Part 3 Draw a graph using the following information.

In a certain video game, a player is confronted with a series of 4 opponents and a(n) 83% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). What is the probability that a player defeats all 4 opponents in a game?  Express your answer to 4 decimal places.

P(A|B) = 0.35, P(A) = 0.35, P(B) = 0.70 Are events A and B independent?

Part 2 Maximize P for the constraints given in Part 1.

Part 1 Graph the region of solutions to the following system of equations.

Part 1 Solve the system by substitution.  Using other methods will not result in credit.

Part 3 Is the given value a solution to the system?  Justify your answer mathematically.  “Yes” or “no” is not sufficient.

Part 1 Is the given value a solution to the system?  Justify your answer mathematically. “Yes” or “no” is not sufficient.  

Find the volume

Part 2 Find the area