To find the height of the ball after 7.5 seconds, we need to substitute \(s = 7.5\) into the function \(h(s) = -s^2 + 10s + 3\).
Let's calculate \(h(7.5)\):
\[ h(7.5) = - (7.5)^2 + 10(7.5) + 3 \]
Calculating \( (7.5)^2 \):
\[ (7.5)^2 = 56.25 \]
Now substitute that value back into the equation:
\[ h(7.5) = -56.25 + 75 + 3 \]
Calculating \( -56.25 + 75 \):
\[ -56.25 + 75 = 18.75 \]
Now adding 3:
\[ h(7.5) = 18.75 + 3 = 21.75 \]
Thus, the height of the ball after 7.5 seconds is \(21.75\).
The correct response is:
21.75