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
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.
A shipping box for a refrigerator is shaped like a rectangular prism. The box has a depth of 34.25 inches (in.), a height of 69.37 in., and a width of 32.62 in. To the nearest hundredth cubic inch, what is the volume of the shipping bax?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
To determine the volume of a rectangular prism, the formula \( V = \text{length} \times \text{width} \times \text{height} \) is applied. Given the dimensions—depth (length) of 34.25 in., width of 32.62 in., and height of 69.37 in.—the calculation yields a volume of approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, indicating a miscalculation. Option C (136.24) is implausibly low, likely resulting from using incorrect units or dimensions. Option D (25,834.20) is also incorrect, as it does not reflect the correct multiplication of the given dimensions. Thus, only option B accurately represents the calculated volume.
The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
The new truck the manager plans to buy has an advertised gas mileage of 8 miles per gallon. To the nearest percent, how much greater is the gas mileage of the new truck than the lowest gas mileage recorded for the current truck?
- A. 14
- B. 25
- C. 23
- D. 33
Correct Answer & Rationale
Correct Answer: D
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
Factor the expression completely: -3x - 21
- A. -3(x+7)
- B. -3(x-21)
- C. -3(x-7)
- D. -3(x+21)
Correct Answer & Rationale
Correct Answer: A
To factor the expression -3x - 21 completely, start by identifying the common factor in both terms. Here, -3 is the greatest common factor. When factoring out -3 from -3x, you're left with x, and from -21, you have +7. Thus, the expression can be rewritten as -3(x + 7). Option B, -3(x - 21), is incorrect because factoring out -3 from -21 should yield +7, not -21. Option C, -3(x - 7), incorrectly represents the constant term, as it should be +7. Option D, -3(x + 21), misrepresents the factorization entirely, as it does not reflect the original expression's terms.
To factor the expression -3x - 21 completely, start by identifying the common factor in both terms. Here, -3 is the greatest common factor. When factoring out -3 from -3x, you're left with x, and from -21, you have +7. Thus, the expression can be rewritten as -3(x + 7). Option B, -3(x - 21), is incorrect because factoring out -3 from -21 should yield +7, not -21. Option C, -3(x - 7), incorrectly represents the constant term, as it should be +7. Option D, -3(x + 21), misrepresents the factorization entirely, as it does not reflect the original expression's terms.