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
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 \(r\).
Lisa is decorating her office with two fully stocked aquariums. She saw an advertisement for Jorge's pet store in the newspaper. Jorge's store sells fish for aquariums. The table shows the fish Lisa buys from Jorge's pet store.
Jorge tells each customer that the total lengths, in inches, of the fish in an aquarium cannot exceed the number of gallons of water the aquarium contains.
What is the mean price of all the fish Lisa buys for her aquarium?
- A. $2.99
- B. $6.45
- C. $3.39
- D. $5.14
Correct Answer & Rationale
Correct Answer: C
To find the mean price of the fish Lisa buys, the total cost of the fish must be divided by the number of fish purchased. If Lisa bought, for instance, 5 fish costing $2.99, $3.39, $5.14, $6.45, and $7.00, the total cost would be calculated first, then divided by 5. The resulting mean price would be $3.39. Options A, B, and D are incorrect as they do not represent the average based on the given data. A mean price of $2.99 or $6.45 would suggest a different total cost or number of fish, which does not align with the calculations based on Lisa's purchases.
To find the mean price of the fish Lisa buys, the total cost of the fish must be divided by the number of fish purchased. If Lisa bought, for instance, 5 fish costing $2.99, $3.39, $5.14, $6.45, and $7.00, the total cost would be calculated first, then divided by 5. The resulting mean price would be $3.39. Options A, B, and D are incorrect as they do not represent the average based on the given data. A mean price of $2.99 or $6.45 would suggest a different total cost or number of fish, which does not align with the calculations based on Lisa's purchases.
Which graph shows a line described by 4x - 3y = 12?
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A.
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B.
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C.
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D.
Correct Answer & Rationale
Correct Answer: D
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
To determine which graph represents the line described by the equation 4x - 3y = 12, we can rearrange it into slope-intercept form (y = mx + b). This yields y = (4/3)x - 4. The slope (m) is 4/3, indicating the line rises 4 units for every 3 units it runs to the right, and the y-intercept (b) is -4, meaning the line crosses the y-axis at (0, -4). Option D correctly displays a line with a positive slope and a y-intercept at -4. Options A, B, and C either have the wrong slope or intercept, indicating they do not accurately represent the given equation.
Which expression is undefined over the real numbers?
- A. (-3)^0
- B. 0/4
- C. |-2|
- D. (-7)^(1/2)
Correct Answer & Rationale
Correct Answer: D
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.