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To find the height of the ball after 7.5 seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).
Let's substitute \( s = 7.5 \) into the function:
\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]
Now, calculate \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
Now, plug it back into the equation:
\[
h(7.5) = -56.25 + 10(7.5) + 3
\]
Calculate \( 10(7.5) \):
\[
10(7.5) = 75
\]
Now substitute and simplify:
\[
h(7.5) = -56.25 + 75 + 3
\]
Calculating step by step:
1. Add \( 75 + 3 = 78 \)
2. Then, \( 78 - 56.25 = 21.75 \)
Thus, the height of the ball after 7.5 seconds is:
\[
h(7.5) = 21.75
\]
The correct response is \( 21.75 \).