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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 & 5 \\
\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 solve the problem of predicting the number of minutes Sam will spend exercising if she watches 30 minutes of television, we can use the provided function:

[tex]\[ y = -0.78x + 95 \][/tex]

This function models the relationship between the minutes of television viewing [tex]\(x\)[/tex] and the minutes of exercising [tex]\(y\)[/tex].

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

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

2. Calculate the value inside the parentheses:
[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]

Therefore, the best prediction for the number of minutes Sam will exercise if she spends 30 minutes watching television is 72 minutes. This corresponds closely to 71.6 minutes when rounded.

The closest option from the provided choices is:
[tex]\[ \boxed{72 \text{ minutes}} \][/tex]

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