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
The width of a painting is 24 centimeters shorter than its length, x. The area of the painting is 4,081 square centimeters. Which equation could be used to find the dimensions of the painting?
- A. x^2 - 24x - 4,081 = 0
- B. x^2 + 24x - 4,081 = 0
- C. x^2 + 24x + 4,081 = 0
- D. x^2 - 24x + 4,081 = 0
Correct Answer & Rationale
Correct Answer: A
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
To find the dimensions of the painting, we start with the relationship between length and width. The width is 24 cm shorter than the length \(x\), so it can be expressed as \(x - 24\). The area of a rectangle is given by the product of its length and width, resulting in the equation \(x(x - 24) = 4,081\). Expanding this leads to \(x^2 - 24x - 4,081 = 0\), which matches option A. Option B incorrectly adds 24x, leading to an incorrect area calculation. Option C incorrectly adds 24 and includes a positive constant, which does not represent the area. Option D incorrectly adds 4,081 and has a positive term that does not reflect the relationship between length and width.
On Monday; Alicia buys x shirts at $8 each and y slacks at $25 each. On Wednesday, Alicia returns 2 pairs of slacks. Which expression represents the total value of her purchases?
- A. 8x + 23y
- B. 8x + 25(y - 2)
- C. 8x - 2) + 25y
- D. 8x + 25y - 2
Correct Answer & Rationale
Correct Answer: B
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
To calculate the total value of Alicia's purchases, we need to account for the cost of shirts and slacks, as well as the return of 2 pairs of slacks. Option B, \(8x + 25(y - 2)\), correctly reflects the initial cost of \(x\) shirts at $8 each and \(y\) slacks at $25 each, while subtracting the cost of the 2 returned slacks, which is \(2 \times 25\). Option A, \(8x + 23y\), incorrectly reduces the price of slacks to $23, which is not stated in the problem. Option C, \(8x - 2 + 25y\), miscalculates by subtracting $2 instead of the cost of the returned slacks. Option D, \(8x + 25y - 2\), also incorrectly subtracts $2 instead of the total cost of the slacks returned.
Solve the inequality for x: -4/3 x + 4 ? 16
- A. x??9
- B. x??9
- C. x??9
- D. x?9
Correct Answer & Rationale
Correct Answer: A
To solve the inequality \(-\frac{4}{3}x + 4 < 16\), first isolate \(x\) by subtracting 4 from both sides, resulting in \(-\frac{4}{3}x < 12\). Next, multiply both sides by \(-\frac{3}{4}\), remembering to reverse the inequality sign, yielding \(x > 9\). Options B and C incorrectly suggest \(x < 9\), which contradicts our solution. Option D, stating \(x \leq 9\), also misrepresents the inequality since it does not include values greater than 9. Thus, only option A accurately reflects the solution \(x > 9\).
To solve the inequality \(-\frac{4}{3}x + 4 < 16\), first isolate \(x\) by subtracting 4 from both sides, resulting in \(-\frac{4}{3}x < 12\). Next, multiply both sides by \(-\frac{3}{4}\), remembering to reverse the inequality sign, yielding \(x > 9\). Options B and C incorrectly suggest \(x < 9\), which contradicts our solution. Option D, stating \(x \leq 9\), also misrepresents the inequality since it does not include values greater than 9. Thus, only option A accurately reflects the solution \(x > 9\).
Which pair of equations represents parallel lines?
- A. -2x + y + 2 = 0, y = -(1/2)x - 4
- B. 3x + y = -8, y = 3x - 8
- C. x + 2y = 8, -x - 2y = 3
- D. -(2/3)x + y = 12, y = -(3/2)x - 1
Correct Answer & Rationale
Correct Answer: C
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.
To identify parallel lines, the slopes of the equations must be equal. Option A has slopes of 1/2 and -1/2, which are not equal. Option B has slopes of 3 and 3, indicating the lines are parallel; however, it is not the correct answer as it does not match the requirement for both equations. Option C has the first equation rearranged to slope -1/2 and the second to slope -1/2, confirming they are parallel. Option D features slopes of 2/3 and -3/2, which are also not equal, indicating the lines intersect. Thus, only option C accurately represents parallel lines.