To determine the prediction about the length of Charles's fishing trip based on the line of best fit, which is given by the equation \( y = 50x + 75 \), we can calculate the price for each proposed trip duration and check the responses.
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For a 6-hour trip: \[ y = 50(6) + 75 = 300 + 75 = 375 \] This indicates that a 6-hour trip costs $375, which is less than $400. So the first response is correct.
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For a $200 trip: Set \( y = 200 \) and solve for \( x \): \[ 200 = 50x + 75 \implies 125 = 50x \implies x = 2.5 \] This means that for $200, Charles can travel for 2.5 hours, not 2 hours, making the second response incorrect.
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For a 1-hour trip: \[ y = 50(1) + 75 = 50 + 75 = 125 \] This indicates that a 1-hour trip costs $125, which is not less than $100. So the third response is incorrect.
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For a 3-hour trip: \[ y = 50(3) + 75 = 150 + 75 = 225 \] This shows that a 3-hour trip costs $225. So the fourth response about paying $300 for a 3-hour trip is incorrect.
Based on these calculations, the only correct prediction is:
Charles can take a 6-hour trip for less than $400.