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Roy is having the carpets in his house cleaned. The area of the carpets is used to calculate the cost of the cleaning.
a= the area of the carpets
c= the cost of the cleaning
Which of the variables is independent and which is dependent?
(A) a is the independent variable and c is the dependent variable
(B) c is the independent variable and a is the dependent variable

Roy is having the carpets in his house cleaned. The area of the carpets is used to calculate the cost of the cleaning.\newlinea= a= the area of the carpets\newlinec= \mathrm{c}= the cost of the cleaning\newlineWhich of the variables is independent and which is dependent?\newline(A) a a is the independent variable and c c is the dependent variable\newline(B) c c is the independent variable and a a is the dependent variable

Full solution

Q. Roy is having the carpets in his house cleaned. The area of the carpets is used to calculate the cost of the cleaning.\newlinea= a= the area of the carpets\newlinec= \mathrm{c}= the cost of the cleaning\newlineWhich of the variables is independent and which is dependent?\newline(A) a a is the independent variable and c c is the dependent variable\newline(B) c c is the independent variable and a a is the dependent variable
  1. Identify Variables: In this context, we need to determine which variable depends on the other. The independent variable is the one that is chosen or controlled by the experimenter, and the dependent variable is the one that changes in response to changes in the independent variable. In the case of carpet cleaning, the area of the carpets aa is what is being measured or controlled, and the cost of the cleaning cc will change depending on the area. Therefore, the area of the carpets is the independent variable, and the cost of the cleaning is the dependent variable.
  2. Confirm Reasoning: To confirm our reasoning, we can think about the situation in practical terms. Roy does not adjust the area of his carpets based on the cost he wants to pay; instead, the cleaning service will charge him based on how large the carpets are. This means that the cost is a result of the area, further confirming that the area is independent and the cost is dependent.

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