inequalities, absolute value, probability

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inequalities, absolute value, probability

13. Which of the following statements are true?

I. −(−6) = 6 and − (−4) > –4

II. −(−4) < 4 or −10 > 10 – 10

III. 5 + 6 = 11 or 9 – 2 = 11

IV. 17 > 2 or 6 < 9

a. I and II
b. I, II, and III

c. I, III, and IV

d. III and IV

18. What is the solution of the inequality |3-x| / 2 < 4?

a. 5<x<11
b. −11<x<−5

c. −5<x<11

d. −1<x<11

19. Which of the following inequalities have the same solutions?

I. |5x – 7| ≤ 8
II. −8≤5x–7 or 5x–7≤8

III. 8 ≤ 5x – 7 and 5x – 7 ≥ −8

IV. −8 ≤ 5x – 7 and 5x – 7 ≤ 8

a. I and II
b. I and III
c. I and IV
d. I, III, and IV

21. What is the theoretical probability of getting a 2 or a 3 when rolling a number cube?

a. 1/2

b. 1/3

c. 1/4

d. 1/6

22. How many outcomes are in the sample space for rolling a number cube and tossing a coin?

a. 2

b. 6

c. 12

d. 24

24. The circumference of a basketball for college women must be between 28.5 in. and 29.0 in. Which absolute value inequality best represents the circumference of the ball?

a. |C – 0.25| ≥ 28.5

b. |C – 0.25| ≤ 29.0

c. |C – 28.75| ≤ 0.25

d. |C – 28.75| ≥ 0.25

25. If 16 less than four times a number is 64, what is the number?

a. 48

b. 20

c. 32

d. 4

26. The measure of the supplement of an angle is 25 more than 7 times the measure of the angle. To the nearest whole degree, what is the measure of the angle?

a. 20

b. 56

c. 19

d. 55

27. The sides of a rectangle are in the ratio 5 : 7, and its perimeter is 96 cm. What is the area of the rectangle in square centimeters?

a. 4
b. 560

c. 280

d. 20

28. The length of a side of an equilateral triangle is 4. Which type of number best describes the length of the altitude of the triangle?

a. whole number
b. integer
c. rational number

d. irrational number

29. Which phrase does not describe the square root of 625?

a. whole number
b. irrational number

c. integer
d. rational number

30. Which value is in the solution set of 4 < −4x – 2 < 8 and 3 > 4x + 2 > −10?

a. −2

b. 0

c. 3

d. 4

40. A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wished to have the length be 3 times the width. Find the dimensions of the fence.

  1. 144 ft by 48 ft
  2. 192ft by 48ft
  3. 120ft by 40ft
  4. 108ft by 58ft

47. Solve:|8–m|+4=21.

a. 9, 25

b. −25, 9

c. −25, −9

d. −9, 25

You roll a twelve-sided number cube with the numbers 1 through 12 on the faces of the number cube. You roll the number cube once. Find the theoretical probability P(factor of 12).

a. 5/12

b. 1/2

c. 7/12

d. 3/4