Praxis Core: Power Practice

Which of the following statements is/are true? Select all that apply. a. The square root of a rational number must be irrational. b. The quotient of two nonzero rational numbers can be an irrational number. c. The product of two irrational numbers can be a rational number. d. The sum of an irrational number and a rational number must be an irrational number. e. The quotient of two irrational numbers can be irrational.

c, d, and e

Which of the following fractions is/are between 1/5 and 1/8. Indicate all that apply. a. 1/4 b. 1/3 c. 1/7 d. 2/7 e. 3/16

c. 1/7 and e. 3/16

Which of the following is equal to √500? a. 50 b. 10√50 c. 10√5 d. 50√10 e. 5√10

c. 10√5

The height of a scuba training pool in the shape of a right circular cylinder is three times the diameter of the base. If the diameter of the base of the cylinder is 60 feet, what is its volume? a. 10,800π cubic feet b. 54,000π cubic feet c. 162,000π cubic feet d. 648,000π cubic feet e. 1,944,000π cubic feet

c. 162,000π cubic feet

Jessica has 3 skirts, 4 shirts, and 2 hats. How many different combinations of skirts, shirts, and hats can she wear? a. 7 b. 14 c. 24 d. 28 e. 32

c. 24

Tom needs to buy paint so that he can paint the emblem on the basketball court. The circular emblem has a diameter of 12 feet. If paint cans come in quarts, and it takes 1 quart to paint 50 square feet, how many quarts of paint will Tom have to buy? Use 3.14 for p. a. 1 b. 2 c. 3 d. 4 e. 5

c. 3

Which of the following is a reasonable estimate for the height of the first hill of a new extreme roller coaster? a. 2,000 mm b. 8 m c. 300 ft. d. 2.0 km e. 5 yards

c. 300 ft.

Neil digitally records birthday parties and charges $120 for the recording. His weekly overhead expenses amount to $390, and he spends $30 on supplies for each recording. How many birthday parties must Neil record each week before he breaks even? a. 3 b. 4 c. 5 d. 10 e. 50

c. 5

John must rent vans to take the children from his summer camp on a field trip. There are 34 children, 6 counselors, and 11 assistants who will be going on the trip. If each van can accommodate 9 people, how many vans must John rent? a. 9 b. 51 c. 6 d. 5 e. 7

c. 6

Mary has exactly 1,560 hours until her vacation begins. How many days are there before her vacation begins? a. 30 b. 50 c. 65 d. 75 e. 37,440

c. 65

The area of Melissa's rectangular garden is 330 square feet. The width of the garden is 15 feet. How many feet of fence does Melissa need to buy to surround the entire garden? a. 20 feet b. 34 feet c. 74 feet d. 85 feet e. 94 feet

c. 74 feet

Jessica received grades of 85, 90, 70, 85, and 100 on her math tests this semester. What grade will she receive in math for the semester? a. 70 b. 85 c. 86 d. 90 e. 100

c. 86

Which of the following collections of data, if any, has/have a median and a mean of 26? I. 26, 26, 0, 26, 26 II. -22, 98, -22, 98, -22 III. 26, 26, 26, 26 a. I only b. II only c. III only d. I and II e. I, II, and III

c. III only

. Which of the following statements is/are true? Select all that apply. a. All rectangles are rhombi. b. There is a rectangle that is not a parallelogram. c. Some rhombi are not squares. d. A parallelogram is a square. e. All squares are rectangles.

c. and e.

. Which of the following is the solution of this system of equations? ⎧ −x + 3y = −4 −x + y = 6 ⎨2x - 3y = 21 3y + 2x = 27 ⎩ a. x = -__3 2 , y = -8 b. x = 0, y = -7 c. x = 12, y = 1 d. x = 0, y = 9 e. no solution

c. x = 12, y = 1

. Solve the equation: 9 - x = -2(2x - 3) a. -6 b. -4 c. -3 d. -1 e. 0

d. -1

Patrick has $1,860 saved up from his past five birthdays. He wants to allot himself $75 per week for social activities and $40 per week for gas and food, and wants to keep $400 in the account to avoid monthly maintenance fees. Which of the following inequalities can be used to determine x as the number of weeks he can continue to withdraw from the account? a. 115x + 1,860 ≥ 400 b. 115 + 1,860x ≥ 400 c. 75x + 1,860 ≤ 400 d. -115x + 1,860 ≥ 400 e. 1,860 ≤ 400 + 115x

d. -115x + 1,860 ≥ 400

Which of the following is equivalent to 30√24/ 6√3 ? a. 5√21 b. 20√3 c. 5√2 d. 10√2 e. 20

d. 10√2

On an amusement park map, 1 inch corresponds to 750 feet. If the length of the path from the Looper Dooper Coaster to the Over the Falls Flume Ride on the map is 3.8 inches, what is the actual distance between these amusement rides? a. 197.4 feet b. 753.8 feet c. 1,508 feet d. 2,850 feet e. cannot determine from the given information

d. 2,850 feet

Nathan spent $1,175 on equipment needed to start a power-washing business. For each deck or fence he power-washes, he earns $50, but it costs $6.50 in gas for each job. Determine the number of decks or fences he must powerwash to break even. a. 21 b. 24 c. 27 d. 28 e. 54

d. 28

The radius of the base of circular cylindrical holding tank is 8 times the radius of the base of a circular cylindrical pipe that empties into it. If they have the same length, say L feet, the volume of the tank is how many times the volume of the pipe? a. 4 b. 8 c. 16 d. 64 e. 512

d. 64

The top of a giant gumball machine is a spherical glass globe with a diameter of 3 feet. What is the volume of the tank in cubic inches? a. 1,296π cubic inches b. 1,944π cubic inches c. 5,184π cubic inches d. 7,776π cubic inches e. 62,208π cubic inches

d. 7,776π cubic inches

Which of the following is equivalent to the expression xy · yzx5? a. 5x2y2z b. x5y2z c. 12xyz d. x6y2z e. x6y6z5

d. x6y2z

If the triangle ABC with vertices A(3,-5), B(-4,4), and C(-6,3) is reflected over the line y = -1, what are the coordinates of the image of vertex C? a. (3,-6) b. (4,-5) c. (4,3) d. (6,-3) e. (-6,-5)

e. (-6, -5)

Jan and her sister entered a raffle at the football game. Jan put her name on 3 tickets, and her sister put her name on 5 tickets. If there are 100 total tickets and only one winner, what are the chances that Jan or her sister will win the raffle? a. 5.0 b. 0.50 c. 0.005 d. 0.8 e. 0.08

e. 0.08

Six students are running for class president. John has a 1 8 chance of winning and is half as likely to win as Mike. Kelly has the same chance of winning as Mike. Julie, Kelvin, and Roger all have the same chance of winning. What chance does Kelvin have of winning? a.1/2 b. 1/3 c. 1/4 d. 3/8 e.1/8

e. 1/8

A rose garden on a square plot of land has an open wooden fence that is 320 feet long around its perimeter. What is the approximate length of the diagonal of this plot of ground to the nearest foot? a. 80 feet b. 226 feet c. 6,400 feet d. 139 feet e. 113 feet

e. 113 feet

Ellen's square kitchen has a perimeter of 48 feet. What is the area of the kitchen? a. 12 square feet b. 12 feet c. 24 square feet d. 560 square feet e. 144 square feet

e. 144 square feet

The ages of the starting lineup for the New York Yankees are as follows: 26, 29, 35, 29, 22, 31, 35, 21, 27 What is the median age of the Yankees' starting lineup? a. 21 b. 35 c. 14 d. 28.5 e. 29

e. 29

Nella wants to buy wood chips to cover the play area in her backyard. The area is 12 feet long and 6 feet wide. She wants the wood chips to be 3 inches deep. How many cubic inches of wood chips does Nella need to buy? a. 216 cubic inches b. 500 cubic inches c. 2,160 cubic inches d. 21,160 cubic inches e. 31,104 cubic inches

e. 31,104 cubic inches

Given the equation y = 7 + 3(2x − 2), what is the value of y when x = 6? a. 14 b. 21 c. 25 d. 35 e. 37

e. 37

A factory operates 15 machines that each make between 90 and 120 tennis balls per minute. Which of the following could be the number of tennis balls produced in an hour if all 15 machines are working at the same time? a. 900 b. 1,200 c. 9,000 d. 28,000 e. 90,000

e. 90,000

Which of the following numerical expressions is an irrational number? a. √8 × √2 b. 125/√5 c. (√21)2 d. 2 - √81 e. √169 - 49

e. √169 - 49

Which of the following quadratic equations has imaginary solutions? Select all that apply. a. 6x2 - 42 = 0 b. 3x2 + x + 8 = 0 c. 4x2 + 20 = 0 d. -8x2 + 40x = 0 e. x2 + 11x + 4 = 0

b and c

Jackie's bank balances were $20 on Monday, $0 on Tuesday, $45 on Wednesday, and $25 on Thursday. What was Jackie's mean balance for the week? a. $20.00 b. $22.50 c. $25.00 d. $25.50 e. $30.00

b. $22.50

The Andersons went out to dinner Saturday night and had a bill of $190.00. They gave the server a 25% tip. How much money did the Andersons tip their server? a. $19 b. $47.50 c. $38 d. $38.50 e. $47

b. $47.50

. Let m(x) = -5x + 4x3 - 3x4 and n(x) = 6x3 - 2x4. Which of the following is equivalent to 4m(x) - 3n(x)? a. -x(5x3 + 14x2 + 20) b. -2x(3x3 + x2 + 10) c. -2x(9x3 + x2 + 10) d. -2x(9x3 - 17x2 + 10) e. -x(x3 + 2x2 + 5)

b. -2x(3x3 + x2 + 10)

Consider the following set of numbers: {6, 16, 26, 36, 46, 56, 66, 108} If a number is selected at random from this set, what is the probability of selecting a number that is divisible by 6 and 9? a. 0.125 b. 0.25 c. 0.50 d. 0.75 e. 1.00

b. 0.25

Out of 100 workers polled at a local factory, 75 said they would favor being offered a course in management. If there are 25,000 workers, how many would you expect to favor being offered such a course? a. 1,875 b. 18,750 c. 15,000 d. 16,000 e. 19,000

b. 18,750

Jake rents a car for $200 each month, which includes 1,000 miles for the month. He is charged an additional $0.55 for each mile driven over 1,000. If x represents the total mileage Jake drives each month, and if he always drives over 1,000 miles per month, which of the following expressions can be used to calculate his total monthly car rental bill? a. 200 + 0.55x b. 200 + 0.55(x - 1,000) c. 200x + 0.55 d. 200 × 0.55x e. 200x + 0.55(x - 1,000)

b. 200 + 0.55(x - 1,000)

Alexa is making costumes for the school play. She needs 15 yards of fabric to make 3 costumes. How many yards of fabric would she need to make 8 costumes? a. 30 yards b. 40 yards c. 45 yards d. 50 yards e. 60 yards

b. 40 yards

Let y = f(x) be a given function and suppose the point (2,-3) lies on its graph. Consider the translation of this function given by g(x) = f(x + 4) - 1. To what point would the given point correspond on the graph of g(x)?

(-2, -4)

Assume the point (-1,6) lies on the graph of the function y = f(x). Consider the translation of this function given by g(x) = f(x - 7) + 2. To what point would the given point correspond on the graph of g(x)?

(6, 8)

Write the following product as a decimal: (30.5 × 104) × (1.2 × 10-7)

0.0366

. Write the following expression as a single decimal: (2.7 × 10-3) ÷ (3.6 × 10-3).

0.75

Tanya can pack 4 boxes of fragile dishware in 25 minutes. How many minutes would it take her to pack 28 boxes of fragile dishware?

175 minutes

A dog boarding facility devotes 4/5 of its time to dog grooming services. Of this time, 7/24 is spent on bathing dogs. What fraction of its dog grooming time does this facility NOT devote to bathing dogs?

23/30

As of 2016, the yearly average birth rate in India is approximately 19.3 births for every 1,000 people. Determine the total number of births expected in one year if India's population is 1.327 billion.

25,611,100

Brett can wash 2 full-length patio doors in 55 minutes. How many minutes would it take him to wash 17 full-length patio doors?

467.5 minutes

The group exercise classes at a local YMCA begin at 7 a.m. and the last class ends at 3:56 p.m. There are 10 classes offered with 4 minutes between classes. What is the duration of each class, in minutes?

50 minutes

Suppose a = -5, b = -2, and c = -3. Evaluate 2ac - abc.

60

John, Mike, and Dillon are painting a fence. John paints 1/4 of the fence and Mike paints 2/5 of the fence. How much of the fence is left to paint for Dillon?

7/20

Corn is being poured out of a silo into a pile in the form of a right circular cone. If the height of the final pile is 12 feet and the volume is 324p cubic feet, what is the radius of the circular base (in feet)?

9 feet

. For which of the following values of a does the trinomial x2 + ax + 24 factor? Select all that apply. a. 25 b. −10 c. −11 d. 11 e. 2

a, b, c, d

Consider the set of whole numbers {6, 12, 18, 24, . . . }. Select all of the following statements that are true about the members of this set. a. None of the numbers are prime. b. All the numbers are divisible by 4. c. None of the numbers are odd. d. All the numbers are multiples of 6. e. All the numbers are factors of 6.

a, c, and e

Which of the following are factors of the number 23 × 32 × 5? Select all that apply. a. 4 b. 7 c. 12 d. 50 e. 72

a, c, and e

Jason was asked to choose a marble from a bag. If he chose a red marble, he would win a prize. The bag contained 20 blue marbles, 20 black marbles, 20 green marbles, 18 yellow marbles, and 2 red marbles. Which of the following decimals shows Jason's chances of choosing a red marble? a. 0.025 b. 0.25 c. 0.08 d. 0.8 e. 2.5

a. 0.025

Alec needs 432 inches of molding to put along the ceiling of his dining room. How many yards of molding should he buy? a. 12 b. 43.2 c. 15,552 d. 36 e. 440

a. 12

The formula for the surface area of a right circular cylinder (including the areas of the two bases) is given by SA = 2pr2 + 2prh, where r is the radius of the base and h is the height of the cylinder. If the height equals 3 times the radius and the surface area is 200p square feet, which of the following is the radius? a. 5 feet b. √50 feet c. 25 feet d. 15 feet e. 5p feet

a. 5 feet

A family goes to an apple orchard to pick apples for autumn baking. The cost for the excursion is a $7.50 entrance fee plus $5.00 per pound of apples. If they want to spend no more than $50, which of the following inequalities can be used to determine the number of pounds of apples, x, they can purchase? a. 5.00x + 7.50 ≤ 50.00 b. 5.00 + 7.50x ≤ 50.00 c. 5.00x + 7.50 ≥ 50.00 d. 5.00 + 7.50x ≥ 50.00 e. 12.50x ≤ 50.00

a. 5.00x + 7.50 ≤ 50.00

Which of the following is equivalent to 6 × 7 + 6 × 9? a. 6(7 + 9) b. 6 + 7 × 6 + 9 c. (6 × 7) + 9 d. (6 × 7) × (6 × 9) e. 6(7 × 9)

a. 6(7 + 9)

Aidan and James sell a total of 48 magazines. If Aidan sells 3 times more magazines than James, how many magazines does James sell?

12

A great room measures 18 feet by 22 feet and the ceiling is 10 feet high. One gallon of paint can be used to apply one coat of paint to 300 square feet of wall or ceiling space. How many gallons of paint will it take to paint all but the floor of the room if three coats of paint must be applied? Round your answer to the nearest tenth of a foot.

12 gallons

Pamela works a 40-hour week as a computer technician at a local library. She earns a base salary of $15 per hour, plus double this amount for any hour she works beyond 40 in a week. Her goal is to earn $960 each week prior to taxes. How many hours beyond the initial 40 must she work in a week to attain her goal?

12 hours