Let 2n (equally spaced) points on a circle be chosen. show that the number of ways to join these points in pairs, so that the resulting n line segments do not intersect, equals the nth catalan number cn.

Which question is not a good survey question? a.don't you agree that the financial crisis is essentially over? 63on average, how many hours do you sleep per day? c. what is your opinion of educational funding this year? d.are you happy with the availability of electronic products in your state?

Due to a packaging error, 4 cans labeled diet soda were accidentally filled with regular soda and placed in a 12 pack carton of diet soda. two cans were randomly selected from this 12 pack. what is the probability that both cans were regular soda?

6x + 3y = -6 2x + y = -2 a. x = 0, y = -2 b. infinite solutions c. x = -1, y = 0 d. no solution