2)2 +10 is (-2, 10).

False

These are two like radicals.

False

Transforming a figure 3 units to the right and 2 units up can be accomplished by adding 3 to each x-coordinate of the vertices and subtracting 2 from the y-coordinates.

False

Two matrices can be subtracted if they have an equal number of rows, regardless of how many columns they have.

False

Two matrices with dimensions 3x1 and 2x4 will produce a product matrix with dimensions 3x4 when multiplied.

False

Using substitution, the equations 2x - 3y = -21 and 3x + 3y = -24 give a solution of (-9,-1).

False

When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.

False

You cannot use a table or graph to show a probability distribution.

False

y = -4* 2x is a reflection of y = -1/4* 2x.

False

Factor m3 - 4m2 + 6m - 24.

(m - 4)(m2 + 6)

Factor t2 - 10t + 25.

(t - 5)2

Factor xy - 6 + 2y - 3x.

(x + 2)(y - 3)

An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.

(x + 3)(y - 2)

Factor x2 - 16.

(x + 4)(x - 4)

Factor x2 - 81.

(x + 9)(x - 9)

Factor x2 - 6x + 8.

(x - 4)(x - 2)

Factor 3xy - 2by + 3ax - 2ab.

(y + a)(3x - 2b)

Find the annual percent increase or decrease that y = 0.35(2.3)x models.

+130%

Find the exact coordinates of the point at which the terminal side of -135° intersects the unit circle.

- sqr 2 / 2

Find the radian measures of the angles whose sine is -0.8. Round to the nearest hundredth.

-0.93 + 2πn and 4.07 + 2πn

Use the graph to find the value of y = sin θ for θ = 270°.

-1

Write the coordinates of the image after a translation 3 units right and 2 units down.

-1 3 -1 -6 -6 -3

Evaluate sec 3.

-1.0101

Evaluate sec 131°.

-1.52

Solve

-1/16

Find the inverse of -2 2 -1

-1/2 1 -1/10

Solve

-1/3

What is the slope of the line through the points P(-5, -6) and Q(-12, 5)?

-11/7

Evaluate the infinite geometric series

-12

Solve |x + 8| ≤ 5.

-13 ≤ x ≤ -3

Find

-14 -1 3 7

Which matrix has determinant -7?

-14 -1 7 1

Find the coordinates of the image of

-14 -3 10 14

Simplify the expression |-3| - |-5|.

-2

Use matrices A, B, and C. Find B-C if possible.

-2 -7 14 -4 7 0

Find the inverse of the relation. Graph the given relation and its inverse.

-2 1 5 10

Write the coordinates of the image after a dilation three times the original size.

-21 -12

Find AB,

-22 74

Evaluate 2a - 5b - 3a for a = -2 and b = 5.

-23

Find

-3 5 9 0

Find

-3 9 1 -3 -6 9 -14 0 6

Two matrices with dimensions 2x2 and 2x2 will result in a product matrix with dimensions 2x2 when multiplied.

-32 28

Evaluate -1x + 7y + 4x + 1y for x = 4 and y = -2.

-4

Solve 11c - 2(2c + 1) = 3(c - 6).

-4

Simplify (3 + 3i) - (7 + 6i).

-4 - 3i

Find g(-2) if g(x) = 4x + 3.

-5

Rationalize the denominator of

-5 -2 sqr 6

Find the coordinates of the image after the reflection in the given line.

-5 6 -1 -3 -9

Evaluate the series

-5.81

Solve the question below.

-6

Find the additive inverse of 6 - 3i.

-6 + 3i

Solve for each variable

-6 -1/4

Find

-70 44 70 -24 71 -73 -71 -71 -35

Let f(x) = 3x + 7 and g(x) = 4x - 2. Find (f composited with g) (-6).

-71

Find all the real cube roots of

-8/9

Let f(x) = 3x2 + 10x- 8 and g(x) = x + 4.

-9x + 6, all real numbers x ≠ -4

Solve 5x - 4 = |2x + 1|. Check for extraneous solutions.

...

Graph y= 2.5 tan 4x/5

/ closer together

A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?

0

Find the slope of the line that passes through (5, -5) and (9, -5).

0

Determine whether

0 -1/3 -1/2 1/6

State the excluded values of a and b in the expression

0 0

Which matrix is the multiplicative inverse of

0 1 -1 -5 5 -4 1 -1 1

What are the coordinates of the image after a rotation of 90°?

0 1 -4 0 -3 1

Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.

0 = x3 + 4x2 - 2x - 20

Find all the real square roots of 0.0036.

0.06 and -0.06

Use the graph to find the value of y = sin θ for θ = 150°.

0.5

For an annual rate of change of -31%, find the corresponding growth or decay factor.

0.69

Find 49° in radians.

0.86 radians

Find the values of cos θ and sin θ for -25°. Round your answers to the nearest hundredth.

0.91, -0.42

Complete the square: x2 + 2x + ____ .

1

Simplify cos θ sec θ.

1

Simplify cot θ tanθ.

1

Simplify csc θ sin θ.

1

Solve

1

Write A. 1 - 4i B. 1 + 4i C. 3i D. -3i

1 - 4i

Without graphing, tell how many x-intercepts y= 2x2 + 4x + 2 has.

1 intercept

Which expression completes the equation to make it an identity?

1+csc2 0 / 1-sin 0

The selling price of x number of a certain stereo can be modeled by the function R ( x ) = 160 x . The total cost of making x stereos is C ( x ) = 71 x - 0.02 x 2. What is the percent markup for 31 stereos?

127%

Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.

128

Find

13 -9 -12 -1 -6 18 1 -1 2

The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).

13/22

Solve

13/3 2/3

Solve the question below.

13x-30/x^2-36

A group of students rolled two number cubes 100 times and recorded a sum of six 14 times. Find the experimental probability of rolling a sum of six.

14%

A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wishes to have the length be three times the width. If the side of the barn accounts for the length of the fence, find the dimensions of the fence.

144 feet by 48 feet

Find the GCF of 14a2b4c and 56ab2c2.

14ab2c

Use inscribed rectangles to approximate the area under g(x) = -0.5x2 + 7 for -3 ≤ x ≤ 0 and rectangle width 0.5.

15.3 units2

Find the next three terms in the sequence 1, 2, 4, 8, ....

16, 32, 64

The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.

162

Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?

176 ways

Multiply

180 sqr 10

Which number is an outlier in the data shown in the table?

19

Find the arithmetic mean an of the terms

19/40

Evaluate the infinite geometric series 1.9 + 0.19 + 0.019 + ....

19/9

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds.

191 feet

Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)

192, 76.8, 30.72

The sequence -12, -6, 0, 6, ... , 48 has 11 terms. Evaluate the related series.

198

Find

2

Simplify 2i(5 - i).

2 + 10i

A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?

2 5 1

Write an equation of the cosine function with amplitude 2 and period 8π.

2 cos 1/4 x

State the excluded values of x in the expression

2 or 3

Divide and simplify sqr 24/ sqr 2

2 sqr 3

Let f ( x ) = x 2 + 2 x - 1 and g ( x ) = 2 x - 4. Find 2 f ( x ) - 3 g ( x ).

2 x 2 - 2 x + 10

For the function f ( x ) = (4 - 2 x )2, find f -1 and the domain and range of f and f -1. Determine whether f -1 is a function.

2 x/2 0

What are the dimensions of the matrix?

2 × 1

Solve |5x - 7| = 3.

2, 4/5

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

2.18

Make a box-and-whisker plot for the set of values. 7.2, 3.2, 5.2, 3.2, 4.2, 7.2, 5.2, 3.2, 6.2, 4.2, 6.2, 3.2, 6.2, 2.2, 4.2

2.2 7.2

The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

2.5%

Use the properties of logarithms to evaluate

2/3

Use the frequency table to find P(more than 3 children).

20%

Simplify

21 16 50 54 / 72

Use the Law of Sines to solve for a to the nearest tenth.

21.2

Seven skiers enter a downhill race. First, second, and third places will be given to the three fastest skiers. How many arrangements of first, second, and third places are possible with seven skiers?

210

How many combinations of four can you make from the set? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

210 combinations

On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 265 feet at an angle of 35° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?

218.2 ft

Multiply

22 + 8 sqr 6

The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.

25,200 coats

Which sample size will produce a margin of error of ±6.3%?

252

The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

260 fish

Four cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of four cards are possible?

270,725

There are 17 students participating in a spelling bee. How many ways can the students who go first and second be chosen?

272 ways

Suppose that x and y vary inversely. Write a function rule for the function that x = 4 when y = 7.

28/x

Solve the question below.

29/4

Simplify

2a3/3b

Solve 2 cos θ + 4 = 3 for 0 ≤ θ < 2π.

2pi/3 4pi/3

Write 2r3 + 8r2 - 10r in factored form.

2r(r - 1)(r + 5)

Divide (2x3 + 4x2 + 3x + 4) ÷ (x + 1) using long division.

2x2 + 2x + 1, R 3

Simplify

2y +1 / y+1

Suppose you take a true/false quiz that contains five true/false questions. Let an even digit represent a correct answer and an odd digit represent an incorrect answer. In the five trials shown, how often did you get at least 3 questions correct? (Note: Assume there is a 0 before the number 4908 in the first trial.)

3

Use the properties of logarithms to evaluate log7343.

3

Rationalize the denominator of

3 sqr t

Determine the number of standard deviations which include all data values listed for the situation.The mean time employees take of a company to commute to work is 40.75 minutes; the standard deviation is 12.9 minutes.42 min, 45 min, 53 min, 34 min, 12 min, 48 min, 52 min, 24 min, 56 min, 47 min, 28 min, 48 min

3 standard deviations

What are the dimensions of the matrix?

3 × 2

What are the dimensions of the matrix? Identify a12.

3 × 2, -4

Factor 3q3 - 81.

3(q - 3)(q2 + 3q + 9)

Solve the problem below.

3.1 m2

In ΔABC, b = 1, c = 3 ma= 138

3.8

Find the value of csc 165°. Round your answer to the nearest hundredth.

3.86

For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°.

3/10

Solve

3/2

What is the probability of getting two heads when tossing a coin four times?

3/8

The diagram shows one solution to the equation 3 - sin θ = 5 sin θ. Find the complete solution of the equation.

30° + n • 360°, 150° + n • 360°

For the geometric sequence 2, -10, 50, -250, ..., find the seventh term.

31, 250

The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).

31.7%

In May, Suzanne bought 32 styrofoam balls and decorated them as toy figurines. In June, she sold 12 figurines. In May, Carrie bought 36 styrofoam balls to decorate and in June, she sold 22 figurines. Which matrix represents all of their May purchases and their June sales?

32 -12 36 -22

Find 8P3.

336

A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 20, 60, 100, 140, .... Find the distance that the projectile traveled in the 9th second.

340 ft

Evalute 9!

362,880

Find the missing term of the arithmetic sequence 25, ___, 49, ....

37

Use the Law of Sines to solve for a to the nearest tenth.

38.1

A set of data that is normally distributed has a mean of 35.6 and standard deviation of 2.5. Which number is between 1 and 2 standard deviations of the mean?

38.3

Find f(-5) if f(x) = -8x - 1.

39

Write

3^13^ sqr x^7

Solve 3 cos 0 = cos 0 - sqr2 for 0 < 0 < 2pi

3pi/4 5pi/4

Use the GCF to factor 15x2 + 6x.

3x(5x + 2)

Divide (3x3 + 4x2 - 5x - 2) ÷ (x + 2) using long division.

3x2 - 2x - 1

Simplify

3|x5|y4

Graph the figure and its image after the given rotation.

4

Solve the question below.

4

Use the properties of logarithms to evaluate log4 256.

4

A summer reading list has 20 books on it. In how many ways can you choose four books to read?

4,845 ways

In ΔABC, b = 4, c = 1, and ma =118

4.56

Simplify

4/3

Solve

4/3

A jar contains 12 blue marbles, 8 red marbles, and 20 green marbles. You pick one marble from the jar. Find the theoretical probability, P(blue or green).

4/5

How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?

42 ways

Use the frequency table to find P(2 or 3 children).

42%

The scores of 36 students on a recent geography test are in the table. If Lupe got a 69 on the test, what percentile would that score represent?

44%

The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?

48

In May, Marcus bought 48 styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lin bought 44 styrofoam balls to decorate and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?

48 -19 44 -21

Simplify

4a^2b sqr 3a

Find

4ax^2 /3by

Multiply

5

Suppose that 80% of people surveyed answered 'Yes' to a certain question. Let the digits 0-7 to represent 'Yes' and let 8 and 9 represent 'No.' Use the random numbers shown below to determine how many people out of 20 answered 'No.'

5

What are the dimensions of the matrix?

5 × 4

A school bought a special type of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. How many different pass codes are possible?

5,040

Find 311° in radians.

5.43 radians

Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.

5/23

Assume red and green are equally likely occurrences. What is probability that you will get one green light in a row of five lights?

5/32

Find the real-number root of

5/7

The box-and-whisker plot represents the test scores of 25 students. What percent of the scores were between 88.5 and 65?

50%

Evaluate. 9!/6!

504

Solve the question below.

505

Use the Law of Sines to solve for c to the nearest tenth.

51.4

A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour?

525

Evaluate e4.

54.5982

Evaluate 3(2m - 3n) - 2(m + 2n) for m = -9 and n = -7.

55

Evaluate 8C3.

56

What is the maximum for the objective function for this graph?

560

Which sample size will produce a margin of error of ±4.1%?

595

Simplify

5x

In how many ways can the three letters A, B, and C be arranged?

6

For the sum

6 terms, 25, 0; 75

Use summation notation to write the arithmetic series -3.9 + (-1.9) + 0.1 + ... for six terms.

6 x=1 -5.9 +2n

pi/3 radians in degrees

60°

Find the degree measures of the angles whose tangent is sqr 3

60° + n • 180°

Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

67.3 in.2

Find the angles in the triangle when a = 13, b = 12, and c = 11. Round your answers to the nearest tenth.

68 59 52

Use the frequency table to find P(0 - 2 children).

68%

Find the angles in the triangle when a = 19, b = 20, and c = 10. Round your answers to the nearest tenth.

69 80 29

Multiply and simplify

6x^2 sqr3^ x

Solve the question below.

7

For x7 - 2x6 + 3x2 - 2x + 5 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

7 complex roots; 1, 3, 5, or 7 real roots possible rational roots: ±1, ±5

Use inscribed rectangles to approximate the area under f(x) = -x2 + 6 for -1.5 ≤ x ≤ 0 and rectangle width 0.5.

7.25 units2

Write the related series for the finite sequence 7.6, 6.3, 5, ... , -1.5. Then evaluate the series.

7.6 + 6.3 + 5 + ... + (-1.5) = 24.4

Evaluate the infinite geometric series 2.1 + 0.21 + 0.021 + ... .

7/3

Identify the outlier in the temperature data shown.

71°

The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?

72

The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.

75.3%

A fifth-degree polynomial equation with rational coefficients has the roots 2, -7i, and -7 + i. Find the remaining roots.

7i, -7 - i

Use synthetic division and the Remainder Theorem to find P(-3) if P(x) = x4 + 19x3 + 108x2 + 236x + 176.

8

Solve the problem below.

80.3°

Simplify

81

Which sample size will produce a margin of error of ±3.5%?

816

Use Pascal's Triangle to expand (3a - b)4.

81a4 - 108a3b + 54a2b2 - 12ab3 + b4

A grocery clerk sets up a display of 12-pack cartons of cola. There are 40 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?

820 cartons

After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?

87

After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?

87

Write

8x -15/7

Complete the square: x2 + 6x + ____ .

9

One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.

9 1/3, 13 1/3, 15 1/3

Find the 11th term of the sequence 11, 19, 27, 35, ....

91

Find the arithmetic mean an of the terms

91/60

In one survey, the shoe sizes of women are distributed normally about the mean. The mean of the data is 7.17, and the standard deviation is 1.44. About what percent of the women are within two standard deviations of the mean in shoe size?

96%

Evaluate the series 3 - 12 + 48 - 192 + ... to the seventh term. Round your answer to the nearest hundredth, if necessary.

9831

A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them. If x represents the number of type A printers sold, and y represents the number of type B printers sold, what are the constraints for a linear program that models this problem?

A.

Find the quadratic function

A.

Graph the system of inequalities.

A.

Graph y = -x2 - 1.

A.

Identify the graph that shows the solution to the system of inequalities.

A.

Identify the vertex and the axis of symmetry of the parabola.

A.

Solve 6x2 = 48. If necessary, round your answer to the nearest hundredth.

A.

Use elimination to solve the system given below. 5x - 2y = 25 5x + 3y = 5

A.

Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.

A.

Which series will converge?

A.

Which statement about 5y = 2x is true?

A.

Which system of inequalities has this graph?

A.

Is the sequence

A. yes .5

Describe the pattern

Add 1 to the numerator and 2 to the denominator of the previous number.

Given log 15 = B and log 3 = C , find log 5.

B - C

An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?

B.

Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2

B.

Simplify C. -500i

B.

Solve -9x + 6 + 5x2 = 0 using the Quadratic Formula.

B.

Solve 8x3 + 27 = 0.

B.

Solve the system of equations. 2x - 4y = 3 -3x + 5y = 1

B.

Use the Rational Root Theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do NOT find the actual roots.

B.

Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?

Brenda ran 9 miles; Anne ran 6 miles

A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?

Bus: d1 = 45t + 90; Car: d2 = 60t

Factor x4 - 8x2 + 15.

C.

For 3x3 -2x + 6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

C.

Graph

C.

Graph y = - (x - 1)2 + 4.

C.

Graph y = x2 - 6.

C.

In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?

C.

Solve -11x + 9 + 5x2 = 0 using the Quadratic Formula.

C.

Solve 7x2 + 28x = 49 by completing the square.

C.

Solve 8x2 - 80x = -24 by completing the square.

C.

Which line, having the given slope and passing through the given point, represents a direct variation?

C.

Which statement describes the relationship between the graph of the equation

C.

Which system of equations is graphed below?

C.

A class of 30 students has 11 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

C. 10/19

Evaluate the area under g(x) = -x2 - 3x + 7 for -4 ≤ x ≤ 1.

C. 35.83

A rubber ball dropped on a hard surface takes a sequence of bounces,

C. 54 24/125

Evaluate the series

C. 5461/ 16,384

A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.

C. 7.87 sec

Solve the question below.

C. h= 3v/piR^2

For 3x9 -7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

D.

For 8 - 4x3 + 4x6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

D.

Graph y = (x - 3)2 + 1.

D.

Solve 9x2 + 6x + 1 = 64.

D.

Solve x2 - 12x + 41 = 0

D.

Write in standard form. Then classify by degree and by number of terms.

D.

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

D. 1/6

Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.

D. an = 120 • 0.3n - 1; 120, 36, 10.8, 3.24, 0.972

Graph

D. vertex (-3,-1) x= -3

Name the property of real numbers illustrated by the equation 3(2x - 14) = 6x - 42.

Distributive Property

Describe the pattern 16, -8, 4, -2, 1, ....

Divide the previous number by -2.

What is the domain and range of this function? Domain: all real numbers; Range: y ≥ -4 Domain: -2 ≤ x ≤ 2; Range: y ≥ -4 Domain: x ≥ -4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0

Domain: all real numbers; Range: y ≥ -4

What is the domain and range of this function? Domain: x > 0; Range: y > 0 Domain: x ≥ 0; Range: y ≥ 0 Domain: all real numbers; Range: all real numbers Domain: positive integers; Range: positive integers

Domain: x > 0; Range: y > 0

4n3 + 5n2 + 6n + 15 factors to (3n2 + 2) (3n + 5).

False

4x3y4 is a 4th degree monomial.

False

4y is the greatest common factor of 4y2 + 6y.

False

5, 7, 11, 15, 21 is an infinite series.

False

7! Is another way of writing 7 * 6 * 5.

False

A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.

False

A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.

False

A matrix with 4 columns and 3 rows is a matrix of dimensions 4x3.

False

A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.

False

A situation may not be described by more than one sample space.

False

An angle in standard position with a positive measurement will extend below the x-axis.

False

An annual rate of change is -10%. The corresponding growth or decay factor is 0.10.

False

If flipping a coin is equally likely to result in heads or tails, the odds of flipping a coin six times and getting only one head are 3 out of 16.

False

If x is at the 63rd percentile, then 37% of the data are less than or equal to x.

False

If y varies inversely with x and y = 6 when x = 9, then y = 96/x.

False

It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.

False

Point M is at the coordinates (-5, 5).

False

Reciprocal functions cannot be evaluated in radians.

False

The determinant of this matrix is 7.

False

The domain of a relation and its inverse are the same.

False

The expression 2y - 5x + 3y + 2x evaluated for x = 3 and y = 2 is -11.

False

The expression | 2 + 4n | - 4 = 14 produces the answers n = 4 and n = 5.

False

The fifth root of 12 is equal to the fifth root of 7 times the fifth root of 5.

False

The graph of an absolute value function will always be an upward-pointing V shape.

False

The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.

False

The length of side RP is approximately 42 cm.

False

The line y = 7x - 2 has a slope of 7 and a y-intercept of (-2 ,0).

False

The missing term of the arithmetic sequence 13, __, 27 is 21.

False

The only restriction of the variable in this equation is that x cannot equal positive or negative 5.

False

The polynomial 3x2 - 7 + 4x3 + x6 is written in standard form.

False

The polynomial x4- 2x2 + x4 - x is written in standard form.

False

The possible rational roots of x3 + 3x2 - 4x + 2 are +/- 3 and +/- 2.

False

The range of the set 12, 18, 19, 22, 25 is 19.

False

The sequence 3, 6, 9, 12 is geometric.

False

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.

T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees

The table shows the number of oak 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 oaks planted in 1998.

T(x) = 0.2x3 + 0.7x2 + 0.2x + 0.1; 353.2 thousand trees

A car salesman receives $50 for each car sale plus 2% of the purchase price. How much must a car sell for in order for the salesperson to earn at least $500?

The car must sell for at least $22,500.

How do the medians of the two sets of exam scores compare?

The median of Exam A is greater than the median of Exam B.

What is true about the system

The system is consistent and independent.

-25 has no real 4th root.

True

15x3 - 10x2 + 3x -2 factors to (5x2 + 1) (3x - 2).

True

17 1/3 is the same as the cube root of 17.

True

3x2 -5x - 2 factors to (3x+1)(x-2).

True

4x2 - 36 = 0 has a solution of x = +/- 3.

True

A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.

True

A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.

True

A dependent system of equations will have infinitely many answers.

True

A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.

True

A jar contains 7 red marbles, 4 blue marble, and 6 green marbles. You draw one marble from the jar. The probability of drawing a blue or red marble is 11/17.

True

A multiple zero has a multiplicity equal to the number of times the zero occurs.

True

A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.

True

An equation using three variables is graphed in coordinate space.

True

An extraneous solution is a solution of the derived equation, but not of the original equation.

True

From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.

True

If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.

True

If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.

True

If f(x) = 3x + 7 and g(x) = 5x - 2 then (f+g)(x) = 8x + 5.

True

In the expression 2(x+4) - 12 = 44, x = 24.

True

In the expression 3(x - 6) - 12 = 33, x = 21.

True

Inscribed rectangles are completely under the curve.

True

Log4 64 = 3

True

Probability over a continuous range of events is cumulative probability.

True

The amplitude of y = 3 sin(2x) is 3.

True

The area approximated by circumscribed rectangles is greater than the area under the curve.

True

The equation f(x) = 4x4 + 4x2 + 9x - 2 can have at most four distinct real roots.

True

The expression 2y - 7x + 3y + 3x evaluated for x = 2 and y = 4 is 12.

True

The law of cosines is used to find the measures of a triangle when only the three sides are known, because the law of sines requires at least one angle measure.

True

The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.

True

The minimum value of a parabola that opens upward will be its vertex.

True

The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.

True

The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.

True

The polynomial 5x3 - 2x2 + x - 13 is written in standard form.

True

The range of the set 2, 5, 8, 19, 33, 45 is 43.

True

The sequence 2, 6, 18, 54, ... is a geometric sequence.

True

The slope of the line that passes through (-2, 6) and (1, 15) is 3.

True

The square root of a negative number is an imaginary number.

True

The tangent of an angle is equal to the ratio of its sine divided by its cosine.

True

The vertex of f(x) = 3(x+2)2 - 4 is (-2,-4).

True

This is the graph of y < |x - 3|.

True

This statement simplifies to 16a2.

True

Two parallel lines form an inconsistent system of equations that has no solution.

True

Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.

True

Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).

True

Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.

True

When dividing polynomials, every term of the numerator must be divided by the entire denominator.

True

When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.

True

Find AB,

[-25 25] TALL

Find

[21 -63]

Find

[6 -34]

Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.

a. 1000 units; b. $400

Write and evaluate a sum to approximate the area under y = (x - 4)2 - 1 for the domain 0 ≤ x ≤ 2. a. Use inscribed rectangles 0.5 units wide. b. Use circumscribed rectangles 0.5 units wide.

a. 13.75 units2; b. 19.75 units2

In a survey of 368 people, 81 drink milk straight from the milk carton. For the sample, find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.

a. 22%; b. ±5%; c. 17% to 27%

Factor 8a4b - 3ab2c.

ab(8a3 - 3bc)

There are 135 girls in the junior class at West High School. Of these 135 girls, 16 are on the volleyball team (V), 22 are on the softball team (S), and 8 are on both the volleyball and softball team. One student is selected at random. Find the probability that the student plays on the softball team but not the volleyball team.

about 10%

Graph Y=-pi/4 cot ( x-pi/4)

about 112 women

The table gives data about municipal waste collected and recycled by type. Find P(recycled | glass).

about 6.7%

Find the amplitude and period of y = -5 sin (5x).

amplitude=5,period=2/5

Which formula does NOT describe the sequence 8, 6, 3, -1, -6, ... ?

an = -0.5n2 - n + 9

Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.

an = 2an - 1 - 4 where a1 = 15; 356

Evaluate the infinite series

It does not have a sum.

If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method? Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations. Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.

Method II

Solve x2 - 10x + 29 = 0.

No Solution

Given log 5 = P and log 2 = Q , find log 10.

P + Q

A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8.

P(x)= 41x2 - 162x + 433; 1761 waterfowl

A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.

P(x)= 42x2 - 186x + 762; 1962 geese

What point has coordinates of (-5, 4)?

Point N

Write 11pi/18 radians in degrees

110°

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 2.5 seconds.

100 feet

Find the perimeter of the figure shown below. Simplify the answer. 8a + 2b 10a + 4b 10a + 2b 10a - 2b

10a + 2b

The formula for the volume of a sphere is

1.63 in.

Find the opposite and reciprocal of -1.8.

1.8, -5/9

Simplify

1/ 4 sqr x^7

Determine whether

1/10 -3/10 -1/5 -2/5

You roll a twelve-sided die with the numbers 1 through 12 on the faces of the die. You roll the die once. Find the theoretical probability P(factor of 12).

1/2

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

1/3 .33333333

Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?

1/32

Identify a31 in the matrix.

10

What steps would you use to plot (-3, -4, 0) in a three-dimensional coordinate system?

From the origin, move back 3 units and left 4 units.

Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?

From the origin, move forward 7 units, left 6 units, and down 5 units.

Graph 2x + 3y = 9.

Graph A

Solve and graph -2x + 7 ≥ 2(3 - x).

Graph A

Solve and graph 13 - 3y < -5.

Graph A

The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?

Graph A

Solve and graph 5x - 2 ≤ 8.

Graph B

Which is the graph of 0.4x + 0.1y ≥ 1?

Graph B

An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?

Graph C

Which is the graph of

Graph C

Which is the graph of the equation y = |x - 1|?

Graph C

Graph the solution of -7x + 4 ≥ 11 and 10 - 3x > 1.

Graph D

What is the graph of

Graph D