Two men are employed at a local supermarket. The table shows James's earnings, and the graph shows Eric's earnings.
Based on the information above, who earns the greater amount per hour, and how much does he earn for a 7-hour shift?
- A. James earns the greater amount per hour and earns $73.50 for a 7-hour shift.
- B. James earns the greater amount per hour and earns $70.00 for a 7-hour shift.
- C. Eric earns the greater amount per hour and earns $70.00 for a 7-hour shift.
- D. Eric earns the greater amount per hour and earns $73.50 for a 7-hour shift.
Correct Answer & Rationale
Correct Answer: D
To determine who earns more per hour, one must compare the hourly rates of James and Eric. If Eric's hourly rate is higher, he earns more for a 7-hour shift, calculated as his hourly rate multiplied by 7. Option A incorrectly states James earns more and miscalculates his earnings. Option B also claims James earns more but provides the wrong total for a 7-hour shift. Option C correctly identifies Eric as the higher earner but misstates his total earnings for a 7-hour shift. Option D accurately identifies Eric as the higher earner and correctly calculates his earnings for a 7-hour shift at $73.50.
To determine who earns more per hour, one must compare the hourly rates of James and Eric. If Eric's hourly rate is higher, he earns more for a 7-hour shift, calculated as his hourly rate multiplied by 7. Option A incorrectly states James earns more and miscalculates his earnings. Option B also claims James earns more but provides the wrong total for a 7-hour shift. Option C correctly identifies Eric as the higher earner but misstates his total earnings for a 7-hour shift. Option D accurately identifies Eric as the higher earner and correctly calculates his earnings for a 7-hour shift at $73.50.
Other Related Questions
What is the area, in square inches, of a circle with diameter 2 inches?
- A. 6.28
- B. 3.14
- C. 1
- D. 12.56
Correct Answer & Rationale
Correct Answer: B
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. Given a diameter of 2 inches, the radius is 1 inch. Substituting this into the formula yields \( A = \pi (1)^2 = \pi \), which approximates to 3.14. Option A (6.28) incorrectly doubles the area, possibly confusing it with the circumference. Option C (1) neglects the use of \(\pi\), leading to an inaccurate calculation. Option D (12.56) mistakenly uses the formula for circumference, multiplying the diameter by \(\pi\) instead of squaring the radius. Thus, 3.14 accurately represents the area of the circle.
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. Given a diameter of 2 inches, the radius is 1 inch. Substituting this into the formula yields \( A = \pi (1)^2 = \pi \), which approximates to 3.14. Option A (6.28) incorrectly doubles the area, possibly confusing it with the circumference. Option C (1) neglects the use of \(\pi\), leading to an inaccurate calculation. Option D (12.56) mistakenly uses the formula for circumference, multiplying the diameter by \(\pi\) instead of squaring the radius. Thus, 3.14 accurately represents the area of the circle.
Simplify 6^2 - 3^2
- A. 6
- B. 9
- C. 27
- D. 3
Correct Answer & Rationale
Correct Answer: C
To simplify \(6^2 - 3^2\), we apply the difference of squares formula, which states \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 6\) and \(b = 3\). Thus, we have: \[ 6^2 - 3^2 = (6 - 3)(6 + 3) = 3 \times 9 = 27 \] Option A (6) is incorrect as it miscalculates the expression. Option B (9) mistakenly considers only one of the squared terms. Option D (3) misinterprets the operations involved, leading to an incorrect result. The correct evaluation yields 27, confirming option C as the accurate answer.
To simplify \(6^2 - 3^2\), we apply the difference of squares formula, which states \(a^2 - b^2 = (a - b)(a + b)\). Here, \(a = 6\) and \(b = 3\). Thus, we have: \[ 6^2 - 3^2 = (6 - 3)(6 + 3) = 3 \times 9 = 27 \] Option A (6) is incorrect as it miscalculates the expression. Option B (9) mistakenly considers only one of the squared terms. Option D (3) misinterprets the operations involved, leading to an incorrect result. The correct evaluation yields 27, confirming option C as the accurate answer.
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 histogram, which statement describes the finishing time of the runner in position 3?
- A. The finishing time was between 30 and 31 minutes
- B. The finishing time was between 33 and 34 minutes
- C. The finishing time was between 31 and 32 minutes
- D. The finishing time was between 32 and 33 minutes
Correct Answer & Rationale
Correct Answer: C
The finishing time for the runner in position 3 falls within the 31 to 32 minutes range, as indicated by the histogram. This range is supported by the data distribution, showing that the majority of runners in the top 10 finished within this timeframe. Option A is incorrect because it suggests a time between 30 and 31 minutes, which does not align with the position 3 runner's time. Option B is inaccurate, as it indicates a finishing time between 33 and 34 minutes, which is too high for this position. Option D, while close, incorrectly suggests a time between 32 and 33 minutes, which does not match the histogram data for the third place runner.
The finishing time for the runner in position 3 falls within the 31 to 32 minutes range, as indicated by the histogram. This range is supported by the data distribution, showing that the majority of runners in the top 10 finished within this timeframe. Option A is incorrect because it suggests a time between 30 and 31 minutes, which does not align with the position 3 runner's time. Option B is inaccurate, as it indicates a finishing time between 33 and 34 minutes, which is too high for this position. Option D, while close, incorrectly suggests a time between 32 and 33 minutes, which does not match the histogram data for the third place runner.
Which pair of equations represents parallel lines?
- A. -2x + y + 2 = 0, y = -(1/2)x - 4
- B. 3x + y = -8, y = 3x - 8
- C. x + 2y = 8, -x - 2y = 3
- D. -(2/3)x + y = 12, y = -(3/2)x - 1
Correct Answer & Rationale
Correct Answer: C
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.