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.
Other Related Questions
What is the volume, in cubic inches, of the pyramid?
- A. 21,600
- B. 1,440
- C. 7,200
- D. 5,760
Correct Answer & Rationale
Correct Answer: C
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). In this case, with the appropriate base area and height values, the calculation leads to a volume of 7,200 cubic inches. Option A, 21,600, is too high, suggesting an error in calculations or misinterpretation of the dimensions. Option B, 1,440, underestimates the volume, likely due to incorrect base area or height. Option D, 5,760, also falls short, as it does not account for the correct scaling of the dimensions. Thus, 7,200 cubic inches accurately reflects the pyramid's volume based on the given measurements.
The Willis Canyon Dam releases an average of 1,733,400 cubic feet of water every day. Based on that average, how many cubic feet of water does the dam release every minute?
Correct Answer & Rationale
Correct Answer: 1200.4167
To find the water released per minute, divide the daily release by the number of minutes in a day. There are 1,440 minutes in a day (24 hours x 60 minutes). Dividing 1,733,400 cubic feet by 1,440 minutes gives approximately 1,200.4167 cubic feet per minute. Other options are incorrect because they either miscalculate the division or fail to account for the total number of minutes in a day, leading to significantly higher or lower values. Accurate conversion of daily figures to minute rates is crucial for proper understanding.
To find the water released per minute, divide the daily release by the number of minutes in a day. There are 1,440 minutes in a day (24 hours x 60 minutes). Dividing 1,733,400 cubic feet by 1,440 minutes gives approximately 1,200.4167 cubic feet per minute. Other options are incorrect because they either miscalculate the division or fail to account for the total number of minutes in a day, leading to significantly higher or lower values. Accurate conversion of daily figures to minute rates is crucial for proper understanding.
Which graph represents a function?
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A.
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B.
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C.
Correct Answer & Rationale
Correct Answer: B
To determine which graph represents a function, we apply the Vertical Line Test. This test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function. Option A fails this test, as a vertical line can intersect the graph at multiple points, indicating it is not a function. Option C also does not satisfy the criteria, showing multiple intersections with vertical lines. In contrast, Option B passes the Vertical Line Test, as any vertical line drawn will intersect the graph at only one point, confirming it represents a function.
To determine which graph represents a function, we apply the Vertical Line Test. This test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function. Option A fails this test, as a vertical line can intersect the graph at multiple points, indicating it is not a function. Option C also does not satisfy the criteria, showing multiple intersections with vertical lines. In contrast, Option B passes the Vertical Line Test, as any vertical line drawn will intersect the graph at only one point, confirming it represents a function.
Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?
- A. x ? 6
- B. x ? 30
- C. x ? 30
- D. x ? 6
Correct Answer & Rationale
Correct Answer: D
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.