To determine which equation represents the scenario where a major-league outfielder can throw a baseball at a speed of 105 miles per hour (which converts to 154 feet per second), we need to understand what each equation is calculating.
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Options A and B multiply either 154 or 105 by 90. The multiple suggests a distance covered over time, where 90 could represent time in seconds. Thus:
- A: \(154 \times 90 = 13,860\) feet (distance thrown if thrown at 154 ft/s for 90 seconds).
- B: \(105 \times 90 = 9,450\) feet (distance thrown if thrown at 105 mph for 90 seconds).
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Option C multiplies 154 by 2.5, which may imply a distance thrown over a shorter time frame (2.5 seconds).
- \(154 \times 2.5 = 385\) feet (distance thrown at maximum speed for 2.5 seconds).
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Option D multiplies 105 by 2.5.
- \(105 \times 2.5 = 262.5\) feet (distance thrown at 105 mph for 2.5 seconds).
Based on the description provided in the scenario (maximum throwing speed of 105 mph or 154 ft/s), options A and B seem to quantify distance over long time frames (90 seconds) using both measurements, but options C and D calculate based on a shorter duration using the relevant conversions.
All options could be valid, depending on what specific scenario or time frame you're considering. However, if we're focusing on a practical immediate throw distance within a short time frame, options C or D may align more closely with typical throw distances.
Ultimately, without additional context on what "the graph" shows or confirms, it's hard to determine the “correct” one if we are considering maximum throw calculations. However, if the goal is simply about the immediate conversion and understanding of the throw's distance at both maximum speeds over shorter time frames, C seems to fit as a sensible equation for immediate throw distance (time of 2.5 seconds).
So, if you are looking for a representation of a major league outfielder's throw, C (154 x 2.5 = 385) becomes a compelling choice based on the 154 ft/s conversion.
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