MATH_130_Midterm_2_Fall_2023 (1).pdf

Math 130 Name: Midterm 2 Discussion: You have 50 minutes to complete the test. This exam contains 4 pages (including this cover page) and 4 questions. You are expected to show work to receive full credit. If you have any questions, raise your hand and wait for the proctor to come to your seat. You may use the backs of the pages of the exam to write your scratch work. Please ask the proctor if you need more paper. BASIC CALCULATORS ONLY. No Laptops, no phones, no graphing calculators. When going to the bathroom, please leave your phone on the proctor’s table. Enjoy! Grade Table (for teacher use only) Question Points Score 1 30 2 20 3 20 4 30 Total: 100

Math 130 Midterm 2 - Page 2 of 4 1. (30 points) The Clearview Transit Authority operates 5 bus routes with a total of 30 buses. The buses are apportioned every month among the routes, based on the average daily number of passengers. For the month of May the averages are given in the following table: Schools A B C D E Passengers 600 800 1100 500 1000 (a) (10 points) Calculate the standard divisor and standard quotas for all the routes. (b) (7 points) Apportion the buses using Hamilton’s method. (c) (5 points) Does the first step of Webster Method (b) apportion the exact number of buses? Do we have a surplus or deficit? Should we increase the divisor, or should we decrease the divisor? (d) (8 points) Do the first step of Huntington-Hill method.(show the corresponding breakpoints) Do we have a surplus or deficit? Should we increase or decrease the divisor?

Math 130 Midterm 2 - Page 3 of 4 2. (20 points) Round the exact quotas below according to each apportionment method. (1 point each) Exact Quota 2.51 3.46 4.37 6.48 7.71 Jefferson’s Adam’s Webster’s Huntington- Hill 3. (20 points) A Cake is to be divided among five players P 1 , P 2 , . . . , P 5 , using the claim- and-challenge method . They decide to proceed in the following manner: in the first round, P 1 goes first, P 2 goes second, etc. In the second round they reverse the order, so P 5 goes first, P 4 goes second, etc. They keep reversing the order after every round. (Explain your answers) (a) (2 points) How many rounds does it take to apportion the cake among the players? (b) (5 points) In the first round, there are no challenges. Who gets the piece of the cake at the end of the first round? (c) (8 points) In the second round, only P 4 and P 3 challenge. Describe the second round in terms of claims, challenges and passes of each player. (d) (5 points) Who are the players in the third round? If there is no challenge, who gets the piece of the cake at the end of the third round?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Math 130 Midterm 2 - Page 4 of 4 4. (30 points) Three friends, Ann, Betsy, and Chad, buy together a $ 12 cake which is half vanilla and half chocolate. Ann likes both flavours equally. Betsy likes vanilla twice as much as she likes chocolate. Chad likes chocolate three times as much as he likes vanilla. They decide to divide it using the cut-and-choose method, with Ann and Betsy doing the first round (Ann is the cutter), and Chad entering in the second round. (a) (7 points) Indicate how Ann, Betsy and Chad view the cake. (indicate the corre- sponding values of each flavor). (b) (6 points) Indicate a cut made by Ann and the portion of Betsy after round one. (along with the corresponding values as viewed by Betsy). (c) (7 points) Indicate one way Betsy may divide her half in the second round (d) (10 points) From the division indicated in (c), show how Chad views each slice. Which slice will Chad choose?