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
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.
Multiply: (x^2 - 3)(x^5 + 2x^3)
- A. x^7,-3x^5,-6x^3
- B. x^10,2x^5,-6x^3
- C. 5x^5,2x^6,-6x^3
- D. x^7,2x^5,-6
Correct Answer & Rationale
Correct Answer: A
To find the product of (x^2 - 3)(x^5 + 2x^3), we apply the distributive property (FOIL method). 1. **First Terms**: x^2 * x^5 = x^7. 2. **Outer Terms**: x^2 * 2x^3 = 2x^5. 3. **Inner Terms**: -3 * x^5 = -3x^5. 4. **Last Terms**: -3 * 2x^3 = -6x^3. Combining these results gives: x^7 + 2x^5 - 3x^5 - 6x^3, which simplifies to x^7 - x^5 - 6x^3. Option A correctly lists the terms as x^7, -3x^5, -6x^3. Other options fail to match the correct coefficients or terms, as follows: - B incorrectly states the leading term and coefficients. - C miscalculates the powers of x and coefficients. - D omits the x terms entirely, providing an incomplete expression.
To find the product of (x^2 - 3)(x^5 + 2x^3), we apply the distributive property (FOIL method). 1. **First Terms**: x^2 * x^5 = x^7. 2. **Outer Terms**: x^2 * 2x^3 = 2x^5. 3. **Inner Terms**: -3 * x^5 = -3x^5. 4. **Last Terms**: -3 * 2x^3 = -6x^3. Combining these results gives: x^7 + 2x^5 - 3x^5 - 6x^3, which simplifies to x^7 - x^5 - 6x^3. Option A correctly lists the terms as x^7, -3x^5, -6x^3. Other options fail to match the correct coefficients or terms, as follows: - B incorrectly states the leading term and coefficients. - C miscalculates the powers of x and coefficients. - D omits the x terms entirely, providing an incomplete expression.
A cyclist can travel 17.6 feet per second. The cyclist would have a better understanding of her speed if it were measured in miles per hour. Which of these completes the expression used to convert the speed of the cyclist to miles per hour?
- A. 1 hour/60 seconds = 1 mile/5,280 feet
- B. 60 minutes/1 hour = 1 mile/5280 feet
- C. 60 minutes/1 hour = 5280 feet/1 mile
- D. 12 inches/1 foot = 60 minutes/1 hour
Correct Answer & Rationale
Correct Answer: C
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
To convert speed from feet per second to miles per hour, the conversion factors must relate time and distance appropriately. Option C correctly expresses the relationship between miles and feet, stating that 1 mile equals 5280 feet. Additionally, it includes the conversion of minutes to hours, with 60 minutes equating to 1 hour, which is essential for converting seconds to hours. Option A incorrectly suggests a different time conversion that mixes hours and seconds without properly aligning the units. Option B, while correctly stating the time conversion, mistakenly places the units in an incorrect order. Option D is irrelevant, as it focuses on inches and does not contribute to the necessary conversions for speed.
The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
- A. 36
- B. 16
- C. 40
- D. 13
Correct Answer & Rationale
Correct Answer: A
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.
To determine the total number of apartments, consider the naming convention: each apartment consists of one letter and one digit. There are 4 letters (A, B, C, D) and 9 digits (1-9). Calculating the combinations, multiply the number of letters by the number of digits: 4 letters × 9 digits = 36 unique apartment names. Options B (16) and D (13) do not account for all possible combinations, while option C (40) incorrectly assumes more letters or digits than provided. Thus, option A accurately reflects the total possible apartments in Greg's building.