To analyze the equation \( y = 2.5x + 5 \), where \( y \) is the time in minutes and \( x \) is the distance in miles, we can break down the components of the model.
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The term \( 2.5x \) represents the time taken to travel \( x \) miles. Specifically, if \( x = 1 \), then: \[ y = 2.5(1) + 5 = 2.5 + 5 = 7.5 \text{ minutes} \] This means that for 1 mile, the travel time is 2.5 minutes, and there is an additional preparation time of 5 minutes.
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Therefore, the average time it takes to prepare the food for delivery is 5 minutes, regardless of the distance.
From this analysis, we can evaluate the options:
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On average, it takes the delivery person 2.5 minutes to travel 1 mile. - CORRECT (This is the travel time per mile.)
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The average amount of time the shop needs to prepare the food for delivery is 5 minutes. - CORRECT (This is explicitly given in the equation.)
Thus, the correct statements according to the model 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.