Let Xn = f1;2;3; :::;ng. For any n 1 and k n, we create the following simple graph Gn;k: The vertices of Gn;k are the subsets of Xn of size k.
Two vertices are adjacent if their corresponding subsets in Xn are disjoint.
(a) Draw G5;2. Label your vertices by the subsets of X5 of size 2.
(b) Find a formula, in terms of n and k, for the number of vertices and for the number of edges in Gn;k.
(c) Show that c(Gn;k) n by showing a way to properly colour the vertices of Gn;k using n colours.

Aschool typically sells 500 yearbooks each year for 50 dollars each. the economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. let x represent the number of $5 decrease in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). to maximize profit, what price should the school charge for the yearbooks? what is the possible maximum revenue? if the school attains the maximum revenue, how many yearbooks will they sell?

In the diagram below, tan θ = sqrt 3. what is the value of m?

Choosing a booth location: your manager is sending two people to work at the conference. she wants a booth that will give your company good visibility for no more than 35% of the total budget ($3000). the conference coordinator just told you there are only five booths left. which booth will you choose? write the inequality that shows how much money you can spend on the booth simplify the inequality that shows how much money you can spend on the booth.