A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you're willing to spend up to $20 trying to win. You estimate that you have about a 10% chance of hitting the balloon on any throw. Find the expected profit for your winnings. Find the expected number of darts you'll throw.

Ibelieve the answer would be a

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .