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
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.
The weight of a red blood cell is about 4.5 × 10*11 grams. A blood sample has 1.6 × 10 red blood cells. What is the total weight, in grams, of red blood cells in the sample the answer with the correct scientific notation.
- A. 2.9 × 10^18
- B. 7.2 × 10^(-4)
- C. 7.2 × 10^(-77)
- D. 6.1 × 10^(-4)
Correct Answer & Rationale
Correct Answer: B
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
To find the total weight of the red blood cells, multiply the weight of one red blood cell (4.5 × 10^-11 grams) by the total number of cells (1.6 × 10^6). This calculation yields 7.2 × 10^-5 grams, which can be expressed in scientific notation as 7.2 × 10^(-4) grams. Option A (2.9 × 10^18) is incorrect because it suggests an unrealistically high total weight, indicating a misunderstanding of scientific notation. Options C (7.2 × 10^(-77)) and D (6.1 × 10^(-4)) also fail to represent the correct multiplication, with C being far too small and D lacking accuracy in the calculated value.
Which expression is undefined over the real numbers?
- A. (-3)^0
- B. 0/4
- C. |-2|
- D. (-7)^(1/2)
Correct Answer & Rationale
Correct Answer: D
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.
The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.
What is the slope of the line represented by the table?
- A. -4
- B. -2.5
- C. -2
- D. -0.5
Correct Answer & Rationale
Correct Answer: C
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.