Yet another college is also facing the same options, and their preference schedule is below. This time, use the Condorcet Method to determine the winner if there is one. If there is no Condorcet winner, explain why. # of votes 18 11 16 5 1st choice R H F H 2nd choice H R H F 3rd choice F F R R Write ONLY your answer in the response box. Show your work which justifies your answer ON YOUR PAPER. No credit is given unless you justify your answer.

Use Jefferson’s Method to determine how many counselors should be assigned to each school as shown below. There are 20 counselors available in total. Use the modified divisor . Write ONLY your answers (the right-hand column) in the response box. Show your work which justifies your answer ON YOUR PAPER. You should copy and complete this entire table on your own paper. Office Students Quota Counselors Ashby 3160 Burr 2300 Cedar 1540 Total 7000

Hamilton’s Method for apportionment could result in the Alabama Paradox. 

A is the data set {10, 20, 30, 40, 50}.  Make up another data set, B, such that B has the same mean as A, has exactly five numbers as A does, and has a bigger standard deviation than A.  Write your answer in the box below. You do not have to show your work for this problem. 

Find the probability that you will get at least one Tails when you toss 2 coins.

The Golden Ratio (often denoted with

Use Jefferson’s Method to determine how many nurses should be assigned to each office as shown below. There are 20 nurses available in total. Use the modified divisor . Write ONLY your answers (the right-hand column) in the response box. Show your work which justifies your answer ON YOUR PAPER. You should copy and complete this entire table on your own paper. Office Residents Quota Nurses Newhall 31,600 Saugus 43,000 Valencia 65,400 Total 140,000  

Another community college is considering how to offer courses. Their  faculty members were asked to rank these three options. The results are as follows.  This time, use the Instant Runoff Voting (IRV) to determine the winner. # of votes 11 14 15 10 1st choice R H F H 2nd choice H R H F 3rd choice F F R R Write ONLY your answer in the response box. Show your work which justifies your answer ON YOUR PAPER. No credit is given unless you justify your answer.

What is log (100,000)?

In the box below, explain how you can obtain the Golden Ratio using the Fibonacci Sequence. You can also answer this question on your own paper.