e2020

According to a poll, 56% of voters support funding a new community center. A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center. If being in favor of the center is a success, what is the probability of a success for this binomial experiment?

0.56

For a standard normal distribution, find the approximate value of P(-0.78<z<1.16). Use the portion of the standard normal table below to help answer the question.

0.6593

What is the sum of the first seven geometric series?

16,383

The lengths of a particular snake are approximately normally distributed with a given mean 15 in and 0.8 in. What percentage of the snakes are longer than 16.6 in?

2.5%

Which graph is an example of a function whose parent graph is of the form y = sqrt x?

A.

Three trigonometric functions for a given angle are shown below. What are the coordinates of point (x, y) on the terminal ray of angle 0, assuming that the values above were not simplified?

A. (-5,12)

The constraints of a problem are graphed below. What are the vertices of the feasible region?

A. (0, 0), (0, 15), (20, 25), (40, 0)

The point P(x,y) is on the terminal ray of angle theta. If theta is between pi radians and 3pi/2 radians and csc theta = -5/2, what are the coordinates of P(x,y)?

A. (sqrt -21, -2)

What is the exact value of cot(3pi/4)?

A. -1

Which of the following could be the measure of the angle below? a. -180 b. -120 c. 140 d. 510

A. -180

What is the solution to log5(x+30)=3?

A. -95

When e = 4, f = 2, and g = 8. If e varies jointly with f and g, what is the constant of variation?

A. 1/4

What is the approximate length of arc s on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth.

A. 14.1

The amount of time it takes p people to paint d doors varies directly with the number of doors and inversely with the number of people. Four people can paint 10 doors in 2 hours. How many people will it take to paint 25 doors in 5 hours?

A. 4

A botanist is using two types of plants for an experiment. She writes inequalities to model the constraints on the number of each type of plant she can use. She uses linear programming to find the vertex of the feasible region that results in the minimum value, in dollars, of the cost function. If that vertex is (5, 39), what do the coordinates represent?

A. Buying five of one type of plant and 39 of the other type of plant results in the lowest cost.

The graph below is used by company 2 to show the average monthly electric cost based on the electricity provider. How could the graph be redrawn so that the difference in monthly electric cost does not appear as great?

A. The scale on the y-axis could be changed to 0-150.

Consider the relationship below, given pi/2 < 0 < pi. Sin^2 0 + cos^2 0 +1. Which of the following best explains how this relationship and the value of sin 0 can be used to find the other trigonometric values?

A. The values of sin 0 and cos 0 represent the legs of a right triangle with a hypotenuse of 1, therefore, solving for cos 0 finds the unknown leg, and then all other trigonometric values can be found.

How does the value of log2^100 compare with the value of log6^20?

A. Value of log2^100 is about 4 times the value of log6^20.

A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation, k?

A. xz/y

Which of the following could be the equation of the function below?

A. y = -3sin(2(x+pi))+2

The graph of y = |x| is transformed as shown in the graph below. Which equation represents the transformed function?

A. y = |1/4x|

What is the equation of the graph below? a. y=sin(x+90) b. y=cos(x+90) c. y=sin(x+45)

A. y=sin(x+90)

A company plans to sell a new type of vacuum cleaner for $280 each. The company's financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?

A. {y = 280x {y = -0.052(x-500)^2+24,000

Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? Round the answer to the nearest thousandth.

B

Which geometric series converges?

B

A lighthouse is located at (1, 2) in a coordinate system measured in miles. A sailboat starts at (-7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, -6). Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

B.

A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store has no more than 80 footballs and baseballs in stock during the month. What is the maximum profit the store can make from selling footballs and baseballs in a month?

B. $460.00

For what value of n does (1/36)^n=216?

B. - 3/2

The kinetic energy, K, of an object varies jointly with the mass of the object and the square of the velocity of the object. A 50-kg object moving at a velocity of 20 meters per second has 10,000 joules of kinetic energy. How many joules of kinetic energy does a 25-kg object moving at a velocity of 10 meters per second have?

B. 1,250 joules

The quantity y varies directly with the square of x and inversely with z. When x is 9 and z is 27, y is 6. What is the constant of variation?

B. 2

The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?

B. 20

If cos = 0.3090, which of the following represents approximate values of sin for 0 degrees<90 degrees?

B. 3.0780

What is the range of y = -3sin(x)-4

B. All real numbers -7 < y < -1

What is the domain of y = log4(x+3)?

B. All real numbers greater than -3.

How many times louder is Braylee's music than Jessica's?

B. Braylee's music is 3 times louder than Jessica's.

The quantity a varies directly with b and c and inversely with d. The quantity d is tripled. Which of the following must be true for the relationship to remain the same?

B. The product of c and b must be tripled.

The first equation in the system models the heights, h, of a falling volleyball as a function of time, t. The second equation models the heights, h, of the hands of a player jumping up to spike the ball as a function of time, t. Which statement describes the situation modeled by this system?

B. The volleyball is 14 feet above the ground at the instant the player begins her jump.

Which of the following is true about the base b of a logarithmic function?

B. b > 0 and b =/ 1

What is the simplest form of the expression below? cot(0)cos(0)/sin(0) x tan(0) / sin(0)/cos(0)tan(0)

B. cot(0)

If csc 0 = 8/7 which equation represents cot 0?

B. cot0 = sqrt15/7

Which function will have a y-intercept at -1 and an amplitude of 2?

B. f(x) = -2sin(x)-1

Which function describes the graph below? a. f(x)=6cos(x) b. f(x)=3cos(x)+3 c. f(x)=6sin(x)

B. f(x)=3cos(x)+3

A chicken farm orders bags of feed from two farmers. Store X charges $20 per bag, and store Y charges $15 per bag. The farm must obtain at least 60 bags per week to care for the chickens properly. Store Y can provide a maximum of 40 bags per week, and the farm has committed to buy at least as many bags from store X as from store Y. The chicken farm wants to minimize the cost of ordering feed. Let x represent the number of bags of feed from store X and y represent the number of bags of feed from store Y. What are the constraints for the problem?

B. x + y > 60 x > y y <40

The graph of y = |x| is transformed as shown in the graph below. Which equation represents the transformed function?

B. y = |x+3| - 2

The local community theater sold a total of 240 tickets for Saturday night's performance. They sold 180 more full-price tickets than discount tickets. Which system of equations can be used to model this situation?

B. {f+d=240 {f-d=180

Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true?

Both the means and the standard deviations of Dwayne's and Alisha's graphs must be the same.

Which ordered pair minimizes the objective function C = 60x + 85y?

C. (80, 50)

The magnitude, M, of an earthquake is defined to be M=log I/S, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a "standard" earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake?

C. 1.5

What is the value of log625^5?

C. 1/4

Sonia rolls a six-sided number cube 12 times and records if she rolls a 2. What is the number of trials for the binomial experiment?

C. 12, Sonia rolls it 12 times, so there's 12 trials.

The length of a rectangular field is 20 less than its width. The area of the field is 12,000 ft^2. What is the width of the field?

C. 120 ft

Hector needs 84 feet of fencing to enclose his rectangular garden. The length of his garden is 12 feet less than twice its width. What is the width of his garden?

C. 18 ft

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle?

C. 2.7 radians

A quantity b varies jointly with c and d and inversely with e. When b is 18, c is 4, d is 9, and e is 6. What is the constant of variation?

C. 3

A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?

C. 3

Which of the following are in the correct order from least to greatest?

C. 38, pi/4, 80, 7pi/6, 2pi

What is 270 converted to radians?

C. 3pi/2

Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Help finding her steps for finding the variance are shown below. What is the first error she made in computing the variance?

C. Emi evaluated (46-78)2 as -(32)2.

To which family does the function y = 2^x + 5 belong?

C. Exponential

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective. She decides to check several monitors and record if they are defective. Which of the following will make this process into a binomial experiment?

C. Glenda chooses to check 300 monitors.

Susan wants to make pumpkin bread and coffee cakes for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her pumpkin bread recipe uses 2 eggs and 3 cups of flour. Her coffee cake recipe uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and coffee cake loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of coffee cake Susan bakes.

C. P = 5x + 4y

The first equation in the system models the heights in feet, h, of a falling baseball as a function of time, t. The second equation models the heights in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t. Which statement describes the situation modeled by this system?

C. The height of the baseball is 35 feet at the moment the player begins to leap.

The histogram below represents the number of points Mandy scored per game. The graph makes the data appear symmetric when it is actually skewed. How can the graph be adjusted to the skew?

C. The scale on the x-axis can be increased to show the interval 25-29.

The mean of a set credit score is u = 690 and o = 14. Which statement must be true?

C. Z690 is between 2 and 3 standard deviations of the mean.

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds.

C. h = 10sin(pi/15t)+35

Which of the following shows the extraneous solution to the logarithmic equation below? log3(18x^3)-log3(2x)=log3(144)

C. x = -4

What is the solution of log2(3x-7)=3?

C. x = 5

What is the true solution to the logarithmic equation below? log2(6x)-log2(/x)=2

C. x =4/9

Which expression is equivalent to log12 x^4...

D

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3sin(pi/2(t+2))+5. Which of the following is the graph of this equation?

D.

The constraints of a problem are listed below. What are the vertices of the feasible region? 2x + 3y > 12 5x + 2y > 15 x > 0 y >0

D. (0, 15/2), (21/11, 30/11), and (6, 0)

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for $8, and nonflowering plants sell for $5. Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants. What are the vertices of the feasible region for this problem?

D. (24, 12), (36, 0)

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58%?

D. 0.79%

What is the approximate value of log6 25?

D. 1.796

The loudness, L, is measured in decibels (Db), of a sound intensity, I, measured in watts per square...

D. 110 Db

It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. If the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how many hours will it take 2 lawnmowers to cut 6 acres of grass?

D. 12

What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below?

D. 40

The graph below shows three different normal distributions. Which statement must be true?

D. Each distribution has the same mean and a different standard deviation.

How is the graph of y = -1/3x related to its parent function, y = 1/x?

D. It is horizontally compressed by a factor of 3 and reflected over the y-axis.

Dana wants to make two types of dog treats. She has 10 cups of peanut butter and 12 cups of flour. Her dog bone treat recipe uses 3 cups of peanut butter and 2 cups of flour to make one tray. A tray of her oatmeal dog treat recipe uses 1 cup of peanut butter and 4 cups of flour. She plans to sell trays of dog treats at the town festival and charge $6 for a tray of dog bone treats and $7 for a tray of oatmeal treats. Dana wants to maximize her income from selling the dog treats.

D. Let x represent the number of trays of dog bone treats made and y represent number of trays of oatmeal dog treats made.

For a standard normal distribution, which of the following expressions must always be equal to 1?

D. P(z<-a)+P(-a<z<a)+P(Z>a)

At a skills competition, a target is being lifted into the air by a cable at a constant speed. An archer standing on the ground launches an arrow toward the target. The system of equations below models the height, in feet, of the target and the arrow t seconds after it was fired. Which statement most likely describes the situation modeled by this system?

D. The arrow is fired with an initial upward velocity of 32 ft/s.

If you are given the graph of h(x)=log6x how could you graph m(x)=log6(x+3)?

D. Translate each point of the graph of h(x) 3 units left.

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute.

D. Y =10sin(pi/15t)+30

The range of which function is (2, infinity)?

D. y=5^x+2

A rectangular swimming pool has a perimeter of 96 ft. The area of the pool is 504 ft2. Which system of equations models this situation correctly?

D. {2l + 2w = 96 { lw = 504

Which normal distribution has the greatest standard deviation?

Graph C

Which statement explains whether Haruto is correct?

Haruto is corrects because the angle is coterminal with... and the reference angle is

The resting heart rates for 80 women aged 46-55 in a simple random sample are normally distributed with a mean of 71 beats per minute and a standard deviation of 6 beats per minute. Assuming a 90% confidence level (90% confidence level = z-score of 1.645), what is the margin of error for the population mean?

ME = 1.645(6)/sqrt80 = 1.1

When making a statistical inference about the mean of a normally distributed population based on a sample drawn from the population, which of the following statements is correct, all else being equal?

The 90% confidence interval is wilder than the 99% confidence interval.

The annual salaries of all employees at a financial company are normally distributed with a mean u = $34,000 and a standard deviation $4,000. What is the z-score of a company employee who makes an annual salary of $28,000?

The answer is -1.5

If the equation below is solved by graphing, which statement is true? log(6x+10)=log1/2x

The curves intersect at approximately x = 0.46

The mean game scores and standard deviations of four seasons of a football team given below? Which statement must be true?

The game scores of season 2005 have a greater speed than the game scores of season 2006.

The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 and hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2. How does the mean and median change from plot 1 to plot 2?

The mean decreases and the median remains the same.

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550. Use the portion of the standard normal table below to help answer the question.

The probability that a randomly selected student has a score between 350 and 550 is 0.5867

Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.

The probability that he got at least 2 questions correct is 0.756

The mean test scores with standard deviations of four English classes are given below. Which statement is most likely to be true?

The scores from Mrs. Rijo's class are the closest to the class mean.

The stem and leaf plot below shows the number of pages each student in a class read the previous evening.

The value of the first quartile is 13.

An angle measuring (486n) is in standard position. For which value of n will the terminal side fall along the negative portion of the x-axis?

b. n = 5

If 1/64=4^2s-1 times 16^2s+2 what is the value of s?

s = -1