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What is the mode of the numbers in the distribution shown in the table?
- A. 1
- B. 2
- C. 3
- D. 4
Correct Answer: A
Rationale: The mode of a set of numbers is the value that appears most frequently. In the distribution shown in the table, the number '1' occurs more times than any other number, making it the mode. Choices B, C, and D are incorrect because they do not represent the number that occurs most frequently in the dataset.
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A rectangular solid box has a square base with a side length of 5 feet and a height of h feet. If the volume of the box is 200 cubic feet, which of the following equations can be used to find h?
- A. 5h = 200
- B. 5h² = 200
- C. 25h = 200
- D. h = 200 · 5
Correct Answer: C
Rationale: The volume formula for a rectangular solid is V = l w h. In this case, the length and width are both 5 feet. Substituting the values into the formula gives V = 5 5 h = 25h = 200. Therefore, h = 200 · 25 = 8. Option A is incorrect because the product of length, width, and height is not directly equal to the volume. Option B is incorrect as squaring the height is not part of the volume formula. Option D is incorrect as it oversimplifies the relationship between height and volume, not considering the base dimensions.
Which of the following is listed in order from least to greatest? (-2, -3/4, -0.45, 3%, 0.36)
- A. -2, -3/4, -0.45, 3%, 0.36
- B. -3/4, -0.45, -2, 0.36, 3%
- C. -0.45, -2, -3/4, 3%, 0.36
- D. -2, -3/4, -0.45, 0.36, 3%
Correct Answer: A
Rationale: To determine the order from least to greatest, convert all the values to a common form. When written in decimal form, the order is -2, -0.75 (which is equal to -3/4), -0.45, 0.03 (which is equal to 3%), and 0.36. Therefore, the correct order is -2, -3/4, -0.45, 3%, 0.36 (Choice A). Choice B is incorrect as it has the incorrect placement of -2 and 0.36. Choice C is incorrect as it incorrectly places -0.45 before -2. Choice D is incorrect as it incorrectly places 0.36 before 3%.
Which of the following is listed in order from least to greatest?
- A. -2 3/4, -2 7/8, -1/5, 2/5, 1/8
- B. -1/5, 1/8, 2/5, -2 3/4, -2 7/8
- C. -2 7/8, -2 3/4, -1/5, 1/8, 2/5
- D. 1/8, 2/5, -1/5, -2 7/8, -2 3/4
Correct Answer: C
Rationale: To determine the order from least to greatest, we can convert all fractions and mixed numbers to decimals or use a least common denominator. Converting the fractions in Choice C to decimals, we get -2.875, -2.75, -0.2, 0.125, and 0.4 when reading from left to right. Negative integers with larger absolute values are less than negative integers with smaller absolute values. Therefore, the correct answer is Choice C. Choices A, B, and D are incorrect because they do not present the numbers in the correct order from least to greatest when converted to decimals or compared using common denominators.
Which of the following algebraic equations correctly represents the sentence 'Four more than a number, x, is 2 less than 1/3 of another number, y'?
- A. x + 4 = (1/3)y - 2
- B. 4x = 2 - (1/3)y
- C. 4 - x = 2 + (1/3)y
- D. x + 4 = 2 - (1/3)y
Correct Answer: A
Rationale: To represent 'Four more than a number, x', we write x + 4. This is equal to '2 less than 1/3 of another number, y', which translates to 1/3y - 2. Therefore, the correct equation is x + 4 = (1/3)y - 2. Choice B is incorrect as it incorrectly combines the values of x and y. Choice C is incorrect as it doesn't properly relate x and y with the given conditions. Choice D is incorrect as it doesn't correctly represent the relationship between x and y according to the given statement.
A lab technician took 100 hairs from a patient to conduct several tests. The technician used 1/7 of the hairs for a drug test. How many hairs were used for the drug test? (Round your answer to the nearest hundredth.)
- A. 14
- B. 14.2
- C. 14.29
- D. 14.3
Correct Answer: C
Rationale: To find how many hairs were used for the drug test, you need to calculate 1/7 of 100. 1/7 of 100 is 14.2857, which rounds to 14.29 when rounded to the nearest hundredth. Therefore, 14.29 hairs were used for the drug test. Choice A is incorrect as it does not account for rounding to the nearest hundredth. Choices B and D are incorrect as they do not accurately reflect the calculated value after rounding.