ACT Math Exam 2

1. What is 604 - 561?

34

43

53

143

B. The correct solution is 43. Use the subtraction algorithm, which will require borrowing once. See Lesson: Basic Addition and Subtraction.

Explanation

B. The correct solution is 43. Use the subtraction algorithm, which will require borrowing once. See Lesson: Basic Addition and Subtraction.

2. A biologist has captured only two kinds of snakes, ringnecks and garters. If she has 6 ringneck snakes and 13 snakes total, how many garter snakes does she have?

6

7

13

19

B. The correct solution is 7. Since the biologist only has ringnecks and garters, any snake in her possession is a garter if it is not a ringneck. Because she has 13 snakes but 6 ringneck snakes, the number of garter snakes is the difference: 13 – 6 = 7. See Lesson: Basic Addition and Subtraction.

Explanation

B. The correct solution is 7. Since the biologist only has ringnecks and garters, any snake in her possession is a garter if it is not a ringneck. Because she has 13 snakes but 6 ringneck snakes, the number of garter snakes is the difference: 13 – 6 = 7. See Lesson: Basic Addition and Subtraction.

3. Evaluate the expression. (3 x (4 + 9) ÷ 13 - 2) + 1

-2

0

2

5

C. Follow the order of operations (the PEMDAS mnemonic). Begin with the innermost parentheses and work outward, multiplying and dividing from left to right before adding and subtracting from left to right.

(3 × (4 + 9) ÷ 13 – 2) + 1

(3 × 13 ÷ 13 – 2) + 1

(39 ÷ 13 – 2) + 1

(3 – 2) + 1

1 + 1

2

See Lesson: Basic Multiplication and Division.

Explanation

C. Follow the order of operations (the PEMDAS mnemonic). Begin with the innermost parentheses and work outward, multiplying and dividing from left to right before adding and subtracting from left to right.

(3 × (4 + 9) ÷ 13 – 2) + 1

(3 × 13 ÷ 13 – 2) + 1

(39 ÷ 13 – 2) + 1

(3 – 2) + 1

1 + 1

2

See Lesson: Basic Multiplication and Division.

4. What is 762 ÷ 127

4

6

8

9

B. Use the division algorithm. Because 127 is greater than 7 and 76, the process begins with all three digits in the dividend.

See Lesson: Basic Multiplication and Division.

Explanation

B. Use the division algorithm. Because 127 is greater than 7 and 76, the process begins with all three digits in the dividend.

See Lesson: Basic Multiplication and Division.

5.

B. The correct solution is B. The two lines intersect at point Z. See Lesson: Congruence.

Explanation

B. The correct solution is B. The two lines intersect at point Z. See Lesson: Congruence.

6. Solve the equation for the unknown. a - 10 = -20

-30

-10

2

200

B. The correct solution is –10 because 10 is added to both sides of the equation. See Lesson: Equations with One Variable.

Explanation

B. The correct solution is –10 because 10 is added to both sides of the equation. See Lesson: Equations with One Variable.

7. If the term of a mobile-phone contract is in multiples of a year, which duration can a customer choose?

6 months

18 months

24 months

32 months

C. A year-long contract is also 12 months long. Multiples of 12 months are 24 months, 36 months, 48 months, and so on. See Lesson: Factors and Multiples.

Explanation

C. A year-long contract is also 12 months long. Multiples of 12 months are 24 months, 36 months, 48 months, and so on. See Lesson: Factors and Multiples.

8. Solve x² = 225.

-5, 5

-10, 10

-15, 15

-20, 20

C. The correct solution is -15, 15 because the square root of 225 is 15. The values of -15 and 15 make the equation true. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

C. The correct solution is -15, 15 because the square root of 225 is 15. The values of -15 and 15 make the equation true. See Lesson: Powers, Exponents, Roots, and Radicals.

9. In which of the following situations is probability sampling used?

Qualitative research

Studies with specific goals

Randomly selected samples

Studies with limited functions

C. The correct solution is randomly selected samples because random sampling techniques are used. See Lesson: Statistical Measures.

Explanation

C. The correct solution is randomly selected samples because random sampling techniques are used. See Lesson: Statistical Measures.

10. Change 2.5 to a fraction. Simplify completely.

Explanation

11. Find the mode for the data set 42, 45, 44, 44, 45, 42, 45, 44, 45, 46, 42, 44, 41, 48, 47, 46, 45, 42, 42, and 44.

42, 43

44, 45

42, 44, 45

42, 43, 44, 45

C. The correct solution is 42, 44, and 45. The modes are 42, 44, and 45 because these values appear four times in the data set. See Lesson: Interpreting Graphics.

Explanation

C. The correct solution is 42, 44, and 45. The modes are 42, 44, and 45 because these values appear four times in the data set. See Lesson: Interpreting Graphics.

12. Find the mean for the data set. 16, 18, 17, 15, 19, 14, 12, 11, 10, 16, 18, and 17.

14.25

15.25

16

17

B. The correct solution is 15.25. The sum of all items is 183, and 183 divided by 12 gives a mean of 15.25. See Lesson: Interpreting Graphics.

Explanation

B. The correct solution is 15.25. The sum of all items is 183, and 183 divided by 12 gives a mean of 15.25. See Lesson: Interpreting Graphics.

13. Multiply. (4y² + 3)(2y + 5)

8y3 + 10y2 + 16y +15

8y3 + 20y2 + 16y +15

8y3 + 10y2 + 6y +15

8y3 + 20y2 + 6y +15

Explanation

14. Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).

B. The first point is in the second quadrant, the second point is in the third quadrant, the third point is in the fourth quadrant, and the last point is in the first quadrant. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

B. The first point is in the second quadrant, the second point is in the third quadrant, the third point is in the fourth quadrant, and the last point is in the first quadrant. See Lesson: Similarity, Right Triangles, and Trigonometry.

15. John spends $21.25 at the movies. His ticket is $7.75, and he buys popcorn, a pretzel, and a drink. If each snack costs the same, what is the price of the pretzel?

$3.58

$4.50

$6.00

$7.08

B. The correct solution is $4.50 because 21.25 - 7.75 = 13.50 ÷ 3 = $4.50. See Lesson: Solving Real World Mathematical Problems.

Explanation

B. The correct solution is $4.50 because 21.25 - 7.75 = 13.50 ÷ 3 = $4.50. See Lesson: Solving Real World Mathematical Problems.

16. One recipe calls for ¾ cup of sugar, and another calls for 2 ½ cups of sugar. The first recipe is tripled, and the second recipe is halved. How many cups of sugar are needed?

1

1¾

3

3½

Explanation

17. Which decimal is the least?

2.22

2.02

2.002

2.2

C. The correct solution is 2.002 because 2.002 contains the smallest values in the tenths and hundredths places. See Lesson: Decimals and Fractions.

Explanation

C. The correct solution is 2.002 because 2.002 contains the smallest values in the tenths and hundredths places. See Lesson: Decimals and Fractions.

18. Jayden rides his bike for 2¾ miles. He takes a break and rides another miles. How many miles does he ride?

Explanation

19. Solve the equation for the unknown. 3x - 8 + 5 + 2x = 4x - x + 6

Explanation

20. Solve the system of equations. -2x + 6y = -6 4x - 5y = 26

(2, 3)

(3, 6)

(6, 9)

(9, 2)

Explanation

21. Solve the system of equations. x + 2y = 5 -5x + 3y = -25

(5, 0)

(0, -5)

(-5, 0)

(0, 5)

Explanation

22. Find the values from the box plot.

Minimum: 0, first quartile: 3, median: 5, third quartile: 7, maximum: 9

Minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9

Minimum: 0, first quartile: 3, median: 5, third quartile: 7, maximum: 10

Minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 10

B. The correct solution is minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9, which are the values of the box plot. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

B. The correct solution is minimum: 0.5, first quartile: 3, median: 4.5, third quartile: 7, maximum: 9, which are the values of the box plot. See Lesson: Interpreting Categorical and Quantitative Data.

23.

Explanation

24. Divide.

Explanation

25. Identify 1920 in 12-hour clock time.

6:20 p.m.

7:20 p.m.

6:20 a.m.

7:20 a.m.

B. The correct solution is 7:20 p.m. Subtract 1200 from the time, 1920 - 1200 = 7: 20 p.m. See Lesson: Standards of Measure.

Explanation

B. The correct solution is 7:20 p.m. Subtract 1200 from the time, 1920 - 1200 = 7: 20 p.m. See Lesson: Standards of Measure.

26. How many dogs are necessary to make a cat-to-dog ratio of 3:2 in an area with 1,425 cats?

285

950

2,138

2,375

B. The correct answer is B. Set up the proportion of dogs to cats (or vice versa):

Since 1,425 ÷ 3 = 475, the number of dogs is the product of 2 and 475, or 950. See Lesson: Ratios, Proportions, and Percentages.

Explanation

B. The correct answer is B. Set up the proportion of dogs to cats (or vice versa):

Since 1,425 ÷ 3 = 475, the number of dogs is the product of 2 and 475, or 950. See Lesson: Ratios, Proportions, and Percentages.

27. A dime has a radius of 8.5 millimeters. Find the circumference in millimeters of the dime. Use 3.14 for π.

11.64

26.69

53.38

106.76

C. The correct solution is 53.38 because C=2πr≈(2)3.148.5≈53.38 millimeters.

See Lesson: Circles.

Explanation

C. The correct solution is 53.38 because C=2πr≈(2)3.148.5≈53.38 millimeters.

See Lesson: Circles.

28. A bucket contains 4 bottles of apple juice, 6 bottles of orange juice, 5 bottles of grape juice, and 10 bottles of water. What is the probability of NOT selecting a bottle of water?

Explanation

29. Solve the system of equations by graphing. 3x + 4y = -5 -2x +2y =8

A. The correct graph has the two lines intersect at (-3, 1). See Lesson: Equations with Two Variables.

Explanation

A. The correct graph has the two lines intersect at (-3, 1). See Lesson: Equations with Two Variables.

30. Simplify.

-343

-49

-21

-7

Explanation

31. How many men does a company employ if it has 420 employees and 35% are women?

35

147

273

420

C. The company employs 273 men. If 35% of the company’s employees are women, 65% are men. Set up a proportion using 65%, which is equal to

The unknown number is the product of 13 and 420 ÷ 20 = 21, which is 273. See Lesson: Ratios, Proportions, and Percentages.

Explanation

C. The company employs 273 men. If 35% of the company’s employees are women, 65% are men. Set up a proportion using 65%, which is equal to

The unknown number is the product of 13 and 420 ÷ 20 = 21, which is 273. See Lesson: Ratios, Proportions, and Percentages.

32. Solve the equation by any method. 9x² - 48x + 64 = 0

Explanation

33. The area of a circular drum top is 175 square inches. Find the diameter to the nearest tenth of an inch. Use 3.14 for π.

7.5

15.0

22.5

30.0

B. The correct solution is 15.0 because A = πr^{^²}; 175 = 3.14r^{^²}; 55.73=r^{^²}; r ≈ 7.5. The diameter is twice the radius, or about 15.0 inches. See Lesson: Circles.

Explanation

B. The correct solution is 15.0 because A = πr^{^²}; 175 = 3.14r^{^²}; 55.73=r^{^²}; r ≈ 7.5. The diameter is twice the radius, or about 15.0 inches. See Lesson: Circles.

34. Identify the coplanar points in the diagram.

Points S, T, U, and Y

Points X, V, S, and z

Points X, Y, U, and V

Points U, Y, Z, and T

A. The correct solution is points S, T, U, and Y because these four points are in plane Z. See Lesson: Congruence.

Explanation

A. The correct solution is points S, T, U, and Y because these four points are in plane Z. See Lesson: Congruence.

35. Given the coordinates for a square (-3, -5), (-3, 4), (6, 4), and (6, -5), find the length of each side of the square.

3 unites

6 units

9 units

12 units

C. The correct solution 9 units. The difference between the x-coordinates is 6 - (-3) = 9 units, and the difference between the y-coordinates is 4 - (-5) = 9 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

Explanation

C. The correct solution 9 units. The difference between the x-coordinates is 6 - (-3) = 9 units, and the difference between the y-coordinates is 4 - (-5) = 9 units. See Lesson: Similarity, Right Triangles, and Trigonometry.

36. Solve the equation by factoring. x² + 3x - 88 = 0.

-8, -11

-8, 11

8, -11

8, 11

Explanation

37. The data below show the number of cars that drove through an intersection on a Saturday. 1, 48, 60, 43, 41, 70, 75, 80, 101, 90, 121, 114, 99, 153, 205, 175, 222, 96, 201, 158, 141, 117, 74, 29 Select a histogram for the data.

D. The correct solution is D. Each bin contains 50 cars, and the frequencies are 4, 8, 5, 3, and 3. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

D. The correct solution is D. Each bin contains 50 cars, and the frequencies are 4, 8, 5, 3, and 3. See Lesson: Interpreting Categorical and Quantitative Data.

38. Convert 2.5 miles to feet.

2,112 feet

2,640 feet

10,560 feet

13,200

Explanation

39. A square pyramid has a volume of 189 cubic feet and a height of 7 feet. Find the length in feet of a side of the base.

3

9

12

18

Explanation

40.

Explanation

41. Convert 8 liters to quarts.

6.94 quarts

7.55 quarts

8.48 quarts

9.06 quarts

Explanation

42. Perform the operation. (8x2 - 6x - 3) - (4x2 - 5x + 4)

4x2 - 11x - 7

4x2 - 11x + 1

4x2 - x - 7

4x2 - x + 1

Explanation

43. Apply the polynomial identity to rewrite 27x³ - 8.

(3x - 2)(9x2 - 6x + 4)

(3x - 2)(9x2 + 6x + 4)

(3x - 2)(9x2 + 6x - 4)

(3x - 2)(9x2 - 6x - 4)

Explanation

44. Solve the equation by completing the square. x² + 12x + 10 = 0

6 ± √26

-6 ± √26

6 ± √10

-6 ± √10

Explanation

45. What is the number of symmetry lines for a regular hexagon?

2

4

6

8

C. The correct solution is six lines of symmetry. There are three lines of symmetry through opposite vertices and three lines through the midpoints of opposite segments. See Lesson: Congruence.

Explanation

C. The correct solution is six lines of symmetry. There are three lines of symmetry through opposite vertices and three lines through the midpoints of opposite segments. See Lesson: Congruence.

46. Which option is the greatest gain on a sale?

50% of gaining $8 million and 50% of gaining $7 million

60% of gaining $9 million and 40% of gaining $6 million

70% of gaining $10 million and 30% of gaining $5 million

80% of gaining $11 million and 20% of gaining $4 million

D. The correct solution is 80% of gaining $11 million and 20% of gaining $4 million. The expected value is 0.80(11) + 0.20(4) = 8.8 + 0.8 = $9.6 million. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

D. The correct solution is 80% of gaining $11 million and 20% of gaining $4 million. The expected value is 0.80(11) + 0.20(4) = 8.8 + 0.8 = $9.6 million. See Lesson: Statistics & Probability: The Rules of Probability.

47. The data set represents the number of weekly pop-up ads for 12 families: 125, 145, 150, 130, 150, 120, 170, 165, 175, 145, 150, and 130. Find the median.

145

145.5

147

147.5

D. The correct solution is 147.5. The data set written in order is 120, 125, 130, 130, 145, 145, 150, 150, 150, 165, 170, 175. The middle two numbers are 145 and 150, and the mean of the numbers is 147.5. See Lesson: Interpreting Graphics.

Explanation

D. The correct solution is 147.5. The data set written in order is 120, 125, 130, 130, 145, 145, 150, 150, 150, 165, 170, 175. The middle two numbers are 145 and 150, and the mean of the numbers is 147.5. See Lesson: Interpreting Graphics.

48. A package of a toy is a cylinder with a cone on top. The radius of the figure is 2 feet, the height of the cylinder is 3 feet, and the height of the cone is 3 feet. Find the volume to the nearest cubic foot. Use 3.14 for π.

12

38

50

76

See Lesson: Measurement and Dimension.

Explanation

See Lesson: Measurement and Dimension.

49. A lysosome has a length of 1m10^-6 meter, and measles virus has a length of 2m10^-9 meter. How many times longer is the lysosome?

5

50

500

5,000

C. The correct solution is 500 because 1×10^-6 is 0.000001 and 2×10^-9 is about 0.000000002. So, the lysosome is 500 times longer. See Lesson: Powers, Exponents, Roots, and Radicals.

Explanation

C. The correct solution is 500 because 1×10^-6 is 0.000001 and 2×10^-9 is about 0.000000002. So, the lysosome is 500 times longer. See Lesson: Powers, Exponents, Roots, and Radicals.

50. A trapezoid has bases of 8 inches and 12 inches and a height of 6 inches. Find the area in square inches.

18

20

60

72

Explanation

51. A car repair shop wants to create a survey about the performance of car batteries. Which is an example of a survey?

Testing all car batteries

Testing car batteries for sale

Testing random car batteries

Testing car batteries returned by customers

C. The correct solution is testing random car batteries because this is a sample of the population and demonstrates the performance of the population. See Lesson: Statistical Measures.

Explanation

C. The correct solution is testing random car batteries because this is a sample of the population and demonstrates the performance of the population. See Lesson: Statistical Measures.

52. Solve the inequality for the unknown.

X ≤ -45

X ≥ -45

X ≤ 90

X ≥ 90

Explanation

53. How many unique prime factors does 75 have?

1

2

3

4

B. The prime factorization—for example, using a factor tree—shows that 75 has the prime factors 3, 5, and 5, since 3 × 5 × 5 = 75. Because 5 repeats, 75 has only two unique prime factors. See Lesson: Factors and Multiples.

Explanation

B. The prime factorization—for example, using a factor tree—shows that 75 has the prime factors 3, 5, and 5, since 3 × 5 × 5 = 75. Because 5 repeats, 75 has only two unique prime factors. See Lesson: Factors and Multiples.

54. Find the radius in meters of a cone with a volume of cubic meters and a height of 8 meters.

2

4

6

8

Explanation

55. A group is conducting a survey at a mall asking shoppers their opinion of the mall. What type of sampling is used?

Quota sampling

Volunteer sampling

Purposive sampling

Convenience sampling

D. The correct solution is convenience sampling because the group is at a mall asking shoppers at the mall for their opinions. See Lesson: Statistical Measures.

Explanation

D. The correct solution is convenience sampling because the group is at a mall asking shoppers at the mall for their opinions. See Lesson: Statistical Measures.

56. If a truck's initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed

17%

33%

40%

67%

Explanation

57.

See Lesson: Decimals and Fractions.

Explanation

See Lesson: Decimals and Fractions.

58. The high temperatures in degrees Fahrenheit for the beginning of April are 45, 48, 53, 57, 52, 60, 58. The last temperature is 28. Compare the standard deviation and interquartile range before and after the last temperature.

The standard deviation and interquartile range increase.

The standard deviation and interquartile range decrease.

The standard deviation increases, and the interquartile range decreases.

The standard deviation decreases, but the interquartile range increases.

A. The correct solution is the standard deviation and interquartile range increase. The standard deviation increases from 5.06 to 9.61, and the interquartile range increases from 9.5 to 11. See Lesson: Interpreting Categorical and Quantitative Data.

Explanation

A. The correct solution is the standard deviation and interquartile range increase. The standard deviation increases from 5.06 to 9.61, and the interquartile range increases from 9.5 to 11. See Lesson: Interpreting Categorical and Quantitative Data.

59. The area of a half circle is 48 square centimeters. Find the circumference of the curved portion of the half circle to the nearest tenth of a centimeter. Use 3.14 for π.

17.3

24.5

34.5

49.0

A. The correct solution is 17.3.

See Lesson: Circles.

Explanation

A. The correct solution is 17.3.

See Lesson: Circles.

60. In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the complement of even cards.

Odd number cards

Even number cards

Green and red cards

Yellow and blue cards

A. The correct solution is odd number cards. The complement of even number cards is odd. See Lesson: Statistics & Probability: The Rules of Probability.

Explanation

A. The correct solution is odd number cards. The complement of even number cards is odd. See Lesson: Statistics & Probability: The Rules of Probability.

ACT Math Exam 2

1. What is 604 - 561?

2.

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

2. A biologist has captured only two kinds of snakes, ringnecks and garters. If she has 6 ringneck snakes and 13 snakes total, how many garter snakes does she have?

3. Evaluate the expression. (3 x (4 + 9) ÷ 13 - 2) + 1

4. What is 762 ÷ 127

5.

6. Solve the equation for the unknown. a - 10 = -20

7. If the term of a mobile-phone contract is in multiples of a year, which duration can a customer choose?

8. Solve x2 = 225.

9. In which of the following situations is probability sampling used?

10. Change 2.5 to a fraction. Simplify completely.

11. Find the mode for the data set 42, 45, 44, 44, 45, 42, 45, 44, 45, 46, 42, 44, 41, 48, 47, 46, 45, 42, 42, and 44.

12. Find the mean for the data set. 16, 18, 17, 15, 19, 14, 12, 11, 10, 16, 18, and 17.

13. Multiply. (4y2 + 3)(2y + 5)

14. Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).

15. John spends $21.25 at the movies. His ticket is $7.75, and he buys popcorn, a pretzel, and a drink. If each snack costs the same, what is the price of the pretzel?

16. One recipe calls for ¾ cup of sugar, and another calls for 2 ½ cups of sugar. The first recipe is tripled, and the second recipe is halved. How many cups of sugar are needed?

17. Which decimal is the least?

18. Jayden rides his bike for 2¾ miles. He takes a break and rides another miles. How many miles does he ride?

19. Solve the equation for the unknown. 3x - 8 + 5 + 2x = 4x - x + 6

20. Solve the system of equations. -2x + 6y = -6 4x - 5y = 26

21. Solve the system of equations. x + 2y = 5 -5x + 3y = -25

22. Find the values from the box plot.

23.

24. Divide.

25. Identify 1920 in 12-hour clock time.

26. How many dogs are necessary to make a cat-to-dog ratio of 3:2 in an area with 1,425 cats?

27. A dime has a radius of 8.5 millimeters. Find the circumference in millimeters of the dime. Use 3.14 for π.

28. A bucket contains 4 bottles of apple juice, 6 bottles of orange juice, 5 bottles of grape juice, and 10 bottles of water. What is the probability of NOT selecting a bottle of water?

29. Solve the system of equations by graphing. 3x + 4y = -5 -2x +2y =8

30. Simplify.

31. How many men does a company employ if it has 420 employees and 35% are women?

32. Solve the equation by any method. 9x2 - 48x + 64 = 0

33. The area of a circular drum top is 175 square inches. Find the diameter to the nearest tenth of an inch. Use 3.14 for π.

34. Identify the coplanar points in the diagram.

35. Given the coordinates for a square (-3, -5), (-3, 4), (6, 4), and (6, -5), find the length of each side of the square.

36. Solve the equation by factoring. x2 + 3x - 88 = 0.

37. The data below show the number of cars that drove through an intersection on a Saturday. 1, 48, 60, 43, 41, 70, 75, 80, 101, 90, 121, 114, 99, 153, 205, 175, 222, 96, 201, 158, 141, 117, 74, 29 Select a histogram for the data.

38. Convert 2.5 miles to feet.

39. A square pyramid has a volume of 189 cubic feet and a height of 7 feet. Find the length in feet of a side of the base.

40.

41. Convert 8 liters to quarts.

42. Perform the operation. (8x2 - 6x - 3) - (4x2 - 5x + 4)

43. Apply the polynomial identity to rewrite 27x3 - 8.

44. Solve the equation by completing the square. x2 + 12x + 10 = 0

45. What is the number of symmetry lines for a regular hexagon?

46. Which option is the greatest gain on a sale?

47. The data set represents the number of weekly pop-up ads for 12 families: 125, 145, 150, 130, 150, 120, 170, 165, 175, 145, 150, and 130. Find the median.

48. A package of a toy is a cylinder with a cone on top. The radius of the figure is 2 feet, the height of the cylinder is 3 feet, and the height of the cone is 3 feet. Find the volume to the nearest cubic foot. Use 3.14 for π.

49. A lysosome has a length of 1m10-6 meter, and measles virus has a length of 2m10-9 meter. How many times longer is the lysosome?

50. A trapezoid has bases of 8 inches and 12 inches and a height of 6 inches. Find the area in square inches.

51. A car repair shop wants to create a survey about the performance of car batteries. Which is an example of a survey?

52. Solve the inequality for the unknown.

53. How many unique prime factors does 75 have?

54. Find the radius in meters of a cone with a volume of cubic meters and a height of 8 meters.

55. A group is conducting a survey at a mall asking shoppers their opinion of the mall. What type of sampling is used?

56. If a truck's initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed

57.

58. The high temperatures in degrees Fahrenheit for the beginning of April are 45, 48, 53, 57, 52, 60, 58. The last temperature is 28. Compare the standard deviation and interquartile range before and after the last temperature.

59. The area of a half circle is 48 square centimeters. Find the circumference of the curved portion of the half circle to the nearest tenth of a centimeter. Use 3.14 for π.

60. In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the complement of even cards.

8. Solve x² = 225.

13. Multiply. (4y² + 3)(2y + 5)

32. Solve the equation by any method. 9x² - 48x + 64 = 0

36. Solve the equation by factoring. x² + 3x - 88 = 0.

43. Apply the polynomial identity to rewrite 27x³ - 8.

44. Solve the equation by completing the square. x² + 12x + 10 = 0

49. A lysosome has a length of 1m10^-6 meter, and measles virus has a length of 2m10^-9 meter. How many times longer is the lysosome?