Nokea
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.
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University X requires some of its nursing students to take an exam before being admitted into the nursing program. In this year's class, half of the nursing students were required to take the exam, and three-fifths of those who took the exam passed. If this year's class has 200 students, how many students passed the exam?
- A. 120
- B. 100
- C. 60
- D. 50
Correct Answer: C
Rationale: If the incoming class has 200 students, then half of those students were required to take the exam. (200)(1/2) = 100. So 100 students took the exam, but only three-fifths of that 100 passed the exam. (100)(3/5) = 60. Therefore, 60 students passed the exam. The correct answer is 60. Choice A is incorrect as it miscalculates the number of students who passed the exam. Choice B is incorrect as it does not consider the passing rate of the exam. Choice D is incorrect as it is much lower than the correct answer.
Simplify the following expression: (2/7) · (5/6)
- A. 2/5
- B. 35/15
- C. 5/21
- D. 12/35
Correct Answer: D
Rationale: To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. In this case, (2/7) · (5/6) becomes (2/7) (6/5) = 12/35. Therefore, the correct answer is 12/35. Choice A (2/5), choice B (35/15), and choice C (5/21) are incorrect because they do not correctly simplify the given expression.
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.
The number of vacuum cleaners sold by a company per month during Year 1 is listed below: 18, 42, 29, 40, 24, 17, 29, 44, 19, 33, 46, 39. Which of the following is true?
- A. The mean is less than the median
- B. The mode is greater than the median
- C. The mode is less than the mean, median, and range
- D. The mode is equal to the range
Correct Answer: D
Rationale: The mean number of vacuum cleaners sold per month is 31.7, the mode is 29, the median is 31, and the range is 29. The mode being equal to the range is the correct statement. Option A is incorrect because the mean (31.7) is greater than the median (31). Option B is incorrect as the mode (29) is not greater than the median (31). Option C is incorrect since the mode (29) is not less than the mean, median, or range.
A farmer had about 150 bags of potatoes on his trailer. Each bag contained from 23 to 27 pounds of potatoes. What is the best estimate of the total number of pounds of potatoes on the farmer's trailer?
- A. 3,000 pounds
- B. 3,700 pounds
- C. 4,100 pounds
- D. 5,000 pounds
Correct Answer: B
Rationale: To estimate the total number of pounds of potatoes on the farmer's trailer, we can use the average weight of a bag of potatoes. The average weight is calculated by adding the minimum and maximum weights of the bags and dividing by 2: (23 + 27) / 2 = 25 pounds. Next, multiply the average weight by the total number of bags: 25 pounds/bag * 150 bags = 3,750 pounds. Therefore, the best estimate of the total number of pounds of potatoes on the farmer's trailer is 3,750 pounds. Choice A (3,000 pounds) is too low as it underestimates the total weight. Choice C (4,100 pounds) and Choice D (5,000 pounds) are too high as they overestimate the total weight.