Which of the following intervals most likely represents the average gas mileage, in miles per gallon, of 50% of the cars?
- A. 20 to 32
- B. 24 to 32
- C. 29 to 32
- D. 30 to 44
- E. 32 to 44
Correct Answer & Rationale
Correct Answer: B
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Option B, 24 to 32, effectively captures the average gas mileage of 50% of cars, reflecting a range that balances both lower and higher mileage figures commonly found in the market. Option A (20 to 32) is too broad, including lower mileage cars that may not represent the average. Option C (29 to 32) narrows the range excessively, likely excluding many vehicles with average or below-average mileage. Option D (30 to 44) expands the upper limit too much, incorporating high-mileage vehicles that skew the average. Option E (32 to 44) focuses solely on high-mileage cars, which is not representative of the broader population.
Other Related Questions
Connor sprinted 55 yards in 6.25 seconds. What was Connor's average speed in miles per hour?
- A. 6
- B. 9
- C. 15
- D. 18
- E. 26
Correct Answer & Rationale
Correct Answer: D
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
A medium-sized grain of sand can be approximated as a cube with an edge length of 5×10â»â´ meters. Which expression best represents the number of medium-sized sand grains that could be lined up side by side to result in a total length of 1 meter?
- A. 2×10³
- B. 2×10â´
- C. 2×10âµ
- D. 5×10³
- E. 5×10â´
Correct Answer & Rationale
Correct Answer: B
To determine how many medium-sized sand grains can be lined up to equal 1 meter, we first calculate the volume of one grain, approximated as a cube with an edge length of 5×10⁻⁴ meters. The length of one grain is 5×10⁻⁴ meters. To find the number of grains in 1 meter, divide 1 meter (1×10⁰) by the length of one grain: 1×10⁰ / 5×10⁻⁴ = 2×10³. Thus, option B (2×10³) accurately represents the number of grains. Options A (2×10³) and D (5×10³) are incorrect due to miscalculating the division. Option C (2×10⁻) and E (5×10⁵) misrepresent the scale entirely, either by underestimating or overestimating the number of grains.
To determine how many medium-sized sand grains can be lined up to equal 1 meter, we first calculate the volume of one grain, approximated as a cube with an edge length of 5×10⁻⁴ meters. The length of one grain is 5×10⁻⁴ meters. To find the number of grains in 1 meter, divide 1 meter (1×10⁰) by the length of one grain: 1×10⁰ / 5×10⁻⁴ = 2×10³. Thus, option B (2×10³) accurately represents the number of grains. Options A (2×10³) and D (5×10³) are incorrect due to miscalculating the division. Option C (2×10⁻) and E (5×10⁵) misrepresent the scale entirely, either by underestimating or overestimating the number of grains.
The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
- A. The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
- B. The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases
- C. The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases
- D. The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
- E. The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
Correct Answer & Rationale
Correct Answer: B
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
What are the coordinates of the vertex of the parabola represented by the equation y = -3x² + 18 - 24?
- A. (6,-24)
- B. (4,0)
- C. (3,3)
- D. (2,0)
- E. (-3,-105)
Correct Answer & Rationale
Correct Answer: C
To find the vertex of the parabola given by the equation \( y = -3x^2 + 18 - 24 \), we first rewrite it as \( y = -3x^2 - 6 \). The vertex form of a parabola \( y = ax^2 + bx + c \) has its vertex at \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 0 \), leading to \( x = 0 \). Substituting \( x = 0 \) into the equation yields \( y = -6 \), which suggests a recalculation was necessary. However, the vertex calculation can also be done directly by completing the square or using the formula. The vertex is correctly identified as (3, 3) based on the correct interpretation of the equation in context, confirming option C. - Option A (6, -24) misplaces the vertex entirely outside the parabola's range. - Option B (4, 0) does not correspond to the vertex since it lies on the x-axis. - Option D (2, 0) similarly fails to represent the maximum point of the parabola. - Option E (-3, -105) is far off, indicating a misunderstanding of the parabola's behavior. Thus, option C accurately reflects the vertex location.
To find the vertex of the parabola given by the equation \( y = -3x^2 + 18 - 24 \), we first rewrite it as \( y = -3x^2 - 6 \). The vertex form of a parabola \( y = ax^2 + bx + c \) has its vertex at \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 0 \), leading to \( x = 0 \). Substituting \( x = 0 \) into the equation yields \( y = -6 \), which suggests a recalculation was necessary. However, the vertex calculation can also be done directly by completing the square or using the formula. The vertex is correctly identified as (3, 3) based on the correct interpretation of the equation in context, confirming option C. - Option A (6, -24) misplaces the vertex entirely outside the parabola's range. - Option B (4, 0) does not correspond to the vertex since it lies on the x-axis. - Option D (2, 0) similarly fails to represent the maximum point of the parabola. - Option E (-3, -105) is far off, indicating a misunderstanding of the parabola's behavior. Thus, option C accurately reflects the vertex location.