Calculating the first eight digits of pi 3/15/15 The answers to the following eight problems will produce the first eight digits of pi. After you obtain an answer, please input your answer to the appropriate place below. Make sure to show your work for each of the problems. 𝜋 = Problem 1 2 3 4 5 6 7 8 Problem 1 You currently have $96, and want to buy tickets so that you and your friends can go to a play. Each ticket was originally priced at $50. However, the theatre placed a 20% discount on the tickets one day, and then another 20% discount on the tickets the next day. After these discounts are in place, how many tickets can you buy? 1 Problem 2 Alex picked up 25% more flowers than Brianna, and Casey picked up 20% more flowers than Alex. If a total of 15 flowers were picked up, how many more flowers did Casey pick than Brianna? Problem 3 If eight teachers were to grade the class exams, it would take them 12 hours. After working for 3 hours, several other colleagues joined them. All of the exams were graded in a total of 9 hours (including the time when the eight teachers worked alone). How many colleagues joined the eight teachers? 2 Problem 4 Two pipes are used to fill up a pool with water. One pipe takes 5 hours to fill up the pool on its own. This pipe is initially left on for 2 hours, and at this point in time, the second pipe is turned on. If it takes an additional 30 minutes to fill up the entire pool, how long would it take the second pipe to fill up the pool on its own? Problem 5 A mini Settler’s of Catan board game can be setup in the following way. There are six tiles that must be placed into the six slots on the hexagon-­‐shaped board. If there are four wood tiles, one wheat tile, and one sheep tile, how many different ways can you set up the board game? 3 Problem 6 There are five girls in a class. The teacher needs to make a team that contains 1 boy and 1 girl. If the total possible number of teams the teacher can make is 20, how many students are in the class? Problem 7 Reduce 5!!" in mod 9 arithmetic. 4 Problem 8 A series of 8 experiments are run in a world where a day takes 8 octahours. The first 5 experiments each take the same amount of time, but the last three experiments each take twice as long as the first experiment. How long is the first experiment if the experiments start at 2:00 and end at 4:00, and the first experiment takes less than a day? (Note: the clock goes from 0:00 to 8:00.) 5