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.
Other Related Questions
Select the factors for the following expression 2x^2 - xy - 3y^2
- A. (2x+3y)(x-y)
- B. (x+y)(2x-3y)
- C. (2x-y)(x+3y)
- D. (2x-3y)(x+y)
Correct Answer & Rationale
Correct Answer: D
To factor the expression \(2x^2 - xy - 3y^2\), we look for two binomials that multiply to give the original expression. Option D, \((2x-3y)(x+y)\), expands to \(2x^2 + 2xy - 3xy - 3y^2\), which simplifies to \(2x^2 - xy - 3y^2\), matching the original expression. Option A, \((2x+3y)(x-y)\), expands to \(2x^2 - 2xy + 3xy - 3y^2\), resulting in \(2x^2 + xy - 3y^2\), which is incorrect. Option B, \((x+y)(2x-3y)\), gives \(2x^2 - 3xy + 2xy - 3y^2\), simplifying to \(2x^2 - xy - 3y^2\), but the signs do not match the original expression. Option C, \((2x-y)(x+3y)\), expands to \(2x^2 + 6xy - xy - 3y^2\), leading to \(2x^2 + 5xy - 3y^2\), which is also incorrect. Thus, only Option D correctly factors the expression.
To factor the expression \(2x^2 - xy - 3y^2\), we look for two binomials that multiply to give the original expression. Option D, \((2x-3y)(x+y)\), expands to \(2x^2 + 2xy - 3xy - 3y^2\), which simplifies to \(2x^2 - xy - 3y^2\), matching the original expression. Option A, \((2x+3y)(x-y)\), expands to \(2x^2 - 2xy + 3xy - 3y^2\), resulting in \(2x^2 + xy - 3y^2\), which is incorrect. Option B, \((x+y)(2x-3y)\), gives \(2x^2 - 3xy + 2xy - 3y^2\), simplifying to \(2x^2 - xy - 3y^2\), but the signs do not match the original expression. Option C, \((2x-y)(x+3y)\), expands to \(2x^2 + 6xy - xy - 3y^2\), leading to \(2x^2 + 5xy - 3y^2\), which is also incorrect. Thus, only Option D correctly factors the expression.
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.
Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in your answer.
A company received a shipment of 8 boxes of metal brackets.
• There are 20 metal brackets in each box.
• The total weight of the shipment is 48 pounds.
What is the weight, in pounds, of each metal bracket?
Correct Answer & Rationale
Correct Answer: 0.3
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
Multiply (5x - 1)(5x - 1)
- A. 25x^2 + 1
- B. 25x^2 - 1
- C. 25x^2 - 2x + 1
- D. 25x^2 - 10x + 1
Correct Answer & Rationale
Correct Answer: D
To find the product of (5x - 1)(5x - 1), we can use the formula for squaring a binomial, which states that (a - b)² = a² - 2ab + b². Here, a = 5x and b = 1. Calculating this gives: - a² = (5x)² = 25x² - 2ab = 2(5x)(1) = 10x - b² = 1² = 1 Thus, the expanded form is 25x² - 10x + 1, matching option D. Option A (25x² + 1) incorrectly omits the linear term. Option B (25x² - 1) miscalculates the constant term. Option C (25x² - 2x + 1) incorrectly computes the coefficient of the x term. Each of these options fails to accurately reflect the multiplication of the binomials.
To find the product of (5x - 1)(5x - 1), we can use the formula for squaring a binomial, which states that (a - b)² = a² - 2ab + b². Here, a = 5x and b = 1. Calculating this gives: - a² = (5x)² = 25x² - 2ab = 2(5x)(1) = 10x - b² = 1² = 1 Thus, the expanded form is 25x² - 10x + 1, matching option D. Option A (25x² + 1) incorrectly omits the linear term. Option B (25x² - 1) miscalculates the constant term. Option C (25x² - 2x + 1) incorrectly computes the coefficient of the x term. Each of these options fails to accurately reflect the multiplication of the binomials.