Hello, epetrik!

1. A gambler sets up a game in which she puts four $10 bills and one $20 bill in one box.

A player randomly tales one of the bills and keep it.

To break even on average, how much must the gambler charge the player to play?

The player will draw: .

In five games, the gambler can expect to pay out $10, $10, $10, $10, $20

. . a total of $60 over 5 game.

That is, he can expect to pay out an average of per game.

To break even, the gambler should *charge* $12 per game.

2. Brittany pays $4.00 for a square piece of wood,

which she makes into a stop sign by cutting the corners off.

What is the cost of the wasted parts? A stop sign is tranditionally a regular *octagon**.* Code:

: - - - x - - - :
- * - - * * * * - - *
: | * * |
: | * * |
: * *
: * *
x * *
: * *
: * *
: | * x-2a * | a
: | * * |
- * - - * * * * - - *
: a : x-2a: a :

The square board is feet.

. . She paid $4 for square feet of wood.

Let the corner pieces be

Then the side of the octagon is

At the lower-right, we have an isosceles right triangle

. . with equal sides and hypotenuse .

Pythagorus: .

Quadratic Formula: .

Since , we have: .

The area of the four triangles is: . square feet

The fraction of wasted wood is: .

The cost of the wasted wood is: .