An airline reservation code consists of two alphabet letters followed by 3 digits. For example, “TL307” is a valid code, and so is “LL222.” Clearly, repetition is allowed. Assume that all 26 letters of the English alphabet are available, how many valid codes are possible?  Write ONLY your answer in the response box. Show your work which justifies your answer ON YOUR PAPER.  

Suppose you randomly pick a card from a standard deck of cards. The probability that you pick a Spade is 1/13. 

A health-care provider has three offices: Newhall, Saugus, and Valencia. The number of residents each office serves is shown below. There are 20 nurses available in total. Using Hamilton’s Method, determine how many nurses should be assigned to each office.  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 Min. Q. Remainder Nurses Newhall 31,600 Saugus 43,000 Valencia 65,400 Total 140,000  

An account with a rate of 15% compounded CONTINUOUSLY earns more interest than an account with a rate of 15% compounded monthly.

The number of students in a local school is increasing by 30 students every year. This is an example of linear growth.

A school district has three high schools: Ashby, Burr, and Cedar. The number of students at each schools shown below. There are 20 counselors available in total. Using Hamilton’s Method, determine how many counselors should be assigned to each school.  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 Min. Q. Remainder Couneslors Ashby 3160 Burr 2300 Cedar 1540 Total 7000

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.