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Jonathan pays a $65 monthly flat rate for his cell phone. He is charged $0.12 per minute for each minute used in a roaming area. Which of the following expressions represents his monthly bill for x roaming minutes?
- A. 65 + 0.12x
- B. 65x + 0.12
- C. 65.12x
- D. 65 + 0.12x
Correct Answer: A
Rationale: The correct expression for Jonathan's monthly bill is 65 + 0.12x, where x represents the number of roaming minutes. The $65 monthly flat rate is added to the product of $0.12 per minute and the number of roaming minutes (x). Choice B is incorrect because it incorrectly multiplies the flat rate by x and adds the per-minute charge. Choice C is incorrect as it combines the flat rate and the per-minute charge into a single value. Choice D is incorrect as it incorrectly multiplies the flat rate by x and adds the per-minute charge separately.
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How many centimeters are in 7 meters?
- A. 7 m = 7 cm
- B. 7 m = 70 cm
- C. 7 m = 700 cm
- D. 7 m = 7000 cm
Correct Answer: C
Rationale: The prefix 'centi-' means one-hundredth. In the metric system, 1 meter is equal to 100 centimeters. Therefore, to convert meters to centimeters, you multiply the number of meters by 100. In this case, 7 meters is equal to 7 * 100 = 700 centimeters. Choice A is incorrect as it does not consider the conversion factor properly. Choice B is incorrect as it only accounts for a factor of 10 instead of 100. Choice D is incorrect as it overestimates the conversion by a factor of 10.
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.
What was the mean time for the women who ran the 200m event at the 2008 Olympic Games (times in seconds: 22.33, 22.50, 22.50, 22.61, 22.71, 22.72, 22.83, 23.22)?
- A. 22.50 sec
- B. 22.66 sec
- C. 22.68 sec
- D. 22.77 sec
Correct Answer: C
Rationale: To find the mean time, you need to add all the times (22.33 + 22.50 + 22.50 + 22.61 + 22.71 + 22.72 + 22.83 + 23.22) and then divide by the total number of times (8). This calculation results in a mean time of 22.68 seconds. Choice A, 22.50 sec, is incorrect because it is the time of one of the runners, not the mean time. Choice B, 22.66 sec, and Choice D, 22.77 sec, are also incorrect as they are not the calculated mean of the given times.
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.
The table below shows the number of books checked out from a library over the course of 4 weeks. Which equation describes the relationship between the number of books (b) and weeks (w)?
- A. b = 10w + 2
- B. b = 5w + 10
- C. b = 8w + 12
- D. b = 4w + 20
Correct Answer: B
Rationale: The relationship between the number of books and weeks is best described by the equation b = 5w + 10. This is because the initial value of books checked out is 10, which indicates that even with 0 weeks, there are already 10 books checked out. The rate at which books are checked out per week is 5, as indicated by the coefficient of w. Therefore, the correct equation should be b = 5w + 10. Choices A, C, and D are incorrect because they do not represent the correct initial value or rate of increase for the given scenario.