The daily cost, C(x), tor a company to produce x microscopes is given by the equation C(x) = 300 + 10.5x. What is the cost of producing 50 microscopes?
- A. $41,250
- B. $360.50
- C. $15,525
- D. $825
Correct Answer & Rationale
Correct Answer: D
To find the cost of producing 50 microscopes, substitute x = 50 into the cost equation C(x) = 300 + 10.5x. This yields C(50) = 300 + 10.5(50), resulting in C(50) = 300 + 525 = 825. Thus, the cost for 50 microscopes is $825. Option A ($41,250) is incorrect as it likely results from a miscalculation or misunderstanding of the equation. Option B ($360.50) underestimates the production cost by omitting the correct multiplication factor. Option C ($15,525) suggests an error in the calculation, possibly misinterpreting the coefficients in the equation.
To find the cost of producing 50 microscopes, substitute x = 50 into the cost equation C(x) = 300 + 10.5x. This yields C(50) = 300 + 10.5(50), resulting in C(50) = 300 + 525 = 825. Thus, the cost for 50 microscopes is $825. Option A ($41,250) is incorrect as it likely results from a miscalculation or misunderstanding of the equation. Option B ($360.50) underestimates the production cost by omitting the correct multiplication factor. Option C ($15,525) suggests an error in the calculation, possibly misinterpreting the coefficients in the equation.
Other Related Questions
Read the phrase below.
the quotient of three less than a number and six more than four times a number
Which expression is equivalent to this phrase?
- A. (3-x)/(4x + 6)
- B. (x - 3)(4x + 6)
- C. (x-3)/(4x + 6)
- D. 4x - 3 + 6
Correct Answer & Rationale
Correct Answer: C
The phrase describes a mathematical expression involving a number, denoted as \( x \). "Three less than a number" translates to \( x - 3 \), while "six more than four times a number" translates to \( 4x + 6 \). Therefore, the entire expression is the quotient of these two parts, resulting in \( \frac{x - 3}{4x + 6} \), which matches option C. Option A incorrectly suggests a subtraction in the numerator, altering the intended expression. Option B implies multiplication instead of division, misrepresenting the relationship. Option D presents a simplified expression rather than a quotient, which does not align with the original phrase.
The phrase describes a mathematical expression involving a number, denoted as \( x \). "Three less than a number" translates to \( x - 3 \), while "six more than four times a number" translates to \( 4x + 6 \). Therefore, the entire expression is the quotient of these two parts, resulting in \( \frac{x - 3}{4x + 6} \), which matches option C. Option A incorrectly suggests a subtraction in the numerator, altering the intended expression. Option B implies multiplication instead of division, misrepresenting the relationship. Option D presents a simplified expression rather than a quotient, which does not align with the original phrase.
Tina Is designing a cabin. One of her plans for the cabin is a rectangle twice as long as it is wide, with 10 feet (ft) of the length reserved for the Kitchen and the bathroom. The diagram shows this basic plan. Tina wants the area of the main room to be 300 square feet. Which equation can be used to find x, the width, in feet, of the main room?
- A. 2x^2 + 10x - 300 = 0
- B. 2x^2 - 10x - 300 = 0
- C. 2x^2 - 20x - 300 = 0
- D. 2x^2 + 20x - 300 = 0
Correct Answer & Rationale
Correct Answer: B
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
To determine the width \( x \) of the main room, we start with the area formula for a rectangle: Area = Length × Width. The cabin's length is twice the width, so it can be expressed as \( 2x \). Since 10 ft is allocated for the kitchen and bathroom, the length of the main room is \( 2x - 10 \). The equation for the area of the main room is therefore \( (2x - 10)x = 300 \), which simplifies to \( 2x^2 - 10x - 300 = 0 \), matching option B. Option A incorrectly adds \( 10x \) instead of subtracting, leading to an incorrect area calculation. Option C miscalculates the length by subtracting 20 instead of 10, while option D incorrectly adds 20, which does not reflect the reserved space. Thus, only option B accurately represents the relationship between length, width, and area.
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.
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 box?
- A. 2,262.85
- B. 77,502.59
- C. 136.24
- D. 25,834.20
Correct Answer & Rationale
Correct Answer: B
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.
To find the volume of a rectangular prism, multiply its depth, height, and width. In this case, the volume calculation is 34.25 in. (depth) × 69.37 in. (height) × 32.62 in. (width), which equals approximately 77,502.59 cubic inches. Option A (2,262.85) is far too small, likely resulting from an incorrect calculation or misunderstanding of the dimensions. Option C (136.24) represents an even smaller volume, which does not align with the dimensions given. Option D (25,834.20) is also incorrect, as it underestimates the overall volume significantly. Thus, only option B accurately reflects the computed volume of the shipping box.