One morning Dave an email message to Alvin that said the following: “You are one of my dearest friends. If you care about me, send a copy of this letter to two of your dearest friends tomorrow. If you do not break this chain, you will live long and prosper.” Alvin followed the directions: the next day he sent a copy of the message to two of his dearest friends. The following day, each of the recipients did the same. Count the day Dave sent the original message as the first day, and assume the chain is unbroken. A. How many copies of the message will be sent on the sixth day? B. Find the n-rule that will show how many copies of the message will sent on the n-th day

Answer ASAP. Thank you. Suppose you are to line up 6 people on a bus. If 4 specific people require to be following each other, how many ways are possible to line the people up?

Ahmad, Jessie, Sarah, Bill, and Andy are all members of the social networking website Instagram. The site allows members to be "friends" with each other. It turns out that Bill and Sarah are friends, as are Ahmad and Andy. Jessie is friends with everyone. Who is "E" ? A E

Please answer both subparts with explanation. Thanks

Question #4. Hehar had lego blocks. He lost 4 pieces home then gave ¼ of the remaining to his friend Jay. After thay, 3 pieces got lost, then gave ⅓ of the new remaining to another friend Arsie. Another 2 pieces were lost, and then he gave half of the new remaining to his brother. At the end, Hehar has 19 lego blocks left. How many lego blocks did Hehar have originally?

In a famous study done in the 1960s two dolphins, Doris and Buzz, were trained to work together to earn fish. Doris was shown a light underwater. If the light was on steadily, her partner Buzz on the other side of the tank needed to press a button on the right for them to earn fish. If the light was blinking, he needed to press a button on the left. At one point in the study, the researcher hung a canvas in the middle of the tank in such a way that Buzz could not see the light. After looking at the light, Doris "swam near the curtain and began to whistle loudly. Shortly after that Buzz whistled back and then pressed the correct button". (Tintle, Rossman and Chance, MAA Prep Workshop) Of course, getting it right once was not enough to convince the scientists that there was really communication going on. It turned out, that in 15 out of 16 trials the dolphin pushed the correct button. Of course, it is possible that this happened just out of random chance - that the second dolphin just…

You are preparing the program for a concert. If the band has 10 songs prepared and will play 6 of them, how many different programs are possible? Assume that changing the order of the songs is a different program.

Annaleigh has dance every 5 days and gymnastics every 4 days. If she has both gymnastics and dance today, in how many days will she have both on the same day?

A clock shop has three cuckoo clocks on display. The cuckoos appear at different time intervals. One comes out every 10 minutes, one comes out every 15 minutes, and one comes out every 20 minutes. If they all appear at 5 o'clock, what is the next time they will all come out together?

The dial of a "combination lock" has the numbers 0 through 32. The "combination" to open the lock is actually an ordered sequence of 3 numbers. Each ordered sequence, from your textbook, is called an 'outcome'. How many outcomes are possible for this lock?