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.
Other Related Questions
On a number line, what is the distance, in units, between 16 and -25
Correct Answer & Rationale
Correct Answer: 41 units
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
To find the distance between two points on a number line, subtract the smaller number from the larger number. Here, the calculation is |16 - (-25)|, which simplifies to |16 + 25| = |41|. This results in a distance of 41 units. Other options may suggest incorrect calculations. For instance, an answer like 9 units might arise from simply adding the two numbers without considering their positions on the number line, leading to an inaccurate interpretation of distance. Similarly, options like 25 or 16 units misrepresent the actual distance by not accounting for both numbers' magnitudes relative to zero.
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 \(r\).
The Great Pyramid at Giza in Egypt is a square pyramid that measures approximately 756 feet on each side. The height of the pyramid is approximately 450 feet. What is the approximate volume, in cubic feet, of the pyramid?
- A. 51,030,000
- B. 85,730,400
- C. 226,800
- D. 453,600
Correct Answer & Rationale
Correct Answer: B
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.
Simplify: (3x - 5) + (-7x + 2)
- A. -4x^2 - 3
- B. -4x - 3
- C. 28
- D. -4x^2 - 10
Correct Answer & Rationale
Correct Answer: B
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.