PROBLEM # 1
x is an integer. x > 4 and  - x < - 1. What are the possible values of x?

PROBLEM #2
The triangle 5,12,13 has an area A=30 and a perimeter P=30, so A/P is 1. The triangle 9,75,78 has an area A=324 and a perimeter P=162, so A/P is 2. Find a triangle whose A/P is 10.

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Problems from 03/31/11

PROBLEM # 1
In blackjack if the dealer is showing an ace you make "take insurance" or bet that his/her other card is a ten. A winning bet pays 2:1 (win $2 for every $1 bet, keeping original bet). What is the house advantage in this bet?  Assume you know nothing about the cards that have already been played (including the dealer's ace and your own).
 

SOLUTION 1


PROBLEM #2
If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid (shown above), combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of 1. 

SOLUTION 2
 

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