Six individuals, including A and B, take seats around a circular table in a completely random fashion. Suppose the seats are numbered 1, …, 6. Let X= A's seat number and Y= B's seat number. If A sends a written message around the table to B in the direction in which they are closest, how many individuals (including A and B) would you expect to handle the message?

In the following diagram it is given that dec,ab || dc, ad || eb, and ad is congruent to bc. a)why isn't abc a parallelogram even though it has a pair of parallel sides and a pair of congruent sides b)explain why be must be congruent to bc. further explain what type of triangle this makes triangle abc and what it tells you about angle 1 and angle 2c) finally why must angle 3 be congruent to angle 1? further, explain why we know that angle 3 is congruent to angle 2

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?

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?