ACT Math Exam 4

1. Apply the polynomial identity to rewrite x² - 100.

(x - 10)2

(x - 10)(x + 10)

(x + 10)2

X2 - 102

B. The correct solution is (x - 10)(x + 10). The expression x² - 100 is rewritten as (x - 10)(x + 10) because the value of a is x and the value of b is 10. See Lesson: Polynomials.

Explanation

B. The correct solution is (x - 10)(x + 10). The expression x² - 100 is rewritten as (x - 10)(x + 10) because the value of a is x and the value of b is 10. See Lesson: Polynomials.

2. The level of a river during a flood was 39.45 feet. After a week, the water level declined to 18.97 feet. What was the amount of decrease in feet?

20.38

20.48

21.38

21.48

B. The correct solution is 20.48 because 39.45 - 18.97 = 20.48 feet. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is 20.48 because 39.45 - 18.97 = 20.48 feet. See Lesson: Solving Real World Mathematical Problems.

3. Convert 0.5 kiloliter to milliliters.

50,000 milliliters

500,000 milliliters

5,000,000 milliliters

50,000,000 milliliters

B. The correct solution is 500,000 milliliters.

See Lesson: Standards of Measure.

Explanation

B. The correct solution is 500,000 milliliters.

See Lesson: Standards of Measure.

4. Evaluate the expression (-224) ÷ 14.

-210

-16

16

210

B. When dividing signed numbers, remember that if the dividend and divisor have different signs, the quotient is negative. Other than the sign, the process is the same as dividing whole numbers. Use the division algorithm to divide 224 by 14. See Lesson: Basic Multiplication and Division.

Explanation

B. When dividing signed numbers, remember that if the dividend and divisor have different signs, the quotient is negative. Other than the sign, the process is the same as dividing whole numbers. Use the division algorithm to divide 224 by 14. See Lesson: Basic Multiplication and Division.

5.

7.55

7.6

7.65

7.7

Explanation

6. A survey group wants to ask the daily commute time for workers at a large company who use a car to get to work. What is the sample for the survey?

Employees who work from home

Employees who drive to work daily

Employees who work for the company

Employees who drive on a highway to work daily

B. The correct solution is employees who drive to work daily because this sample represents an accurate sample from the population of all employees. See Lesson: Statistical Measures.

Explanation

B. The correct solution is employees who drive to work daily because this sample represents an accurate sample from the population of all employees. See Lesson: Statistical Measures.

7. Solve the equation for the unknown.

6

26

Explanation

8. Write 1.5 as a percent.

0.15%

1.5%

15%

150%

D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

Explanation

D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

9. Which statement about multiplication is true?

Multiplication is impossible.

Multiplication is repeated division.

Multiplication is repeated addition.

Multiplication is repeated subtraction.

C. Instead of adding the same number over and over (for example, 5 + 5 + 5 + 5 + 5 + 5), multiplication enables a more concise expression. In this example, because the expression adds 6 terms of 5, it becomes 6 x 5, or 30. See Lesson: Basic Multiplication and Division.

Explanation

C. Instead of adding the same number over and over (for example, 5 + 5 + 5 + 5 + 5 + 5), multiplication enables a more concise expression. In this example, because the expression adds 6 terms of 5, it becomes 6 x 5, or 30. See Lesson: Basic Multiplication and Division.

10. A gymnastics team has the following scores for an event: 12.3, 12.7, 14.1, 14.5, 13.8, 13.6, 14.2, 15.2, 14.8, 13.9, 15.4, 14.3. Find the mean score for the team to the nearest hundredth.

14.07

14.15

14.57

14.71

A. The correct solution is 14.07. The sum of the scores is 168.8, and the average is 14.07 for the 12 scores. See Lesson: Interpreting Graphics.

Explanation

A. The correct solution is 14.07. The sum of the scores is 168.8, and the average is 14.07 for the 12 scores. See Lesson: Interpreting Graphics.

11. Evaluate the expression 1,004 + 110.

2104

1411

1204

1114

D. The correct solution is 1,114. Use the addition algorithm or note the two numbers never have nonzero digits in the same place. This fact allows addition by inspection.

Explanation

D. The correct solution is 1,114. Use the addition algorithm or note the two numbers never have nonzero digits in the same place. This fact allows addition by inspection.

12. Solve the equation by the square root method. x² + 10 = 110

± 8

± 9

± 10

± 11

Explanation

13. Which number is not a factor of 1,155?

22

33

55

77

A. To determine whether a number is a factor of another number, divide the second number by the first number. If the quotient is whole, the first number is a factor. In this case, 1,155 is not divisible by 22. See Lesson: Factors and Multiples.

Explanation

A. To determine whether a number is a factor of another number, divide the second number by the first number. If the quotient is whole, the first number is a factor. In this case, 1,155 is not divisible by 22. See Lesson: Factors and Multiples.

14. Multiply. (2y² - 1)(y² - 3y + 5)

2y4 - 6y3 + 10y2 + 3y - 5

2y4 - 6y3 + 9y2 + 3y - 5

2y4 - 6y3 + 11y2 + 3y - 5

2y4 - 6y3 + 8y2 + 3y - 5

Explanation

15. Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)

3x3 - 6x2 + 8x + 1

3x3 - 2x2 + 8x + 1

3x3 + 6x2 + 8x + 1

3x3 + 2x2 + 8x + 1

Explanation

16. An even roll of a number cube results in +2 points, and an odd roll of a number cube is -3 points. If there are 14 even numbers and 11 odd numbers, then how many points are scored?

-61

-5

5

61

B. The correct solution is -5 because 14(2) + 11(-3) = 28+(-33) = -5 points. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is -5 because 14(2) + 11(-3) = 28+(-33) = -5 points. See Lesson: Solving Real World Mathematical Problems.

17. In a state, the highest elevation is 1,450 feet and the lowest elevation is - 80 feet. What is the difference in the elevations in feet?

1,370

1,430

1,530

1,570

C. The correct solution is 1,530 because 1,450 – (-80) = 1,450 + 80 = 1530 feet. See Lesson: Solving Real World Mathematical Problems.

Explanation

C. The correct solution is 1,530 because 1,450 – (-80) = 1,450 + 80 = 1530 feet. See Lesson: Solving Real World Mathematical Problems.

18. Solve the inequality for the unknown, 2(3x - 1) +5 ≥ 3x - 4 - 4x.

X ≥ -7

X ≥ -4

X ≥ -1

X ≥ 0

Explanation

19. Solve the system of equations. y = -2x x² + y² = 5

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

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

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

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

Explanation

20. Students were surveyed on if they liked math, social studies, or science as a subject. Describe an intersection of the events.

Students who like math or social studies

Students who like math and social studies

Students who do not like math, social studies, or science

Students who like math

B. The correct solution is students who like math and social studies because it is the intersection of two events. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

B. The correct solution is students who like math and social studies because it is the intersection of two events. See Lesson: Statistics & Probability: The Rules of Probability.

21. The land area of Colorado is about 1 x 10⁵ square miles, and the land area of Ohio is about 4 x 10⁴ square miles. How many times larger is the land area of Colorado?

2

3

4

5

B. The correct solution is 3 because the land area of Colorado is about 100,000 square miles and the land area of Ohio is about 40,000 square miles. So, the land area is about 3 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

B. The correct solution is 3 because the land area of Colorado is about 100,000 square miles and the land area of Ohio is about 40,000 square miles. So, the land area is about 3 times larger. See Lesson: Powers, Exponents, Roots, and Radicals.

22. Which percent is closest to the ratio 7 : 3?

23%

43%

73%

233%

D. To convert a ratio to a percent, divide the numbers in the ratio (noting that its equivalent fraction is 7/3) to get approximately 2.33. Then, multiply by 100%. See Lesson: Ratios, Proportions, and Percentages.

Explanation

D. To convert a ratio to a percent, divide the numbers in the ratio (noting that its equivalent fraction is 7/3) to get approximately 2.33. Then, multiply by 100%. See Lesson: Ratios, Proportions, and Percentages.

23. Divide.

Explanation

24. Identify the diameter of the circle.

Explanation

25. If a company's revenue changes from $123 million to $118 million in a month, how quickly is it increasing in a year?

–$60 million

–$5 million

$5 million

$60 million

Explanation

26. Find the circumference in centimeters of a circle with a radius of 11 centimeters. Use 3.14 for π.

3.14

6.28

34.54

69.08

D. The correct solution is 69.08 because C = 2πr ≈ (2)3.14(11) ≈ 69.08 centimeters. See Lesson: Circles.

Explanation

D. The correct solution is 69.08 because C = 2πr ≈ (2)3.14(11) ≈ 69.08 centimeters. See Lesson: Circles.

27. Write 290% as a fraction.

Explanation

28. The number 36 is what percent of 16?

31%

44%

69%

225%

D. The fraction 36/16 is 225%, meaning 36 is 225% of 16. See Lesson: Ratios, Proportions, and Percentages.

Explanation

D. The fraction 36/16 is 225%, meaning 36 is 225% of 16. See Lesson: Ratios, Proportions, and Percentages.

29. Given the coordinates for a rectangle (-4, -1), (-9, -1), (-9,-8), and (-4,-8), find the length of each side of the rectangle.

2 units and 3 units

2 units and 7 units

5 units and 3 units

5 units and 7 units

D. The correct solution is 5 units and 7 units. The difference between the x-coordinates is -4 - (-9) = 5 units, and the difference between the y-coordinates is -1 - (-8) = 7 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

D. The correct solution is 5 units and 7 units. The difference between the x-coordinates is -4 - (-9) = 5 units, and the difference between the y-coordinates is -1 - (-8) = 7 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

30. A box in the shape of a right rectangular prism has dimensions of 6 centimeters by 7 centimeters by 8 centimeters. What is the volume in cubic centimeters?

280

336

560

672

B. The correct solution is 336. Substitute the values into the formula and simplify using the order of operations, V = lwh = 6(7)(8) cubic centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The correct solution is 336. Substitute the values into the formula and simplify using the order of operations, V = lwh = 6(7)(8) cubic centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

31. A sign stating "Do Not Enter" is in the shape of a square with side lengths of 75 centimeters. What is the area in square centimeters?

150

300

5,325

5,625

D. The correct solution is 5,625. Substitute the values into the formula and simplify using the order of operations, A = s² = 75² = 5,625 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

D. The correct solution is 5,625. Substitute the values into the formula and simplify using the order of operations, A = s² = 75² = 5,625 square centimeters. See Lesson: Similarity, Right Triangles, and Trigonometry.

32. The last 8 transactions at a shoe store in dollars are 5, 39, 49, 50, 52, 35, 44, 100. What is the effect of removing the outliers on the mean and median?

The mean and median increase.

There is no effect on the mean or median.

The mean decreases, but the median does not change.

The median decreases, but the mean does not change.

C. The correct solution is the mean decreases, but the median does not change. The mean decreases from 46.75 to 44.83, but the median does not change from 46.5. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

C. The correct solution is the mean decreases, but the median does not change. The mean decreases from 46.75 to 44.83, but the median does not change from 46.5. See Lesson: Interpreting Categorical and Quantitative Data.

33. Select the figure that is translated (x + 2, y + 1).

A. The correct solution is A. The translation for the points is (x + 2, y + 1). The points of the original square, (–4, –4), (–4, 2), (2, 2), and (2, –4), become (–2, –3), (–2, 3), (4, 3), and (4, –3). See Lesson: Congruence.

Explanation

A. The correct solution is A. The translation for the points is (x + 2, y + 1). The points of the original square, (–4, –4), (–4, 2), (2, 2), and (2, –4), become (–2, –3), (–2, 3), (4, 3), and (4, –3). See Lesson: Congruence.

34. A mixture for a cake has various parts. Select the correct circle graph for the data.

Explanation

35.

Explanation

36. If Professor Markham has 127 students in her calculus course but 37 drop out because it is too difficult, how many students remain?

37

90

127

164

B. The correct solution is 90. This situation requires finding the difference between 127 and 37. Use the subtraction algorithm if necessary: 127 – 37 = 90.

See Lesson: Basic Addition and Subtraction.

Explanation

B. The correct solution is 90. This situation requires finding the difference between 127 and 37. Use the subtraction algorithm if necessary: 127 – 37 = 90.

See Lesson: Basic Addition and Subtraction.

37. Divide.

Explanation

38. The dot plot shows the results of rolling a dice for a game. Which statement is true for the dot plot?

There were 60 turns in the game.

More than half of the turns were 3 or less.

1 and 6 occurred the same number of times.

The difference between the lowest and highest frequency is 3.

A. The correct solution is there were 60 turns in the game. The sum of the results is 12 + 9 + 8 + 13 + 7 + 11, which is 60 turns. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is there were 60 turns in the game. The sum of the results is 12 + 9 + 8 + 13 + 7 + 11, which is 60 turns. See Lesson: Interpreting Categorical and Quantitative Data.

39. Solve. x³ = -8

-4

-2

2

4

B. The correct solution is -2 because the cube root of -8 is -2. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

B. The correct solution is -2 because the cube root of -8 is -2. See Lesson: Powers, Exponents, Roots, and Radicals.

40. Solve the system of equations by graphing. y = -x + 7 y = 2x - 8

D. The correct graph has the two lines intersect at (5, 2).

See Lesson: Equations with Two Variables.

Explanation

D. The correct graph has the two lines intersect at (5, 2).

See Lesson: Equations with Two Variables.

41. Simplify.

Y4

X4y4

Explanation

42. Solve the equation for c. 2a(b + c) = c

Explanation

43. There are 12 boys' and 14 girls' names in a hat. What is the probability of selecting a boy's name twice in a row without replacement?

See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

See Lesson: Statistics & Probability: The Rules of Probability.

44. Solve for the system of equations. -4x + 3y = 30 3x + 4y = 15

(3, -6)

(-3, 6)

(-3, -6)

(3, 6)

Explanation

45. Select the figure that is rotated 90° counterclockwise about the origin.

C. The correct solution is C. This is a rotation of 90° counterclockwise because the point (x, y) becomes (–y, x). See Lesson: Congruence.

Explanation

C. The correct solution is C. This is a rotation of 90° counterclockwise because the point (x, y) becomes (–y, x). See Lesson: Congruence.

46. Identify the variables from a study on cereal that is quantitative.

Fat calories

Cereal name

Manufacturer

Target audience

A. The correct solution is fat calories because this is a numerical value. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is fat calories because this is a numerical value. See Lesson: Interpreting Categorical and Quantitative Data.

47. Solve the equation by any method. x² + 4x - 15 = 0

2 ± √19

-2 ± √19

2 ± √15

-2 ± √15

Explanation

48. The volume of a hemi-sphere is cubic feet. What is the diameter in feet?

1

2

3

4

Explanation

49. Convert 1,000 fluid ounces to gallons.

7.8125 gallons

15.625 gallons

31.25 gallons

62.5 gallons

A. The correct solution is 7.8125 gallons.

See Lesson: Standards of Measure.

Explanation

A. The correct solution is 7.8125 gallons.

See Lesson: Standards of Measure.

50. Convert 6 meters to feet.

1.52 feet

1.72 feet

18.68 feet

19.68 feet

Explanation

51. Which option results in the greatest gain on an investment?

60% of gaining $5,000 and 40% of gaining $0

70% of gaining $4,500 and 30% of gaining $0

80% of gaining $4,000 and 20% of gaining $0

90% of gaining $3,500 and 10% of gaining $0

C. The correct solution is 80% of gaining $4,000 and 20% of gaining $0. The expected value is 0.80(40) =$3,200. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

C. The correct solution is 80% of gaining $4,000 and 20% of gaining $0. The expected value is 0.80(40) =$3,200. See Lesson: Statistics & Probability: The Rules of Probability.

52. A rug is shaped in a half circle. The curved edge of the rug has a circumference of 74 inches. Find the area of the rug to the nearest tenth of a square inch. Use 3.14 for π.

296.0

874.4

1,113.9

1,748.9

Explanation

53. DDEF has points D (–3, 6), E (–2, –4), and F (5, 0). After a transformation, the points are D' (6, 3), E' (–4, 2), and F' (0, –5). What is the transformation between the points?

Reflection across the x-axis

Reflection across the y-axis

Rotation of 90° counterclockwise

Rotation of 270° counterclockwise

D. The correct solution is a rotation of 270° counterclockwise because the points (x, y) become (y, –x). See Lesson: Congruence.

Explanation

D. The correct solution is a rotation of 270° counterclockwise because the points (x, y) become (y, –x). See Lesson: Congruence.

54. Solve the equation by the quadratic formula. 12x² + x - 3 = 0

-0.46 and -0.54

0.46 and -0.54

-0.46 and 0.54

0.46 and 0.54

Explanation

55. If a number has 3 and 5 as factors, which statement best describes that number?

The number is 15.

The number is prime.

The number has 15 as a factor.

The number has only two prime factors.

C. Because 3 and 5 are prime factors of the number, its prime factorization includes them. Furthermore, because a number is the product of all its prime factors, the number in this question must either be 15 or have 15 as a factor. It may or may not be 15, so it may have more than two prime factors. See Lesson: Factors and Multiples.

Explanation

C. Because 3 and 5 are prime factors of the number, its prime factorization includes them. Furthermore, because a number is the product of all its prime factors, the number in this question must either be 15 or have 15 as a factor. It may or may not be 15, so it may have more than two prime factors. See Lesson: Factors and Multiples.

56. The double line chart shows the number of points scored and points given up by a basketball team over the first 10 games. Which statement is true?

B. The correct solution is the team scored more than 65 points in a majority of games and gave up fewer than 65 points in a majority of games. From the graph, there are 6 games during which the team scored more than 65 points and 6 games during which it gave up fewer than 65 points.

See Lesson: Interpreting Graphics.

Explanation

B. The correct solution is the team scored more than 65 points in a majority of games and gave up fewer than 65 points in a majority of games. From the graph, there are 6 games during which the team scored more than 65 points and 6 games during which it gave up fewer than 65 points.

See Lesson: Interpreting Graphics.

57. A basketball has a diameter of 10 inches. What is the volume in cubic inches inside the ball? Use 3.14 for π.

261.67

523.33

1,046.67

2,093.33

Explanation

58. A jar of salsa has a diameter of 12 centimeters and a height of 10 centimeters. There are 4 centimeters of salsa left in the jar. How much salsa was used if the jar was originally filled to the top? State the answer in cubic centimeters in terms of π.

216π

360π

864π

1,440π

A. The correct solution is 216π. The radius is one-half of the diameter, 6 centimeters. The height of the used salsa is 10 – 4, or 6 centimeters. Substitute the values into the formula and simplify using the order of operations, V = πr²h = π6²(6) = π(36)(6) = 216π cubic centimeters. See Lesson: Measurement and Dimension.

Explanation

A. The correct solution is 216π. The radius is one-half of the diameter, 6 centimeters. The height of the used salsa is 10 – 4, or 6 centimeters. Substitute the values into the formula and simplify using the order of operations, V = πr²h = π6²(6) = π(36)(6) = 216π cubic centimeters. See Lesson: Measurement and Dimension.

59. A group of researchers is studying dog behavior. They study the number of hours dogs sleep when music is playing and when it is not playing. What type of study is this?

Census

Survey

Experiment

Observational study

C. The correct solution is experiment because the number of hours of sleep are observed with and without music. See Lesson: Statistical Measures.

Explanation

C. The correct solution is experiment because the number of hours of sleep are observed with and without music. See Lesson: Statistical Measures.

60. A coin is flipped 10 times, and the results are 5 heads and 5 tails. Choose the statement that correctly explains why or why not this result questions this model of probability.

Yes, because there are not enough simulations.

Yes, because there are only two options, heads or tails.

No, because the probability is the same as the simulation.

No, because each flip of the coin is independent of all others.

A. The correct solution is yes, because there are not enough simulations. Only 10 simulations can lead to questioning the probability because there are a small number of simulations. See Lesson: Statistical Measures.

Explanation

A. The correct solution is yes, because there are not enough simulations. Only 10 simulations can lead to questioning the probability because there are a small number of simulations. See Lesson: Statistical Measures.

ACT Math Exam 4

1. Apply the polynomial identity to rewrite x2 - 100.

2.

What first name or nickname would you like us to use?

2. The level of a river during a flood was 39.45 feet. After a week, the water level declined to 18.97 feet. What was the amount of decrease in feet?

3. Convert 0.5 kiloliter to milliliters.

4. Evaluate the expression (-224) ÷ 14.

5.

6. A survey group wants to ask the daily commute time for workers at a large company who use a car to get to work. What is the sample for the survey?

7. Solve the equation for the unknown.

8. Write 1.5 as a percent.

9. Which statement about multiplication is true?

10. A gymnastics team has the following scores for an event: 12.3, 12.7, 14.1, 14.5, 13.8, 13.6, 14.2, 15.2, 14.8, 13.9, 15.4, 14.3. Find the mean score for the team to the nearest hundredth.

11. Evaluate the expression 1,004 + 110.

12. Solve the equation by the square root method. x2 + 10 = 110

13. Which number is not a factor of 1,155?

14. Multiply. (2y2 - 1)(y2 - 3y + 5)

15. Perform the operation. (-2x2 + 8x) + (3x3 - 4x2 + 1)

16. An even roll of a number cube results in +2 points, and an odd roll of a number cube is -3 points. If there are 14 even numbers and 11 odd numbers, then how many points are scored?

17. In a state, the highest elevation is 1,450 feet and the lowest elevation is - 80 feet. What is the difference in the elevations in feet?

18. Solve the inequality for the unknown, 2(3x - 1) +5 ≥ 3x - 4 - 4x.

19. Solve the system of equations. y = -2x x2 + y2 = 5

20. Students were surveyed on if they liked math, social studies, or science as a subject. Describe an intersection of the events.

21. The land area of Colorado is about 1 x 105 square miles, and the land area of Ohio is about 4 x 104 square miles. How many times larger is the land area of Colorado?

22. Which percent is closest to the ratio 7 : 3?

23. Divide.

24. Identify the diameter of the circle.

25. If a company's revenue changes from $123 million to $118 million in a month, how quickly is it increasing in a year?

26. Find the circumference in centimeters of a circle with a radius of 11 centimeters. Use 3.14 for π.

27. Write 290% as a fraction.

28. The number 36 is what percent of 16?

29. Given the coordinates for a rectangle (-4, -1), (-9, -1), (-9,-8), and (-4,-8), find the length of each side of the rectangle.

30. A box in the shape of a right rectangular prism has dimensions of 6 centimeters by 7 centimeters by 8 centimeters. What is the volume in cubic centimeters?

31. A sign stating "Do Not Enter" is in the shape of a square with side lengths of 75 centimeters. What is the area in square centimeters?

32. The last 8 transactions at a shoe store in dollars are 5, 39, 49, 50, 52, 35, 44, 100. What is the effect of removing the outliers on the mean and median?

33. Select the figure that is translated (x + 2, y + 1).

34. A mixture for a cake has various parts. Select the correct circle graph for the data.

35.

36. If Professor Markham has 127 students in her calculus course but 37 drop out because it is too difficult, how many students remain?

37. Divide.

38. The dot plot shows the results of rolling a dice for a game. Which statement is true for the dot plot?

39. Solve. x3 = -8

40. Solve the system of equations by graphing. y = -x + 7 y = 2x - 8

41. Simplify.

42. Solve the equation for c. 2a(b + c) = c

43. There are 12 boys' and 14 girls' names in a hat. What is the probability of selecting a boy's name twice in a row without replacement?

44. Solve for the system of equations. -4x + 3y = 30 3x + 4y = 15

45. Select the figure that is rotated 90° counterclockwise about the origin.

46. Identify the variables from a study on cereal that is quantitative.

47. Solve the equation by any method. x2 + 4x - 15 = 0

48. The volume of a hemi-sphere is cubic feet. What is the diameter in feet?

49. Convert 1,000 fluid ounces to gallons.

50. Convert 6 meters to feet.

51. Which option results in the greatest gain on an investment?

52. A rug is shaped in a half circle. The curved edge of the rug has a circumference of 74 inches. Find the area of the rug to the nearest tenth of a square inch. Use 3.14 for π.

53. DDEF has points D (–3, 6), E (–2, –4), and F (5, 0). After a transformation, the points are D' (6, 3), E' (–4, 2), and F' (0, –5). What is the transformation between the points?

54. Solve the equation by the quadratic formula. 12x2 + x - 3 = 0

55. If a number has 3 and 5 as factors, which statement best describes that number?

56. The double line chart shows the number of points scored and points given up by a basketball team over the first 10 games. Which statement is true?

57. A basketball has a diameter of 10 inches. What is the volume in cubic inches inside the ball? Use 3.14 for π.

58. A jar of salsa has a diameter of 12 centimeters and a height of 10 centimeters. There are 4 centimeters of salsa left in the jar. How much salsa was used if the jar was originally filled to the top? State the answer in cubic centimeters in terms of π.

59. A group of researchers is studying dog behavior. They study the number of hours dogs sleep when music is playing and when it is not playing. What type of study is this?

60. A coin is flipped 10 times, and the results are 5 heads and 5 tails. Choose the statement that correctly explains why or why not this result questions this model of probability.

1. Apply the polynomial identity to rewrite x² - 100.

12. Solve the equation by the square root method. x² + 10 = 110

14. Multiply. (2y² - 1)(y² - 3y + 5)

15. Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)

19. Solve the system of equations. y = -2x x² + y² = 5

21. The land area of Colorado is about 1 x 10⁵ square miles, and the land area of Ohio is about 4 x 10⁴ square miles. How many times larger is the land area of Colorado?

39. Solve. x³ = -8

47. Solve the equation by any method. x² + 4x - 15 = 0

54. Solve the equation by the quadratic formula. 12x² + x - 3 = 0