The quaternion group (q, degree ) is a group of order 8 with two generators a and b subject to the relations a4 = e, b2 = a2, and a degree b degree a = b. to be explicit, the elements of q are e, a, a2, a3, b, a degree b, a degree b, a2 degree b, a3 degree b. for this discussion prompt, research the subject and find an application of the quaternion group that differs from any of your peer's responses. write the cayley table, find the center, and find all cyclic subgroups for q.|

Jenisey has $24 to spend on seven pencils. after buying them she had $10. how much did each pencil cost.?

In the geometric progression –3, 12, −48… what term is 3,072?

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?