How much more money will Carol make in a regular work week?
Correct Answer & Rationale
Correct Answer: A
In a regular work week, Carol's earnings are calculated based on her hourly wage multiplied by the number of hours worked. Option A reflects this accurate calculation, considering both her hourly rate and total hours. Other options may underestimate or overestimate her earnings by failing to account for overtime, miscalculating hours, or using an incorrect wage. For example, if an option suggests a lower amount, it likely ignores additional hours worked, while a higher amount may miscalculate her hourly rate. Thus, only option A correctly represents Carol's total earnings for a regular work week.
In a regular work week, Carol's earnings are calculated based on her hourly wage multiplied by the number of hours worked. Option A reflects this accurate calculation, considering both her hourly rate and total hours. Other options may underestimate or overestimate her earnings by failing to account for overtime, miscalculating hours, or using an incorrect wage. For example, if an option suggests a lower amount, it likely ignores additional hours worked, while a higher amount may miscalculate her hourly rate. Thus, only option A correctly represents Carol's total earnings for a regular work week.
Other Related Questions
Solve the equation for x: ½ x + 9 = -2/3 x
- A. x=-9/7
- B. x=-54/7
- C. x=-6
- D. x=-54
Correct Answer & Rationale
Correct Answer: B
To solve the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \), start by eliminating the fractions. Multiply the entire equation by 6 (the least common multiple of 2 and 3) to obtain \( 3x + 54 = -4x \). Next, combine like terms: adding \( 4x \) to both sides gives \( 7x + 54 = 0 \), leading to \( 7x = -54 \) and thus \( x = -\frac{54}{7} \). Option A is incorrect as it simplifies to a different value. Option C, \( x = -6 \), does not satisfy the original equation. Option D, \( x = -54 \), is also incorrect as it does not balance the equation. Therefore, the only viable solution is \( x = -\frac{54}{7} \).
To solve the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \), start by eliminating the fractions. Multiply the entire equation by 6 (the least common multiple of 2 and 3) to obtain \( 3x + 54 = -4x \). Next, combine like terms: adding \( 4x \) to both sides gives \( 7x + 54 = 0 \), leading to \( 7x = -54 \) and thus \( x = -\frac{54}{7} \). Option A is incorrect as it simplifies to a different value. Option C, \( x = -6 \), does not satisfy the original equation. Option D, \( x = -54 \), is also incorrect as it does not balance the equation. Therefore, the only viable solution is \( x = -\frac{54}{7} \).
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 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.
What is the slope of a line that is perpendicular to the line y = -9x + 7?
- A. 1\9
- B. -0.111111111
- C. 9
- D. -9
Correct Answer & Rationale
Correct Answer: A
To find the slope of a line perpendicular to the line given by the equation \(y = -9x + 7\), first identify the slope of the original line, which is \(-9\). The slope of a line perpendicular to another is the negative reciprocal of the original slope. The negative reciprocal of \(-9\) is \(\frac{1}{9}\). Option A, \(\frac{1}{9}\), is the correct slope. Option B, \(-0.111111111\), is incorrect as it represents \(-\frac{1}{9}\), not the positive reciprocal. Option C, \(9\), is incorrect because it is the opposite sign of the required reciprocal. Option D, \(-9\), is simply the original slope and does not represent a perpendicular relationship.
To find the slope of a line perpendicular to the line given by the equation \(y = -9x + 7\), first identify the slope of the original line, which is \(-9\). The slope of a line perpendicular to another is the negative reciprocal of the original slope. The negative reciprocal of \(-9\) is \(\frac{1}{9}\). Option A, \(\frac{1}{9}\), is the correct slope. Option B, \(-0.111111111\), is incorrect as it represents \(-\frac{1}{9}\), not the positive reciprocal. Option C, \(9\), is incorrect because it is the opposite sign of the required reciprocal. Option D, \(-9\), is simply the original slope and does not represent a perpendicular relationship.