alg 2 fianal (kinda useless

Consider the rational function shown in the graph below.

Vertical asymptotes at x=-2 and x=3 ; horizontal asymptote at y=2

Which population parameter corresponds to this scenario? Shandra wants to determine the percentage of females in the senior class who plan to attend college.

population proportion

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

Use elimination to solve the system of equations.

(-1, -4)

A circle has an equation of (x+3)^2+(y+4)^2=9 ( x + 3 ) 2 + ( y + 4 ) 2 = 9 . What are the coordinates of the center point of this circle?

(-3, -4)

Look at the ellipse graphed below. Its center is at (-3, 2), and two of its vertices are at (2, 2) and (-3, 5).

(-7, 2) and (1, 2)

Solve the rational inequality: \frac{1}{4a}+\frac{5}{8a}<\frac{1}{2} 1 4 a + 5 8 a < 1 2 . Select the set of a-values that make the inequality true.

(-\infty ,0)\cup (2,\infty )

Solve the system of linear equations shown below. \\2a-3b=18\\5a+2b=7 2 a − 3 b = 18 5 a + 2 b = 7 Choose the correct solution in the form (a, b).

(3, -4)

Given the center and radius of a circle, what is the equation of the circle? Center: (2,4) ; Radius: 3

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

Which of the following is the radian equivalent of −165° ?

-11pi/12 radians

What is the product of \sqrt{-6}\cdot\sqrt{-8}

-4\sqrt{3}

Which of these statements are true about complex numbers? 1. Complex numbers have the form a+bi a + b i , where a and b are real numbers. 2. Complex numbers are a subset of real numbers. 3. Irrational numbers are a subset of complex numbers.

1 and 3

As part of an experiment you are asked to flip a coin, roll a number cube, and then flip another coin. What is P(2\; \text{heads and an even number}) P ( 2 heads and an even number ) ?

1/8

Police use the formula s=\sqrt{24d} s = 24 d to estimate the speed of a vehicle after leaving skid marks on the road. If s represents the speed of the vehicle in miles per hour and d represents the length in feet of the skid mark, approximately how long were the skid marks if the car was traveling 50 mph?

104 feet

The magnitude of earthquakes is measured on a logarithmic scale called the Richter scale. The explosive power of bombs is often measured on a linear scale based on the equivalent amount of TNT. The Richter scale is compared to the TNT-equivalent scale in the following table. The relationship between Richter magnitude, M, of an earthquake and the equivalent explosive power in tons of TNT, t, is given by the formula M=\frac{2}{3}\log_{10}t+3.2 M = 2 3 log 10 ⁡ t + 3.2 . Using this formula, what is the explosive power of a 9.2 magnitude earthquake in tons of TNT?

10^9

Jax is playing a game called Sweeps. To play this game, Jax rolls 5 six-sided number cubes. He has three chances to roll some or all of the cubes. His goal is to get "5-of-a-kind," which is called a "Sweep" and is worth the most points. Jax's first roll results in the following outcome:

11/36

60.75, 40.5, 27, 18, __ Which of the following numbers comes next in the sequence above?

12

A deck of playing cards contains 52 cards equally divided into four different suits (Spades, Diamonds, Clubs, and Hearts).

16/52

Evaluate

15

Suppose that the box has a volume of 4x^3+22x^2+24x 4 x 3 + 22 x 2 + 24 x cubic inches, and that its height is 2x 2 x inches. Use the formula V=Bh V = B h , where B B represents the area of the base and h h represents height, to derive a polynomial expression for the area of the base, B B .

2x^2+11x+12

Factor the cubic polynomial completely. 6x^3+15x^2-36x

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

Suppose you mix-up the cards below and choose one without looking. What is the probability of selecting neither "E" nor "G"?

4/7

Which equation describes a parabola?

6y^2 +11x - 13y = -1

The weight of a group of sixteen year olds is normally distributed with a mean of 140 and a standard deviation of 15. What is the probability that a sixteen year old chosen at random from this group has a weight between 110 and 170?

95%

Edward is playing a board game called Real Estate Bubble with his brother. It is his turn to roll the two number cubes. If the sum is 8, Edward will move his game piece to the penalty box. If the sum is 5, Edward will have to pay the property owner $2,000 of game money. What is the probability that he will NOT roll a sum of 8 or a sum of 5?

75%

What are the first two terms of the function f(x)=2x^2+1 f ( x ) = 2 x 2 + 1 given x_0=2 x 0 = 2 ?

9,19

Classify this function by type. j(x)=-3x^2

Polynomial

Choose the type of statistical study this statement defines: A study in which the researcher chooses a representative group of a population to learn about a particular characteristic of the population.

Sample Survey

Raul generated the graph below when he was asked to compare the two logarithmic functions

The graph of y_1 extends farther to the left than the graph of y_2 . Where defined, the graph of y_1 is always above the graph of y_2 . It looks like the graphs approach each other for large values of x.

Lou works in the quality control department for a company that manufactures 8,000 widgets every day. His job is to determine the percentage of defective widgets being produced by the company. Each day Lou randomly selects 500 widgets from the production line to check for defects. On Monday Lou found 12 defective widgets in his sample. Which statement is true?

The population parameter can be estimated as 2.4%, but there will be a margin of error.

This equation and graph represent two different functions. f(x)=2\cdot3^x-2

The rate of change from x=0 to x=1 is approximately the same for both functions.

Sarah is comparing two values. The first is \sqrt{49}-2 49 − 2 . The second is |-3+4i| | − 3 + 4 i | . What is true of these values?

The two values are equal.

The graph represents an exponential function. Which statement accurately describes the function?

The x-intercept of the graph is (2,0).

Define the domain of the inverse function of y=\frac{(x+3)}{4} y = ( x + 3 ) 4 .

all real numbers except x=3

Which graph in the diagram is the graph of f(x)=|x+5| f ( x ) = | x + 5 | ? cant use graph just follow the answer

graph b

In which quadrants will the parts of the graph of f(x)=-\frac{3}{x} f ( x ) = − 3 x lie?

ii and iv

What is the equation for the vertical asymptote of f(x)=\frac{x-4}{x^2-16} f ( x ) = x − 4 x 2 − 16 ? If there is no vertical asymptote, select None. The equation for the vertical asymptote is:

x=-4

Write the equation in standard form and classify the conic section it defines.

(x-7)^2+(y+6)^2= -4 ellipse

A certain type of wood weighs an average of 60 pounds per cubic foot with a standard deviation of 0.75 pounds. A researcher finds a tree that appears to be of this same species, but it is found in a location where the species does not normally grow. The researcher decides to weigh a cubic foot to see if it may be of this species. The sample she takes weighs 62.25 pounds. If it is the type of species she thinks it is, what is the probability that the sample would weigh 62.25 pounds or more? Use the empirical rule to approximate. Probability =

0.15%

Mia is staring at a bag of miniature chocolate bars. The bag contains 5 choco-bursts, 3 choco-berrys, and 2 choco-chunks. Her favorite is the choco-chunk bars. She randomly selects one bar from the bag and eats it. Then she randomly selects a second bar to eat. Which statement below is NOT true about Mia's selection of 2 choco-chunk bars?

The probability of selecting 2 choco-chunk bars is \tfrac{1}{50}

A rock is thrown into the air from 5 feet above ground at an initial velocity of 64 feet per seond. The height of the rock, h h , at any time t t seconds can be determined by the function h(t)=-16t^2+64t+5 h ( t ) = − 16 t 2 + 64 t + 5 . Carl says that he can tell when the rock will reach a height of 50 feet. Marco says that he can tell when the rock will reach a height of 80 feet. Each uses the quadratic formula to calculate their answers. A portion of their calculations are shown below. Carl: t=\frac{-64\sqrt{1216}}{-32}\approx\frac{-64\pm34.9}{-32} t = − 64 1216 − 32 ≈ − 64 ± 34.9 − 32 Marco: t=\frac{-64\sqrt{-704}}{-32}\approx\frac{-64\pm26.5i}{-32} t = − 64 − 704 − 32 ≈ − 64 ± 26.5 i − 32 What can you conclude about the times at which the rock will reach the heights that Carl and Marco are calculating?

The rock will reach a height of 50 feet at t\approx 0.9 seconds and t\approx 3.10 seconds. The rock will not reach a height of 80 feet since t is an imaginary number resulting in no real solutions (times).

The upper branch of a hyperbola centered at the origin is defined by the equation y=a\sqrt{\frac{x^2}{b^2}+1} y = a x 2 b 2 + 1 , with a being a positive constant. A second function, a parabola, is defined by the equation y=ax^2 y = a x 2 . Which statement is true for BOTH the hyperbola and the parabola?

The y-intercept is located at (0,a)

Given the polynomial expression (2t-k)^5 ( 2 t − k ) 5 , use Pascal's Triangle to create the first three terms of the binomial expansion in standard form. The first three terms in the expansion of the expression (2t-k)^5 ( 2 t − k ) 5 in standard form are:

\left(32t^5\right)-\left(80t^4k\right)+\left(80t^3k^2\right)+...

Rewrite the rational expression as one rational term, reducing all common factors. Multiply:

a^3/2b

Given the function f(x)=|x| f ( x ) = | x | , match the description of the transformed graph with the function. The graph is shifted up 1.5 units.

f(x)=|x|+1.5

Which of these statements is true?

x^{3/2}=x\sqrt{x} for all x\ge0

Which polynomial function best matches with this category describing its end behavior?

p(x)=-4x^4+4x^2-3

Solve the system of equations by substitution.

(5, 1, 3)

Given the equation of a circle shown below, determine the center and the radius of the circle. x^2+y^2-2x+6y-15=0

Center = (1,-3) radius = 5 units

Anna is working at a summer camp. Of the campers in her section, a total of 80 have signed up for swimming, and a total of 65 have signed up for canoeing; 32 signed up for both. There are 12 students who are not doing either water sport. Anna organized the information she had in a two-way table.

0.26

Jamie wants to know how much the students in her school sleep on average. She conducts a random survey of 45 students from the 722 that attend her school. She finds that they sleep an average of 7.7 hours per night with a standard deviation of 0.9 hours. Which is the approximate margin of error for a 95% confidence level?

0.268

In a lucky draw, the probability of winning a prize is 0.25 and that of winning the first prize is 0.15. What is the probability that John wins the first prize, given that he wins a prize?

0.60

A certain type of male gecko has lengths that are normally distributed with a mean of 8 centimeters and a standard deviation of 1 centimeter. What percent of all male geckos of this species will measure between 9 and 10 centimeters according to this distribution?

13.5%

When subtracting the rational expressions shown below, Simone used 12x^2y 12 x 2 y as as the common denominator. \frac{5}{3x^2y}-\frac{1}{4xy} 5 3 x 2 y − 1 4 x y If Simone does all of her calculations correctly, what will be the numerator of the answer?

20-3x

Four students, Dawn, Charles, Kesha, and Dionne, tried to use graphing to solve the polynomial equation: x^2+2x-1=-x^2-2x+5 x 2 + 2 x − 1 = − x 2 − 2 x + 5 All four students agreed that they should use the method of graphing both sides of the polynomial on one graph as shown here.

Dionne says the solutions are -3 and 1.

Classify this function by type. f(x)=2\left(3\right)^{-x}

Exponential

Maggie is conducting a study on the attitudes of young adults, ages 18 - 25, about the no-smoking laws in her state. Which of the following strategies would introduce the least amount of bias into her study?

Maggie chooses a sample at a local mall by surveying every 5th person between the ages of 18 and 25 who walks by.

Consider the system of equations. \\3x-3y=10\\2x-2y=15 3 x − 3 y = 10 2 x − 2 y = 15 Choose the statement that describes this system of equations.

No solution to the system of equations.

What is the value of i^4 ?

None of the listed answers are correct

Choose the type of statistical study this statement defines: A study in which the researcher measures characteristics of members of a population without influencing or modifying these characteristics.

Observational Study

Look at the graph of f(x)=\tan x f ( x ) = tan ⁡ x shown below.

Period: \pi Zeros: \left\{x\;{:}\;x=k\pi \right\} where k is an integer.

For the function description below, select the function family to which it belongs. g(x) g ( x ) has asymptotes at every multiple of 5 units and an identical pattern of behavior between asymptotes. g(x) g ( x ) is a:

Periodic Function

Which of these functions has a graph containing the following points?

f(x) = x^2/x-2

Given the function f(x)=|x| f ( x ) = | x | , match the description of the transformed graph with the function. The graph is vertically stretched, shifted 3 units to the right and up 2 units.

f(x)=|x-3|+2

Which function is the inverse of f(x)=\frac{2x}{3}-6 f ( x ) = 2 x 3 − 6 ?

f^-1 (x)=2x/3 -6

Two functions are shown below. One shows a graph of f(t) f ( t ) and the other shows an equation for g(t) g ( t ) .

g(t)

Which function is best represented by the graph shown? graph cant be shown just follow the answers

g(x)= 1/3|x|

Which polynomial function best matches with this category describing its end behavior?

p(x) = 2x^5 + 8

Logarithmic functions are used for relations that involve large ranges of numbers that continually increase, although at a slower and slower rate. The effect of the logarithmic expression brings the range down to a smaller range. Which of the following relations could be represented by a logarithmic function?

the brightness of stars as related to the distance of the stars to the telescope

Consider one of the equations in the system of equations, y=4x^5+8x^4... y = 4 x 5 + 8 x 4 . . . What is the maximum amount of solutions this system can have if the other equation is linear?

three

Simplify the rational expression.

x + 49/2x

Which answer is a valid solution for the equation \frac{-3}{x^2-1}=-2x+3 − 3 x 2 − 1 = − 2 x + 3 ?

x=-\frac{1}{2}

Write the solution to the following equation as a logarithm, and then evaluate the solution. Round your answer to the nearest thousandth. 7\cdot e^{4x}=21

x=in3/4 ~ 0.275

Find the standard equation for the ellipse, using the given characteristics. verticies: ; foci:

x^2/4 - y^2/36 = 1

Write the product as a polynomial in standard form

x^3 - 5x^2 - 26x + 120

Which rational function is best represented by the graph below?

y= 2/x^2

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. when x = - 11 and z = 4. Find y when x = 2 and z = - 8.

y= 9x/z ; -9/4

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

On Sia's first birthday, her uncle gave her $25. For every subsequent birthday, he gives her $15 more than the previous year. What will Sia's gift be on her 21st birthday? What is the total amount Sia's has received from her uncle through her 21st birthday?

21st birthday: $325, Total amount: $3675

Simplify.

21x^3 - 8x^2 + 14x - 36 ------------------------- 36x^2

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.

24 watts.

Rewrite the expression 3i(2-i^2+i^3) 3 i ( 2 − i 2 + i 3 ) as a complex number in the form a+bi a + b i .

3+9i

In your state, 70% of high school students graduate high school, 30% of high school graduates go to college, and 15% of those who go to college attend a private school. What is the percent chance that a student entering high school will end up going to a private college?

3.15%

Marco has been saving his loose change for the past month. When Marco took his change to the bank he received $11.42. He knows he had 83 coins in all. There were 18 nickels, 7 pennies, and the rest were quarters and dimes. To find out the number of quarters he had, Marco set up and solved the system of equations shown below. How many quarters did Marco have?

31

The diagram below shows a pencil and its image after passing through a lens. The distance from the pencil to the lens is shown as s_1 s 1 , and the distance from the lens to the image of the pencil is s_2 s 2 . The formula for determining the focal length f f of a simple lens is

6 inches

The average monthly temperature for a city in Colorado can be modeled using the sinusoidal function f(m)=-23\cos\left(\tfrac{\pi m}{6}\right)+65 f ( m ) = − 23 cos ⁡ ( π m 6 ) + 65 , where f(m) f ( m ) represents the average monthly temperature in ^\circ \text{F} ∘ F , and m m represents the month. (For January, m=1 m = 1 , and for December, m=12 m = 12 .) Using this function, which of these would be an accurate prediction for the average monthly temperature during April in this city in Colorado?

76 degrees f

Consider the function f(x)=5\sin\left(\tfrac{\pi}{2}(x+7)\right)-3 f ( x ) = 5 sin ⁡ ( π 2 ( x + 7 ) ) − 3 , where x x is measured in radians. Identify the function's amplitude, period, and midline.

Amplitude: 5 Period: 4 Equation of Midline: y= -3

Look at the following graph of a function f(x)=\log x f ( x ) = log ⁡ x .

As x gets closer to the vertical asymptote x=0, f(x)approaches -\infty.

Ashley used synthetic division to determine that \frac{x^3-x^2-11x-6}{x+2} x 3 − x 2 − 11 x − 6 x + 2 is equal to x^2+x-9-\frac{24}{x+2} x 2 + x − 9 − 24 x + 2 . Which of the following correctly explains whether Ashley is correct or incorrect?

Ashley is incorrect because she incorrectly used synthetic division. She should have used LaTeX: x=-2 as a root.

Isabella used her graphing calculator to generate the following table for the two logarithmic functions y_1=3\log(x-4)+5 y 1 = 3 log ⁡ ( x − 4 ) + 5 and y_2=\log(x-4)+5

Both functions are undefined for values of x less than or equal to 4; for values of x greater than 4, but less than 5, function y_2 is greater than function y_1 ; for the value of 5, the two functions are equal; for values of x greater than 5, function y_1 is greater than function y_2 .

The parabola y=f(x) y = f ( x ) and the line y=g(x) y = g ( x ) are shown on the graph below.

Regions 3 and 5

Which statement below is NOT true about the trigonometric ratios sine and cosine?

Sine and cosine values for an angle \theta can be negative only if \theta<0 .

Each of the three points of intersection (L, M, L , M , and N N ) formed by the lines shown on the graph represents a solution to one of the systems of linear equations below. For each pair of equations, enter the letter of its corresponding solution point.

System A: L System B: N System C: M

On a test, Caleb solved the equation \sqrt{x+2}=x x + 2 = x . He wrote his solutions, 2 and -1, in the answer blank.

The correct solution is 2; -1 is an extraneous solution.

Consider the polynomial function p(x)=3x^4-11x^3-4x^2 p ( x ) = 3 x 4 − 11 x 3 − 4 x 2 . Which statement is NOT true about this function?

The end behaviors of the graph of This answer is set as correct are in the same direction.

Let f(x)=x^4-6x^3-2x^2+12x+3 f ( x ) = x 4 − 6 x 3 − 2 x 2 + 12 x + 3 and g(x)=x-6 g ( x ) = x − 6 . Which of the following correctly explains how the remainder of \frac{f(x)}{g(x)} f ( x ) g ( x ) compares to the value of f\left(6\right) f ( 6 ) ?

The value of f(6) is equal to the remainder of \frac{f\left(x\right)}{g(x)} because the product of the quotient and g(6) is 0.

Shelly is graphing a parabola with focus (5,-2) ( 5 , − 2 ) and directrix, x=12 x = 12 . At what ordered pair should she plot the vertex of the parabola and in which direction will the parabola open?

The vertex of the parabola is (8.5, -2) and the parabola will open left

Jamal is going to add the rational expressions shown below. \frac{x+3}{x-4}+\frac{5}{x} x + 3 x − 4 + 5 x He knows that when adding or subtracting rational expressions he must first determine a common denominator. What should he use for his common denominator?

This answer is set as correct

A car is driving at a constant speed around a circular track with a radius of 2 miles. The circle representing the track is centered at the origin of a standard x-y coordinate system, with positive x to the right and positive y upward. The equation representing the value of x, in miles, is x=-2\sin\left(\tfrac{2\pi t}{6}\right) x = − 2 sin ⁡ ( 2 π t 6 ) , using radians and time t in minutes. A plot of the car's speed in the y-direction is shown in the graph; positive speed represents motion in the +y + y direction, and negative speed represents motion in the -y − y direction.

y=+2 ; counterclockwise