## Friday, July 19, 2013

### Problem of the Week Day 5: Week of 7/15/13 - 7/19/13

Today is the final day of the problem of the week. In all three problems, your goal is to find the value of x. Good luck!

Easy:
Find the mean of the following list of numbers:

a
b
f
g
q

x = ____

Medium:
The data set below represents the test scores of nine students based on the amount of absences they had.

 x y f - f1 - f2 - f3 - f4 ceiling(n ÷ f - r) floor(f4 - f2 - r) floor(8r) floor(f2 ÷ f3) ceiling(2f4 - r) 3√(f1 - f4) f ÷ 2 ceiling(f2 - f3 - r) 2f2 √(f3) floor(f1 - r) floor(n ÷ 1000) floor(n ÷ 100) f1 - f4 f1 f4 - f2 f4

Find the line of best fit for this data set. It should be of the form y = mx + b.

m = ____
b = ____

Now, find the predicted score of a student with ten absences.

x = ____

Hard:
Take the following matrix that represents the payoffs in a mathematical game.

 A B 1 b, w - 6 s, -t 2 -b, a -a, c 3 -g, -d -f, b

After eliminating any dominated strategies, use mixed strategy Nash equilibria to determine the percent of the time that strategy 1 should be played.

x = ____

The answers to the problem will be up in a month. I will post the answers to June’s problem of the week with tomorrow's post.