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On a school baseball diamond, the distance from the pitcher’s mound to home plate is about 15 m . Data for the pitching speed o...Question
On a school baseball diamond, the distance from the pitcher’s mound to home plate is about 15 m
. Data for the pitching speed of two pitchers was collected by finding the number of seconds it took for four pitched balls to go from the mound to home plate. Lou’s times were 1.2 s
, 2.0 s
, 3.1 s
, and 2.5 s
. Jamie’s times were 1.7 s
, 2.3 s
, 3.0 s
, and 2.2 s
. Who was the better pitcher (had the higher average speed), and what was their average speed in m/s
?(1 point)
Responses
Jamie, 1.6 m/s
Jamie, 1.6 meters per second
Jamie, 1.7 m/s
Jamie, 1.7 meters per second
Lou, 1.6 m/s
Lou, 1.6 meters per second
Lou, 1.7 m/s
Lou, 1.7 meters per second
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. Data for the pitching speed of two pitchers was collected by finding the number of seconds it took for four pitched balls to go from the mound to home plate. Lou’s times were 1.2 s
, 2.0 s
, 3.1 s
, and 2.5 s
. Jamie’s times were 1.7 s
, 2.3 s
, 3.0 s
, and 2.2 s
. Who was the better pitcher (had the higher average speed), and what was their average speed in m/s
?(1 point)
Responses
Jamie, 1.6 m/s
Jamie, 1.6 meters per second
Jamie, 1.7 m/s
Jamie, 1.7 meters per second
Lou, 1.6 m/s
Lou, 1.6 meters per second
Lou, 1.7 m/s
Lou, 1.7 meters per second
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Answers
GPT-4o mini
To find out who was the better pitcher based on average speed, we need to calculate the average time for both pitchers and then determine their speeds.
**Step 1: Calculate the average time for each pitcher.**
**Lou's times:**
- 1.2 s
- 2.0 s
- 3.1 s
- 2.5 s
Average time for Lou:
\[
\text{Average time}_{\text{Lou}} = \frac{1.2 + 2.0 + 3.1 + 2.5}{4} = \frac{8.8}{4} = 2.2 \text{ s}
\]
**Jamie’s times:**
- 1.7 s
- 2.3 s
- 3.0 s
- 2.2 s
Average time for Jamie:
\[
\text{Average time}_{\text{Jamie}} = \frac{1.7 + 2.3 + 3.0 + 2.2}{4} = \frac{9.2}{4} = 2.3 \text{ s}
\]
**Step 2: Calculate the average speed for each pitcher.**
Average speed is calculated using the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
For our case, the distance from the pitcher’s mound to home plate is 15 m.
**Speed for Lou:**
\[
\text{Speed}_{\text{Lou}} = \frac{15 \text{ m}}{2.2 \text{ s}} \approx 6.82 \text{ m/s}
\]
**Speed for Jamie:**
\[
\text{Speed}_{\text{Jamie}} = \frac{15 \text{ m}}{2.3 \text{ s}} \approx 6.52 \text{ m/s}
\]
**Conclusion:**
- Lou's average speed: approximately 6.82 m/s
- Jamie's average speed: approximately 6.52 m/s
**Answer:** Lou was the better pitcher, with an average speed of approximately 6.82 m/s. (Note that none of the provided responses match this, indicating possible confusion or error in problem context wording about speed.)
**Step 1: Calculate the average time for each pitcher.**
**Lou's times:**
- 1.2 s
- 2.0 s
- 3.1 s
- 2.5 s
Average time for Lou:
\[
\text{Average time}_{\text{Lou}} = \frac{1.2 + 2.0 + 3.1 + 2.5}{4} = \frac{8.8}{4} = 2.2 \text{ s}
\]
**Jamie’s times:**
- 1.7 s
- 2.3 s
- 3.0 s
- 2.2 s
Average time for Jamie:
\[
\text{Average time}_{\text{Jamie}} = \frac{1.7 + 2.3 + 3.0 + 2.2}{4} = \frac{9.2}{4} = 2.3 \text{ s}
\]
**Step 2: Calculate the average speed for each pitcher.**
Average speed is calculated using the formula:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]
For our case, the distance from the pitcher’s mound to home plate is 15 m.
**Speed for Lou:**
\[
\text{Speed}_{\text{Lou}} = \frac{15 \text{ m}}{2.2 \text{ s}} \approx 6.82 \text{ m/s}
\]
**Speed for Jamie:**
\[
\text{Speed}_{\text{Jamie}} = \frac{15 \text{ m}}{2.3 \text{ s}} \approx 6.52 \text{ m/s}
\]
**Conclusion:**
- Lou's average speed: approximately 6.82 m/s
- Jamie's average speed: approximately 6.52 m/s
**Answer:** Lou was the better pitcher, with an average speed of approximately 6.82 m/s. (Note that none of the provided responses match this, indicating possible confusion or error in problem context wording about speed.)