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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.

[tex]\[
\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Recreational Time} \\
\hline
Minutes of Television Viewing, \( x \) & Minutes of Exercising, \( y \) \\
\hline
45 & 60 \\
\hline
65 & 45 \\
\hline
120 & 6 \\
\hline
22 & 80 \\
\hline
80 & 25 \\
\hline
\end{tabular}
\][/tex]

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 Sam will spend exercising if she watches 30 minutes of television, we use the given function [tex]\( y = -0.78x + 95 \)[/tex].

Here is the step-by-step solution:

1. Identify the value of [tex]\( x \)[/tex]:
- [tex]\( x = 30 \)[/tex] (minutes spent watching television)

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

3. Calculate the expression:
- First, multiply [tex]\(-0.78\)[/tex] by [tex]\(30\)[/tex]:
[tex]\[ -0.78 \times 30 = -23.4 \][/tex]
- Then add [tex]\(95\)[/tex]:
[tex]\[ y = -23.4 + 95 = 71.6 \][/tex]

So, if Sam watches 30 minutes of television, the best prediction for the number of minutes she will spend exercising is approximately 72 minutes.

Therefore, the correct answer is:

72 minutes

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