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The total amount of money that needs to be paid to wholesale a batch of cakes is considered a function of the quantity it has wholesed. To estimate this relationship, a cake wholesaler randomly selected 20 customers and collected information on their patterns of total payment amount (Y, USD) and wholesale quantity (X, a cake) in May of this year. Assuming a linear relationship between Y and X, the professor uses the least squares method and finds that the Y intercept = 15.90 and the slope = -0.55. Based on this information, the slope should be interpreted as:A.For each additional cake purchase, the total amount that customers will pay for wholesale cakes is estimated to be decreased by $0.55B.For each additional cake purchase, the total amount customers will have to pay for wholesale cakes is estimated to increase by $15.90C.For each additional cake purchase, the total amount customers will pay for wholesale cakes is estimated to decrease by $15.35D.For each additional cake purchase, the total amount paid by the customer for wholesale cake is estimated to increase by $0.55SUBMIT ANSWER

Question

The total amount of money that needs to be paid to wholesale a batch of cakes is considered a function of the quantity it has wholesed. To estimate this relationship, a cake wholesaler randomly selected 20 customers and collected information on their patterns of total payment amount (Y, USD) and wholesale quantity (X, a cake) in May of this year. Assuming a linear relationship between Y and X, the professor uses the least squares method and finds that the Y intercept = 15.90 and the slope = -0.55. Based on this information, the slope should be interpreted as:A.For each additional cake purchase, the total amount that customers will pay for wholesale cakes is estimated to be decreased by 0.55B.Foreachadditionalcakepurchase,thetotalamountcustomerswillhavetopayforwholesalecakesisestimatedtoincreaseby0.55B.For each additional cake purchase, the total amount customers will have to pay for wholesale cakes is estimated to increase by 15.90C.For each additional cake purchase, the total amount customers will pay for wholesale cakes is estimated to decrease by 15.35D.Foreachadditionalcakepurchase,thetotalamountpaidbythecustomerforwholesalecakeisestimatedtoincreaseby15.35D.For each additional cake purchase, the total amount paid by the customer for wholesale cake is estimated to increase by 0.55SUBMIT ANSWER

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Solution

The correct interpretation of the slope in this context is: A. For each additional cake purchase, the total amount that customers will pay for wholesale cakes is estimated to be decreased by 0.55.Thisisbecauseinalinearrelationship,thesloperepresentsthechangeinthedependentvariable(inthiscase,thetotalpaymentamount)foreachunitincreaseintheindependentvariable(inthiscase,thequantityofcakes).Sincetheslopeis0.55,thismeansthatforeachadditionalcakepurchased,thetotalpaymentamountdecreasesby0.55. This is because in a linear relationship, the slope represents the change in the dependent variable (in this case, the total payment amount) for each unit increase in the independent variable (in this case, the quantity of cakes). Since the slope is -0.55, this means that for each additional cake purchased, the total payment amount decreases by 0.55.

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