Suppose that we generate a random graph g = (v, e) on the vertex set v = {1, 2, . . , n} in the following way. for each pair of vertices i, j ∈ v with i < j, we flip a fair coin, and we include the edge i−j in e if and only if the coin comes up heads. how many edges should we expect g to contain? how many cycles of length 3 should we expect g to contain?

Alex drew a circle with right triangle prq inscribed in it, as shown below: the figure shows a circle with points p, q, and r on it forming an inscribed triangle. side pq is a chord through the center and angle r is a right angle. arc qr measures 80 degrees.

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply

5/6+7/8what is the answer sealsdbdbshd