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.
What is the value of 2/5 multiplied by 5/4 divided by 4/3
- A. 32/75
- B. 3\8
- C. 6\25
- D. 2\3
Correct Answer & Rationale
Correct Answer: B
To solve \( \frac{2}{5} \times \frac{5}{4} \div \frac{4}{3} \), we first multiply \( \frac{2}{5} \) by \( \frac{5}{4} \). This results in \( \frac{2 \times 5}{5 \times 4} = \frac{10}{20} = \frac{1}{2} \). Next, dividing by \( \frac{4}{3} \) is the same as multiplying by its reciprocal, \( \frac{3}{4} \). Therefore, \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \). Option A, \( \frac{32}{75} \), is incorrect as it does not simplify from the given operations. Option C, \( \frac{6}{25} \), results from miscalculating the division. Option D, \( \frac{2}{3} \), is also incorrect as it doesn't follow from the correct operations.
To solve \( \frac{2}{5} \times \frac{5}{4} \div \frac{4}{3} \), we first multiply \( \frac{2}{5} \) by \( \frac{5}{4} \). This results in \( \frac{2 \times 5}{5 \times 4} = \frac{10}{20} = \frac{1}{2} \). Next, dividing by \( \frac{4}{3} \) is the same as multiplying by its reciprocal, \( \frac{3}{4} \). Therefore, \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \). Option A, \( \frac{32}{75} \), is incorrect as it does not simplify from the given operations. Option C, \( \frac{6}{25} \), results from miscalculating the division. Option D, \( \frac{2}{3} \), is also incorrect as it doesn't follow from the correct operations.
The width of a painting is 24 centimeters shorter than its length, x. The area of the painting is 4,081 square centimeters. Which equation could be used to find the dimensions of the painting?
- A. x^2 - 24x - 4,081 = 0
- B. x^2 + 24x - 4,081 = 0
- C. x^2 + 24x + 4,081 = 0
- D. x^2 - 24x + 4,081 = 0
Correct Answer & Rationale
Correct Answer: A
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
- A. -0.4
- B. 2\5
- C. 5\2
- D. -2.5
Correct Answer & Rationale
Correct Answer: B
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.