Monique is punting a football and the height the ball travels is a function of time. The function h(s)=−s^2+10s+3

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 each term step-by-step:

1. Calculate \( (7.5)^2 \): \[ (7.5)^2 = 56.25 \]

2. Calculate \( 10(7.5) \): \[ 10(7.5) = 75 \]

Now, substitute these values back into the height function:

\[ h(7.5) = -56.25 + 75 + 3 \] \[ = -56.25 + 78 \] \[ = 21.75 \]

So, the height of the ball after 7.5 seconds is \( \boxed{21.75} \).