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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 \( s = 7.5 \).
Calculating \( h(7.5) \):
\[
h(7.5) = -(7.5)^2 + 10(7.5) + 3
\]
Calculating \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
Now substituting this into the function:
\[
h(7.5) = -56.25 + 10 \times 7.5 + 3
\]
\[
h(7.5) = -56.25 + 75 + 3
\]
\[
h(7.5) = -56.25 + 78
\]
\[
h(7.5) = 21.75
\]
So, the height of the ball after 7.5 seconds is **21.75**.