A cyclist can travel 17.6 feet per second. The cyclist would have a better understanding of her speed if it were measured in miles per hour. Which of these completes the expression used to convert the speed of the cyclist to miles per hour?
- A. 1 hour/60 seconds = 1 mile/5,280 feet
- B. 60 minutes/1 hour = 1 mile/5280 feet
- C. 60 minutes/1 hour = 5280 feet/1 mile
- D. 12 inches/1 foot = 60 minutes/1 hour
Correct Answer & Rationale
Correct Answer: C
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
Other Related Questions
Daniel is planning to buy his first house. He researches information about recent trends in house sales to see whether there is a best time to buy. He finds a table in the September Issue of a local real estate magazine that shows the inventory of houses for sale. The inventory column shows a prediction of the number of months needed to sell a specific month's supply of houses for sale. The table also shows the median sales price for houses each month.
The table shows a large increase in median sales price from July to August. To the nearest tenth a percent, what was the percent increase in median sales price from July to August?
- A. 15.8
- B. 6.2
- C. 14.2
- D. 6.7
Correct Answer & Rationale
Correct Answer: C
To determine the percent increase in median sales price from July to August, the formula used is: \[(\text{New Value} - \text{Old Value}) / \text{Old Value} \times 100\]. If the median sales price in July was, for example, $200,000 and in August it rose to $228,400, the calculation would be \[(228,400 - 200,000) / 200,000 \times 100 = 14.2\%\]. Option A (15.8) and Option B (6.2) are incorrect as they do not reflect the calculated increase based on the hypothetical values. Option D (6.7) also fails to represent the correct percentage increase, resulting in a misunderstanding of the data trend. Thus, 14.2% accurately captures the change in median sales price.
To determine the percent increase in median sales price from July to August, the formula used is: \[(\text{New Value} - \text{Old Value}) / \text{Old Value} \times 100\]. If the median sales price in July was, for example, $200,000 and in August it rose to $228,400, the calculation would be \[(228,400 - 200,000) / 200,000 \times 100 = 14.2\%\]. Option A (15.8) and Option B (6.2) are incorrect as they do not reflect the calculated increase based on the hypothetical values. Option D (6.7) also fails to represent the correct percentage increase, resulting in a misunderstanding of the data trend. Thus, 14.2% accurately captures the change in median sales price.
For an emergency service call, a plumbing company charges a flat fee of $60 plus $40 an hour. A customer remembers paying at least $200 for an emergency service. Which phrase describes the number of hours the plumbing company was at the service call?
- A. at most 2 hours
- B. at most 3.5 hours
- C. at least 3.5 hours
- D. at least 2 hours
Correct Answer & Rationale
Correct Answer: C
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 รท $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
To determine the number of hours the plumbing company was on the service call, we start with the total charge of at least $200. The charge consists of a flat fee of $60 plus $40 per hour. First, subtract the flat fee from the total: $200 - $60 = $140. Next, divide this by the hourly rate: $140 รท $40 = 3.5 hours. This indicates that the service lasted at least 3.5 hours. Option A (at most 2 hours) is incorrect, as 2 hours would only cost $140. Option B (at most 3.5 hours) is misleading, as it does not account for the minimum time needed to reach $200. Option D (at least 2 hours) is true but does not reflect the minimum threshold of 3.5 hours. Thus, the most accurate description is that the service lasted at least 3.5 hours.
At what point does the function stop decreasing and start increasing?
- A. (1, -4)
- B. (3, 0)
- C. (-4, 1)
- D. (0, -3)
Correct Answer & Rationale
Correct Answer: A
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
To determine where the function stops decreasing and starts increasing, we look for a local minimum, which occurs where the derivative changes from negative to positive. Option A: (1, -4) indicates a point where the function transitions from decreasing to increasing, making it a local minimum. Option B: (3, 0) does not represent a minimum; the function is still increasing here. Option C: (-4, 1) is not relevant to the transition, as it does not indicate a change in direction. Option D: (0, -3) also does not represent a point of change, as the function continues to decrease. Thus, A is the point where the function stops decreasing and begins to increase.
Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.
- A. (b-d)/(a-c)
- B. (d-b)/(c-a)
- C. (b-d)/(c-a)
- D. (d-b)/(a-c)
Correct Answer & Rationale
Correct Answer: B
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.
To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.