Bot GPT 4-o mini To analyze the equation \( y = 2.5x + 5 \), where \( x \) is the distance in miles and \( y \) is the total delivery time in minutes, we can deduce the following:
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The term \( 5 \) represents the fixed time (in minutes) that it takes for food preparation before the delivery begins. This can be interpreted as the average amount of time the shop needs to prepare the food for delivery.
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The coefficient \( 2.5 \) indicates that for each mile traveled, an additional 2.5 minutes is added to the total time. This means that it takes the delivery person an average of 2.5 minutes to travel 1 mile.
Now let's evaluate the given statements:
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On average, it takes the delivery person 2.5 minutes to travel 1 mile. - This statement is correct because, according to the equation, for every mile (1 unit of \( x \)), it adds 2.5 minutes to \( y \).
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On average, the delivery person travels 2.5 miles every 1 minute. - This statement is incorrect. Since it takes 2.5 minutes to travel 1 mile, they would travel 1 mile in 2.5 minutes, which means they travel less than 1 mile in 1 minute.
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On average, it takes the delivery person 5 minutes to travel 1 mile. - This statement is incorrect. As established earlier, it takes 2.5 minutes to travel 1 mile.
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On average, the delivery person travels 5 miles every 1 minute. - This statement is incorrect. The speed implied by the equation doesn’t support this.
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The average amount of time the shop needs to prepare the food for delivery is 5 minutes. - This statement is correct as the constant \( 5 \) in the equation represents the preparation time before delivery starts.
Based on this analysis, the two correct statements are:
- On average, it takes the delivery person 2.5 minutes to travel 1 mile.
- The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
1 answer