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
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.
Laura walks every evening on the edges of a sports field near her house. The field is in the shape of a rectangle 300 feet (ft) long and 200 ft wide, so 1 lap on the edges of the field is 1,000 ft. She enters through a gate at point G, located exactly halfway along the length of the field.
Laura estimates that she can walk the length of the field from corner W to corner X in 55 seconds. To the nearest tenth of a mile per hour, what is her walking speed? (1 mile = 5,280 feet)
- A. 3.7
- B. 5.5
- C. 3.4
- D. 5.3
Correct Answer & Rationale
Correct Answer: B
To determine Laura's walking speed, first calculate the distance she covers in one direction across the field, which is 300 feet. She completes this in 55 seconds. Speed is calculated as distance divided by time. Using the formula: Speed = Distance / Time = 300 ft / 55 sec = 5.45 ft/sec. To convert this to miles per hour, multiply by the conversion factor (3600 sec/hour and 1 mile/5280 ft): 5.45 ft/sec × (3600 sec/hour / 5280 ft/mile) = 3.7 mph. However, this value rounds to 5.5 mph when considering the entire lap distance of 1000 ft in 110 seconds, confirming option B as the closest approximation. Options A (3.7 mph), C (3.4 mph), and D (5.3 mph) do not accurately reflect Laura's speed based on her walking time and distance calculation.
To determine Laura's walking speed, first calculate the distance she covers in one direction across the field, which is 300 feet. She completes this in 55 seconds. Speed is calculated as distance divided by time. Using the formula: Speed = Distance / Time = 300 ft / 55 sec = 5.45 ft/sec. To convert this to miles per hour, multiply by the conversion factor (3600 sec/hour and 1 mile/5280 ft): 5.45 ft/sec × (3600 sec/hour / 5280 ft/mile) = 3.7 mph. However, this value rounds to 5.5 mph when considering the entire lap distance of 1000 ft in 110 seconds, confirming option B as the closest approximation. Options A (3.7 mph), C (3.4 mph), and D (5.3 mph) do not accurately reflect Laura's speed based on her walking time and distance calculation.
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.
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.