Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1 , a2 , ak , where a1 = 1, ak = n, and aⱼ < aⱼ ₊ ₁ for j = 1, 2, . . , k − 1.

Hii1977 cleaner shrimp are a species of shrimp that clean parasites from other organisms. fish allow the shrimp to eat the parasites in their mouth. the shrimp get a source of nutrition. the relationship between the shrimp and the fish is this association indicates that for the smaill aneser arecommensal,mutualistic,or parasitic for the begger one the anser are the shrimp and fish benefit each other , the shrimp harm the fish, or the fish do not benetit from the shrimp

Evaluate each expression. determine if the final simplified form of the expression is positive or negative -42 (-4)2 42

Astandard deck of cards contains 52 cards. one card is selected from the deck. (a) compute the probability of randomly selecting a diamond or heart. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability of randomly selecting a diamond or heart or club. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability of randomly selecting queen or club. (type an integer or a decimal rounded to three decimal places as needed.)