The equation d/f = g represents gallons of gasoline used, g, in terms of distance traveled in miles, d, and fuel efficiency, / miles per gallon of gasoline. Which combination of distance traveled and fuel efficiency uses 3 gallons of gasoline?
- A. 7 miles and 21 miles per gallon
- B. 57 miles and 19 miles per gallon
- C. 23 miles and 20 miles per gallon
- D. 32 miles and 35 miles per gallon
Correct Answer & Rationale
Correct Answer: B
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
To determine which combination uses 3 gallons of gasoline, we can rearrange the equation d/f = g to find d = g * f. For g = 3 gallons, we calculate d for each option. A: 7 miles and 21 mpg results in d = 3 * 21 = 63 miles, which is incorrect. B: 57 miles and 19 mpg gives d = 3 * 19 = 57 miles, matching the distance traveled. C: 23 miles and 20 mpg leads to d = 3 * 20 = 60 miles, which is incorrect. D: 32 miles and 35 mpg results in d = 3 * 35 = 105 miles, which is also incorrect. Only option B correctly satisfies the equation for 3 gallons of gasoline used.
Other Related Questions
Last weekend, 625 runners entered a 10,000-meter race. A 10,000- meter race is 6.2 miles long. Ruben won the race with a finishing time of 29 minutes 51 seconds.
The graphs show information about the top 10 runners.
Based on the scatter plot, what is the range of ages of the top 10 runners?
- A. 9
- B. 1
- C. 16
- D. 40
Correct Answer & Rationale
Correct Answer: C
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.
The range of ages is determined by subtracting the youngest runner's age from the oldest runner's age. In this case, the scatter plot indicates that the youngest runner is 16 years old and the oldest is 32 years old. Thus, the range is 32 - 16 = 16 years. Option A (9) incorrectly suggests a smaller age difference, while B (1) implies almost no age variation, neither of which aligns with the data presented. Option D (40) overestimates the age range, indicating a misunderstanding of the plotted values. Therefore, the accurate calculation of 16 years reflects the true age span of the top 10 runners.
A manufacturing plant makes dog toys in the shape of a sphere. The diameter of each dog toy is 3 inches. What is the surface area, in square inches of each dog toy?
- A. 113.04
- B. 75.36
- C. 28.26
- D. 37.68
Correct Answer & Rationale
Correct Answer: C
To find the surface area of a sphere, the formula used is \(4\pi r^2\). Given the diameter of the dog toy is 3 inches, the radius \(r\) is half of that, which is 1.5 inches. Plugging this into the formula: \[ Surface Area = 4\pi (1.5)^2 = 4\pi (2.25) \approx 28.26 \text{ square inches.} \] Option A (113.04) results from incorrectly using the diameter instead of the radius. Option B (75.36) arises from miscalculating the radius or misapplying the formula. Option D (37.68) likely results from a miscalculation of the surface area formula, possibly using an incorrect value for \(r\).
To find the surface area of a sphere, the formula used is \(4\pi r^2\). Given the diameter of the dog toy is 3 inches, the radius \(r\) is half of that, which is 1.5 inches. Plugging this into the formula: \[ Surface Area = 4\pi (1.5)^2 = 4\pi (2.25) \approx 28.26 \text{ square inches.} \] Option A (113.04) results from incorrectly using the diameter instead of the radius. Option B (75.36) arises from miscalculating the radius or misapplying the formula. Option D (37.68) likely results from a miscalculation of the surface area formula, possibly using an incorrect value for \(r\).
A landscape worker is building a rock wall around a triangular flower garden. He has completed the rock wall on two sides of the garden.
The perimeter of the garden is 239 feet. What is the length, in feet, of the rock wall that the worker still needs to complete?
- A. 101
- B. 185
- C. 54
- D. 138
Correct Answer & Rationale
Correct Answer: D
To determine the length of the rock wall still needed, first, the total perimeter of the triangular garden is 239 feet. The worker has already completed two sides, leaving one side to be built. To find the length of the remaining side, we subtract the lengths of the two completed sides from the total perimeter. The answer of 138 feet indicates that the lengths of the two sides combined equal 101 feet (239 - 138 = 101). Option A (101) represents the combined length of the two completed sides, not the remaining side. Option B (185) exceeds the total perimeter, which is impossible. Option C (54) does not fit the calculations based on the perimeter. Thus, only option D accurately reflects the length of the remaining side to complete the wall.
To determine the length of the rock wall still needed, first, the total perimeter of the triangular garden is 239 feet. The worker has already completed two sides, leaving one side to be built. To find the length of the remaining side, we subtract the lengths of the two completed sides from the total perimeter. The answer of 138 feet indicates that the lengths of the two sides combined equal 101 feet (239 - 138 = 101). Option A (101) represents the combined length of the two completed sides, not the remaining side. Option B (185) exceeds the total perimeter, which is impossible. Option C (54) does not fit the calculations based on the perimeter. Thus, only option D accurately reflects the length of the remaining side to complete the wall.
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.