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Which of the following lists is in order from least to greatest? (1/7), 0.125, (6/9), 0.60
- A. (1/7), 0.125, (6/9), 0.60
- B. (1/7), 0.125, 0.60, (6/9)
- C. 0.125, (1/7), 0.60, 6/9
- D. 0.125, (1/7), (6/9), 0.60
Correct Answer: C
Rationale: To determine the order from least to greatest, convert all fractions to decimals and compare them. Converting the fractions: (1/7) ≈ 0.14, (6/9) ≈ 0.67. The decimals in order from least to greatest are: 0.125 < 0.14 < 0.60 < 0.67. Therefore, the correct order is 0.125, (1/7), 0.60, 6/9, making choice C the correct answer. Choice A is incorrect as it lists (1/7) before 0.125. Choice B is incorrect as it places 0.60 before (6/9). Choice D is incorrect as it lists (6/9) before 0.60.
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Which of the following is equivalent to 8 pounds and 8 ounces? (Round to the nearest tenth of a kilogram.)
- A. 3.6 kilograms
- B. 3.9 kilograms
- C. 17.6 kilograms
- D. 18.7 kilograms
Correct Answer: B
Rationale: To convert 8 pounds and 8 ounces to kilograms, first convert 8 ounces to pounds by dividing by 16 (since 1 pound = 16 ounces): 8 ounces / 16 = 0.5 pounds. Then add this to the original 8 pounds: 8 pounds + 0.5 pounds = 8.5 pounds. To convert pounds to kilograms, use the conversion factor 1 pound = 0.453592 kilograms. Therefore, 8.5 pounds 0.453592 kg = 3.855 kilograms, which rounds to 3.9 kilograms. Choice A (3.6 kilograms), Choice C (17.6 kilograms), and Choice D (18.7 kilograms) are incorrect conversions or have errors in calculation compared to the correct conversion of 3.9 kilograms.
After taxes, a worker earned $15,036 in 7 months. What is the amount the worker earned in 2 months?
- A. $2,148
- B. $4,296
- C. $6,444
- D. $8,592
Correct Answer: B
Rationale: To find the amount earned in 2 months, set up a proportion using two ratios relating amount earned to months: (15,036/7) = (x /2). Cross-multiply and solve for x: 7x = 30,072, x = 4,296. Therefore, the worker earned $4,296 in 2 months. Choice A, $2,148, is incorrect as it is half of the correct answer. Choices C and D, $6,444 and $8,592, are incorrect as they do not correspond to the calculated proportion.
Which statement about the following set is true? {60, 5, 18, 20, 37, 37, 11, 90, 72}
- A. The median and the mean are equal.
- B. The mean is less than the mode.
- C. The mode is greater than the median.
- D. The median is less than the mean.
Correct Answer: D
Rationale: To find the median, we first need to arrange the set in ascending order: {5, 11, 18, 20, 37, 37, 60, 72, 90}. The median is the middle value, which is 37 in this case. The mean is calculated by adding all numbers and dividing by the total count, which gives a mean greater than 37. Therefore, the statement that the median is less than the mean is correct. Choice A is incorrect because the median and mean are not equal in this set. Choice B is incorrect as the mean is greater than the mode in this set. Choice C is incorrect as the mode is 37, which is equal to the median, not greater.
Adam is painting the outside of a 4-walled shed. The shed is 5 feet wide, 4 feet deep, and 7 feet high. Which of the following is the amount of paint Adam will need for the four walls?
- A. 80 ft²
- B. 126 ft²
- C. 140 ft²
- D. 560 ft²
Correct Answer: B
Rationale: To find the amount of paint needed for the four walls of the shed, calculate the total area of the four walls. The shed has two pairs of identical walls. The area of one pair of walls is 5 feet (width) x 7 feet (height) + 4 feet (depth) x 7 feet (height) = 35 ft² + 28 ft² = 63 ft². Since there are two pairs of walls, the total area for the four walls is 2 x 63 ft² = 126 ft². Therefore, Adam will need 126 ft² of paint for the four walls. Choice A, 80 ft², is incorrect as it does not account for the total surface area of all four walls. Choice C, 140 ft², is incorrect as it overestimates the area required. Choice D, 560 ft², is incorrect as it significantly overestimates the amount of paint needed for the shed.
Which of the following lists is in order from least to greatest? 2−1 , −(4/3), (−1)3 , (2/5)
- A. 2−1 , −(4/3), (−1)3 , (2/5)
- B. −(4/3), (−1)3 , 2−1 , (2/5)
- C. −(4/3), (2/5), 2−1 , (−1)3
- D. −(4/3), (−1)3 , (2/5), 2−1
Correct Answer: D
Rationale: To determine the correct order from least to greatest, start by simplifying the expressions. 2^(-1) = 1/2 and (-1)^3 = -1. Now, comparing the values, (-4/3) is the most negative, followed by -1, then (2/5), and finally 1/2. Therefore, the correct order is (-4/3), (-1)^3, (2/5), 2^(-1), making choice D the correct answer. Choices A, B, and C are incorrect because they do not follow the correct order from least to greatest as determined by comparing the values of the expressions after simplification.