To find the best prediction for the number of minutes Sam will spend exercising if she spends 30 minutes watching television, we use the given linear function that models the relationship between the minutes of television viewing ([tex]$x$[/tex]) and the minutes of exercising ([tex]$y$[/tex]):
[tex]\[ y = -0.78x + 95 \][/tex]
Here, [tex]\( x \)[/tex] is the number of minutes Sam watches television, and we are given that [tex]\( x = 30 \)[/tex].
1. Substitute [tex]\( x = 30 \)[/tex] into the equation:
[tex]\[ y = -0.78(30) + 95 \][/tex]
2. First, calculate [tex]\( -0.78 \times 30 \)[/tex]:
[tex]\[ -0.78 \times 30 = -23.4 \][/tex]
3. Next, add 95 to the result from step 2:
[tex]\[ y = -23.4 + 95 = 71.6 \][/tex]
So, the number of minutes Sam will spend exercising if she watches 30 minutes of television is [tex]\( 71.6 \)[/tex] minutes.
Among the given options, the closest prediction is:
- 45 minutes
- 72 minutes
- 83 minutes
- 118 minutes
The best prediction matches almost exactly to 72 minutes. Therefore, the answer is:
[tex]\[ \boxed{72 \text{ minutes}} \][/tex]
