Let s be a finite set of positive integers whose largest element is n. prove that there exists a graph g of order n +1 such that (1) deg u es for every 48 chapter 1. introduction to graphs vertex u of g and (2) for every de s, there exists a vertex v in g such that deg v= d.

The weights of players in a basketball league are distributed normally. the distance (d) of each player's weight (w) from the mean of 86 kilograms was computed as follows: d = |w - 86| if d is greater than 7 for approximately 5% of the players, what is the approximate standard deviation of the players' weights? a. 1.75 kilograms b. 3.5 kilograms c. 4.3 kilograms d. 7 kilograms

Identify the function that contains the data in the following table: x     -2         0         2         3         5     f(x)     5         3         1         2         4     possible answers: f(x) = |x| + 1 f(x) = |x - 2| f(x) = |x - 2| - 1 f(x) = |x - 2| + 1

Sections of prefabricated wood are each 5 1/3 feet long. how long are 7 1/2 sections placed end to end?