Recall that ann-cyclic graphcnhas vertex setv={1,2, . . , n}and edge sete={{k, k+ 1} |1≤k≤n−1}∪{{n,1}}. prove thatc2nis bipartite. (hint: how is the parity (even/oddness) of adjacent vertices related? )

(08.01)consider the following pair of equations: x + y = −2 y = 2x + 10 if the two equations are graphed, at what point do the lines representing the two equations intersect? (−4, 2) (4, 2) (−2, 4) (2, 4)

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

A. the probability that a product is defective is 0.1. what is the probability that there will be 1 or less defective products out of the next 8 produced products b. the expected number of imperfections in the coating nylon for parachutes is 6 per 100 yards. what is the probability of finding 12 or fewer imperfections in 260 yards c. in a lot of 54 products there are 9 defective products. calculate the probability that not more than 1 is defective from a random sample of 17 products.