To analyze the model \( y = 2.5x + 5 \):
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Understanding the equation:
- \( x \) represents the number of miles between the shop and the delivery location.
- \( y \) represents the total time in minutes from when an order is placed until it is delivered.
- The equation indicates that the delivery time consists of two parts: a constant preparation time of 5 minutes (the y-intercept) and a variable travel time that depends on the distance (the term \( 2.5x \)).
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Breaking down the components:
- The constant term (5 minutes) reflects the average preparation time for food.
- The coefficient of \( x \) (which is 2.5) represents the delivery time per mile. Therefore, it takes 2.5 minutes to travel 1 mile.
Now, let's evaluate the statements based on the model:
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On average, the delivery person travels 5 miles every 1 minute.
- This is incorrect. The delivery time is 2.5 minutes per mile, not 5 miles per minute.
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On average, the delivery person travels 2.5 miles every 1 minute.
- This is also incorrect. The delivery person travels 1 mile in 2.5 minutes, not 2.5 miles in 1 minute.
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On average, it takes the delivery person 5 minutes to travel 1 mile.
- This is incorrect. It takes 2.5 minutes to travel 1 mile, not 5 minutes.
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The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.
- This is incorrect. The preparation time is represented by the constant term of 5 minutes.
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On average, it takes the delivery person 2.5 minutes to travel 1 mile.
- This statement is correct. This matches our understanding of how the equation represents travel time.
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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. This is directly indicated by the y-intercept of the equation.
Correct Statements:
- 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.