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A city has three libraries and 15 librarians. Use Hamilton’s Method to determine how many librarians each library should get. (Hint: first, find the standard divisor.) Library Residents Quota Min. Q. Remainder Librarians East 3200 South 4500 North 7300 15,000 Write ONLY your answers (the right column) in the box below. On your own paper, show all your work and justify your answers. You will be submitting the paper at the end of this test. You should copy the entire table.    

The following options are available for a mortgage:  [Option 1] 30-year mortgage with monthly payments of $1818.60. [Option 2] 15-year mortgage with monthly payments of $2879.21.  How much will you save overall (for the term of the mortgage) by choosing Option 2 (the shorter loan) compared to Option 1? Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test. 

Hamilton’s Method of apportionment is the fairest of all because it favors more popular states.

A market researcher is surveying 50 people he met in a shopping mall when he went there last Thursday afternoon. Which sampling method is used here?

If the population increases by 8% every year, how many years does it take for the population to double? Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test. 

Which one of the following best describes the “Golden Ratio”

Find the negation of the statement “Everyone needs to be tested for COVID-19.” 

The table below shows how many male and female applicants were hired at a large company.  Hired Not Hired Total Male 145 75 220 Female 60 30 90 Total 205 105 310 (a) Find the probability that an applicant was hired given that it was a male applicant.  (b) Find the probability that an applicant was a male given that the applicant was hired.  Write ONLY your answer(s) in the box below. On your own paper, show all your work and justify your answer(s). You will be submitting the paper at the end of this test.     

An association is voting on the type of food for their conference. The results are as follows:  # votes 12 10 8 5 1st choice Italian French Chinese Chinese 2nd choice French Italian French Italian 3rd choice Chinese Chinese Italian French (a) Which food wins by plurality? (3 pts.) (b) Which food wins by the Instant Runoff Voting? (4 pts.) (c) Is there a Condorcet winner? If so, identify it. (3 pts.) Write ONLY your answers in the box below. On your own paper, show all your work and justify your answers. You will be submitting the paper at the end of this test. Credit will not be given unless you show your work. 

Your friend tosses two coins, and you win $20 if you get two Tails but loses $8 if you don’t get two Tails. What is your expected value each time your friend tosses two coins?