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The table compares [tex]\( x \)[/tex], the number of minutes of television Sam watched each day, to [tex]\( y \)[/tex], the number of minutes she spent exercising. The function [tex]\( y = -0.78x + 95 \)[/tex] models the data in the table.

\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Recreational Time} \\
\hline
Minutes of Television Viewing, [tex]\( x \)[/tex] & Minutes of Exercising, [tex]\( y \)[/tex] \\
\hline
45 & 60 \\
\hline
65 & 45 \\
\hline
120 & 5 \\
\hline
22 & 80 \\
\hline
80 & 25 \\
\hline
\end{tabular}

Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?

A. 45 minutes

B. 72 minutes

C. 83 minutes

D. 118 minutes



Answer :

GinnyAnswer
To predict the number of minutes of exercising Sam will do if she spends 30 minutes watching television, we can use the given function [tex]\( y = -0.78x + 95 \)[/tex], where [tex]\( x \)[/tex] represents the number of minutes of television watched and [tex]\( y \)[/tex] represents the number of minutes spent exercising.

Given:
[tex]\( x = 30 \)[/tex]

1. Substitute [tex]\( x = 30 \)[/tex] into the function:
[tex]\[ y = -0.78(30) + 95 \][/tex]

2. Calculate the product [tex]\(-0.78 \times 30\)[/tex]:
[tex]\[ -0.78 \times 30 = -23.4 \][/tex]

3. Add this result to 95:
[tex]\[ y = -23.4 + 95 \][/tex]
[tex]\[ y = 71.6 \][/tex]

From these steps, the predicted number of minutes Sam will spend exercising when she watches 30 minutes of television is 71.6 minutes.

Thus, the best prediction from the given options is approximately 72 minutes.

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