An expression for a company's cost to make n bicycles is -0.017n? - 6.8n + 690. An expression for the revenue from selling these n bicycles is 70n. Profit is revenue minus cost. Which is an expression for the profit for making and selling n bicycles?
- A. -0.017n^2 - 76.8n + 690
- B. 0.017n^2 + 76.8n - 690
- C. 0.017n^2 + 63.2n + 690
- D. -0.017n^2 + 63.2n + 690
Correct Answer & Rationale
Correct Answer: D
To find the profit from selling n bicycles, subtract the cost expression from the revenue expression. The cost is given as -0.017n² - 6.8n + 690, and the revenue is 70n. Calculating profit: Profit = Revenue - Cost = 70n - (-0.017n² - 6.8n + 690) simplifies to 70n + 0.017n² + 6.8n - 690, which results in 0.017n² + 63.2n - 690. Option D, -0.017n² + 63.2n + 690, incorrectly presents the quadratic term with the wrong sign. Options A and B incorrectly combine terms or misrepresent the coefficients. Option C miscalculates the constant term. Thus, only option D maintains the correct profit structure.
To find the profit from selling n bicycles, subtract the cost expression from the revenue expression. The cost is given as -0.017n² - 6.8n + 690, and the revenue is 70n. Calculating profit: Profit = Revenue - Cost = 70n - (-0.017n² - 6.8n + 690) simplifies to 70n + 0.017n² + 6.8n - 690, which results in 0.017n² + 63.2n - 690. Option D, -0.017n² + 63.2n + 690, incorrectly presents the quadratic term with the wrong sign. Options A and B incorrectly combine terms or misrepresent the coefficients. Option C miscalculates the constant term. Thus, only option D maintains the correct profit structure.
Other Related Questions
Solve the inequality for x: (1/8)x ? (1/2)x + 15
- A. x ? -24
- B. x ? -40
- C. x ? -40
- D. x ? -24
Correct Answer & Rationale
Correct Answer: C
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).
Daniel is planning to buy his first house. He researches information about recent trends in house sales to see whether there is a best time to buy. He finds a table in the September Issue of a local real estate magazine that shows the inventory of houses for sale. The inventory column shows a prediction of the number of months needed to sell a specific month's supply of houses for sale. The table also shows the median sales price for houses each month.
Daniel wants to create a scatter plot of the data in the table to determine whether inventory affects median sales price. Which scatter plot will help Daniel make his determination?
- A. M-12A.png
- B. M-12B.png
- C. M-12C.png
- D. M-12D.png
Correct Answer & Rationale
Correct Answer: A
Option A presents a scatter plot that effectively correlates inventory (months needed to sell) on the x-axis with median sales price on the y-axis. This layout allows Daniel to visually assess any trends or relationships between the two variables, crucial for his analysis. Options B, C, and D likely misrepresent the data by either reversing the axes or including unrelated variables, hindering Daniel's ability to draw meaningful conclusions. Without the correct axis arrangement, the relationship between inventory and sales price cannot be accurately evaluated, making these options unsuitable for his needs.
Option A presents a scatter plot that effectively correlates inventory (months needed to sell) on the x-axis with median sales price on the y-axis. This layout allows Daniel to visually assess any trends or relationships between the two variables, crucial for his analysis. Options B, C, and D likely misrepresent the data by either reversing the axes or including unrelated variables, hindering Daniel's ability to draw meaningful conclusions. Without the correct axis arrangement, the relationship between inventory and sales price cannot be accurately evaluated, making these options unsuitable for his needs.
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 carpenter is installing shelves in 2 offices. Each office will have 4 shelves. The wood the carpenter wants to use comes in 6-foot-long boards. Each shelf is 2 ¼ feet long and is constructed from a single board. How many boards does the carpenter need to buy to make the shelves?
- A. 2
- B. 8
- C. 3
- D. 4
Correct Answer & Rationale
Correct Answer: D
To determine how many boards are needed, first calculate the total length of wood required for the shelves. Each office has 4 shelves, and with 2 offices, that totals 8 shelves. Each shelf is 2 ¼ feet long, which equals 2.25 feet. Therefore, the total length required is 8 shelves x 2.25 feet = 18 feet. Each board is 6 feet long. Dividing the total length (18 feet) by the length of each board (6 feet) gives 3 boards. However, since each board can only be used for one shelf, and we can't cut a board to make multiple shelves, we need to round up to the nearest whole number of boards needed, which is 4. - Option A (2 boards) is insufficient for the total length required. - Option B (8 boards) exceeds the necessary amount. - Option C (3 boards) miscalculates the total need based on the cut requirement. Thus, 4 boards are necessary to accommodate all shelves without waste.
To determine how many boards are needed, first calculate the total length of wood required for the shelves. Each office has 4 shelves, and with 2 offices, that totals 8 shelves. Each shelf is 2 ¼ feet long, which equals 2.25 feet. Therefore, the total length required is 8 shelves x 2.25 feet = 18 feet. Each board is 6 feet long. Dividing the total length (18 feet) by the length of each board (6 feet) gives 3 boards. However, since each board can only be used for one shelf, and we can't cut a board to make multiple shelves, we need to round up to the nearest whole number of boards needed, which is 4. - Option A (2 boards) is insufficient for the total length required. - Option B (8 boards) exceeds the necessary amount. - Option C (3 boards) miscalculates the total need based on the cut requirement. Thus, 4 boards are necessary to accommodate all shelves without waste.