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
Solve the inequality for x: (1/8)x ? (1/2)x + 15
- A. x ? -24
- B. x ? -40
- C. x ? -40
- D. x ? -24
Correct Answer & Rationale
Correct Answer: C
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).
To solve the inequality \((1/8)x < (1/2)x + 15\), first, subtract \((1/2)x\) from both sides, yielding \(-\frac{3}{8}x < 15\). Next, multiply both sides by \(-\frac{8}{3}\) (remembering to reverse the inequality), resulting in \(x > -40\). Option A (\(x < -24\)) and Option D (\(x < -24\)) suggest \(x\) values that are too high, contradicting the derived solution. Option B (\(x < -40\)) incorrectly indicates that \(x\) must be less than \(-40\), rather than greater. Thus, Option C accurately represents the solution \(x > -40\).
What is the equation, in standard form, of the line that passes through the points (-3, -4) and (3, -12)?
- A. 4x + 3y = 24
- B. 3x + 4y = -25
- C. 4x + 3y = -24
- D. 3x + 4y = -39
Correct Answer & Rationale
Correct Answer: C
To find the equation of the line through the points (-3, -4) and (3, -12), we first calculate the slope (m). The slope is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - (-4)}{3 - (-3)} = \frac{-8}{6} = -\frac{4}{3} \). Using the slope-intercept form \( y = mx + b \), we can find the y-intercept (b) by substituting one of the points. This leads us to the equation \( y = -\frac{4}{3}x - 4 \). Rewriting it in standard form gives \( 4x + 3y = -24 \), matching option C. Option A does not satisfy the points, as substituting either point does not yield a true statement. Option B also fails for the same reason, as neither point satisfies this equation. Option D is incorrect as substituting the points results in contradictions. Thus, option C is the only one that accurately represents the line through the given points.
To find the equation of the line through the points (-3, -4) and (3, -12), we first calculate the slope (m). The slope is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - (-4)}{3 - (-3)} = \frac{-8}{6} = -\frac{4}{3} \). Using the slope-intercept form \( y = mx + b \), we can find the y-intercept (b) by substituting one of the points. This leads us to the equation \( y = -\frac{4}{3}x - 4 \). Rewriting it in standard form gives \( 4x + 3y = -24 \), matching option C. Option A does not satisfy the points, as substituting either point does not yield a true statement. Option B also fails for the same reason, as neither point satisfies this equation. Option D is incorrect as substituting the points results in contradictions. Thus, option C is the only one that accurately represents the line through the given points.
The manager of a shipping company plans to use a small truck to ship pipes: The truck has a flatbed trailer with a rectangular surface that is 27 feet long and 8 feet wide. The truck will travel from Atherton to Bakersfield, where some pipes will be delivered, and then on to Castlewood to deliver the remaining pipes. The map shows the roads that connect Atherton. Bakersfield. and Castlewood.
The manager is planning to buy a new truck with better gas mileage. He collected data bout the gas mileage of one of the company's trucks. The table shows the gas mileage or that truck based on the distances traveled on five recent trips.
The new truck the manager plans to buy has an advertised gas mileage of 8 miles per gallon. To the nearest percent, how much greater is the gas mileage of the new truck than the lowest gas mileage recorded for the current truck?
- A. 14
- B. 25
- C. 23
- D. 33
Correct Answer & Rationale
Correct Answer: D
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
To determine how much greater the new truck's gas mileage is compared to the lowest recorded gas mileage of the current truck, first identify the lowest gas mileage from the provided data. If the lowest mileage is, for example, 6 miles per gallon, the difference between the new truck's 8 miles per gallon and the lowest mileage is 2 miles per gallon. To find the percentage increase, divide the difference (2) by the lowest mileage (6) and multiply by 100, resulting in approximately 33%. Options A (14%), B (25%), and C (23%) are incorrect as they do not accurately reflect the percentage increase based on the lowest mileage recorded.
What is the slope of the line shown on the graph
- A. -0.333333333
- B. -3
- C. 3
- D. 1\3
Correct Answer & Rationale
Correct Answer: D
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.