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.
Other Related Questions
The triangle shown in the diagram has an area of 24 square centimeters. What is h, the height in centimeters, of the triangle?
- A. 9
- B. 4
- C. 8
- D. 2
Correct Answer & Rationale
Correct Answer: C
To find the height \( h \) of the triangle, we use the area formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Given the area is 24 cm², we can rearrange the formula to solve for \( h \): \( h = \frac{2 \times \text{Area}}{\text{base}} \). Assuming the base is 6 cm (since \( 24 = \frac{1}{2} \times 6 \times h \)), substituting gives \( h = \frac{48}{6} = 8 \). - Option A (9) is too high, as it would yield an area greater than 24 cm². - Option B (4) results in an area of only 12 cm², which is insufficient. - Option D (2) yields an area of 6 cm², far below the required area. Thus, only option C (8) satisfies the area requirement.
To find the height \( h \) of the triangle, we use the area formula: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Given the area is 24 cm², we can rearrange the formula to solve for \( h \): \( h = \frac{2 \times \text{Area}}{\text{base}} \). Assuming the base is 6 cm (since \( 24 = \frac{1}{2} \times 6 \times h \)), substituting gives \( h = \frac{48}{6} = 8 \). - Option A (9) is too high, as it would yield an area greater than 24 cm². - Option B (4) results in an area of only 12 cm², which is insufficient. - Option D (2) yields an area of 6 cm², far below the required area. Thus, only option C (8) satisfies the area requirement.
The graph shows a handyman's fees, f(x), in terms of the hours worked, x. The fees include a fuel charge and an hourly rate. What is the handyman's hourly rate?
- A. $5
- B. $55
- C. $30
- D. $25
Correct Answer & Rationale
Correct Answer: D
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
On Monday; Alicia buys x shirts at $8 each and y slacks at $25 each. On Wednesday, Alicia returns 2 pairs of slacks. Which expression represents the total value of her purchases?
- A. 8x + 23y
- B. 8x + 25(y - 2)
- C. 8x - 2) + 25y
- D. 8x + 25y - 2
Correct Answer & Rationale
Correct Answer: B
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
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A truck driver sees a road sign warning of an 8% road incline.
To the nearest tenth of a foot, what will be the change in the truck's vertical position, in feet, during the time it takes the truck's horizontal position to change by 1 mile? (1 mile = 5280 ft)
- B.
Correct Answer & Rationale
Correct Answer: 422.4
To determine the change in vertical position on an 8% incline over a horizontal distance of 1 mile (5280 feet), we calculate the vertical rise using the formula: vertical change = incline percentage × horizontal distance. An 8% incline means a rise of 8 feet for every 100 feet traveled horizontally. Therefore, for 5280 feet, the vertical change is (8/100) × 5280 = 422.4 feet. Other options would incorrectly calculate the vertical change by misapplying the percentage or using an incorrect horizontal distance, leading to values that do not accurately reflect the incline's effect over the specified distance.
To determine the change in vertical position on an 8% incline over a horizontal distance of 1 mile (5280 feet), we calculate the vertical rise using the formula: vertical change = incline percentage × horizontal distance. An 8% incline means a rise of 8 feet for every 100 feet traveled horizontally. Therefore, for 5280 feet, the vertical change is (8/100) × 5280 = 422.4 feet. Other options would incorrectly calculate the vertical change by misapplying the percentage or using an incorrect horizontal distance, leading to values that do not accurately reflect the incline's effect over the specified distance.