The daily cost, C(x), for 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 determine the cost of producing 50 microscopes, substitute x = 50 into the equation C(x) = 300 + 10.5x. This gives C(50) = 300 + 10.5(50) = 300 + 525 = 825. Thus, the total cost is $825. Option A ($41,250) is incorrect as it miscalculates the cost by multiplying incorrectly. Option B ($360.50) results from a misunderstanding of the equation, possibly neglecting the fixed cost. Option C ($15,525) likely arises from an error in multiplying the variable cost without adding the fixed cost. Each incorrect option fails to follow the proper calculation method outlined in the cost equation.
To determine the cost of producing 50 microscopes, substitute x = 50 into the equation C(x) = 300 + 10.5x. This gives C(50) = 300 + 10.5(50) = 300 + 525 = 825. Thus, the total cost is $825. Option A ($41,250) is incorrect as it miscalculates the cost by multiplying incorrectly. Option B ($360.50) results from a misunderstanding of the equation, possibly neglecting the fixed cost. Option C ($15,525) likely arises from an error in multiplying the variable cost without adding the fixed cost. Each incorrect option fails to follow the proper calculation method outlined in the cost equation.
Other Related Questions
The top speed of the aircraft carrier USS Enterprise is 33 knots. A knot is the speed of a ship in nautical miles per hour. What is the top speed, in miles per hour? (1 nautical mile = 6,076 feet; 1 mile - 5,280 feet)
- A. 24 miles per hour
- B. 38 miles per hour
- C. 33 miles per hour
- D. 29 miles per hour
Correct Answer & Rationale
Correct Answer: B
To convert knots to miles per hour, it’s essential to understand the relationship between nautical miles and standard miles. Since 1 nautical mile equals 6,076 feet and 1 mile equals 5,280 feet, we can set up the conversion: 1 nautical mile = 6,076 feet / 5,280 feet/mile = 1.151 miles. Thus, to convert 33 knots to miles per hour: 33 knots × 1.151 miles/nautical mile = 38.0 miles per hour. Option A (24 mph) is too low, failing to account for the conversion factor. Option C (33 mph) incorrectly assumes knots and miles per hour are equivalent. Option D (29 mph) underestimates the conversion, not reaching the correct calculation.
To convert knots to miles per hour, it’s essential to understand the relationship between nautical miles and standard miles. Since 1 nautical mile equals 6,076 feet and 1 mile equals 5,280 feet, we can set up the conversion: 1 nautical mile = 6,076 feet / 5,280 feet/mile = 1.151 miles. Thus, to convert 33 knots to miles per hour: 33 knots × 1.151 miles/nautical mile = 38.0 miles per hour. Option A (24 mph) is too low, failing to account for the conversion factor. Option C (33 mph) incorrectly assumes knots and miles per hour are equivalent. Option D (29 mph) underestimates the conversion, not reaching the correct calculation.
The equation and the graph represent two linear functions.
Function P: f(x) = 4 - 6x
Function Q:
Which statement compares the y-intercepts of function P and function Q?
- A. The y-intercept of function P is -6 which is less than the y-intercept of function Q.
- B. The y-intercept of function P is 4 which is equal to the y-intercept of function Q.
- C. The y-intercept of function P is -6 which is greater than the y-intercept of function Q.
- D. The y-intercept of function P is 4 which is greater than the y-intercept of function Q.
Correct Answer & Rationale
Correct Answer: D
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
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.
Type your answer in the box. You may use numbers, a decimal point (.), and/or negative sign (-) in your answer.
One evening on her walk, Laura walks across the field from point W back to the gate at point G. What is the distance she walks, in feet, from point W to point G?
Correct Answer & Rationale
Correct Answer: 250
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
The graph shows a handyman's fees, f(x), in terms of the hours worked, x. The fees include a fuel charge and an hourly rate. What is the handyman's hourly rate?
- A. $5
- B. $55
- C. $30
- D. $25
Correct Answer & Rationale
Correct Answer: D
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.