To determine the best prediction for the number of minutes Sam will spend exercising if she spends 30 minutes watching television, we'll use the given function [tex]\( y = -0.78x + 95 \)[/tex], where [tex]\( x \)[/tex] represents the number of minutes of television viewing and [tex]\( y \)[/tex] represents the number of minutes of exercising.
Here's the step-by-step solution:
1. Identify the variables:
- [tex]\( x = 30 \)[/tex] minutes (the number of minutes Sam watches television).
2. Substitute the value of [tex]\( x \)[/tex] into the function:
[tex]\[
y = -0.78(30) + 95
\][/tex]
3. Calculate the value:
- First, calculate [tex]\( -0.78 \times 30 \)[/tex]:
[tex]\[
-0.78 \times 30 = -23.4
\][/tex]
- Next, add the result to 95:
[tex]\[
y = -23.4 + 95
\][/tex]
4. Find the final value:
[tex]\[
y = 71.6
\][/tex]
Thus, the best prediction for the number of minutes Sam will spend exercising if she spends 30 minutes watching television is 71.6 minutes.
Since the given options are 45, 72, 83, and 118 minutes, the closest and best prediction is:
72 minutes.
