To find the height of the ball at \( s = 7.5 \) seconds, we need to evaluate the function \( h(s) = -s^2 + 10s + 3 \) at \( s = 7.5 \).
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 this back into the equation:
\[ h(7.5) = -56.25 + 10(7.5) + 3 \]
Calculating \( 10(7.5) \):
\[ 10(7.5) = 75 \]
Now substituting \( 75 \) back into the equation:
\[ h(7.5) = -56.25 + 75 + 3 \] \[ h(7.5) = -56.25 + 78 \] \[ h(7.5) = 21.75 \]
Therefore, the height of the ball after 7.5 seconds is \( h(7.5) = 21.75 \).
The correct response is:
21.75