answer

Answer each of the following clearly and completely. Show your work and reasoning. Partial credit is based on work shown. Unsupported correct answers may not receive full credit. Once you are finished, upload your work to the Exam 1 Assignment area in Canvas.

1. You have two measuring cups: one holds exactly 5 ounces of water and the other holds exactly 3 ounces of water. There are no markings on the cups, and you are not able to mark the cups in any way. You are given a huge bucket of water. Is it possible to measure and place exactly 4 ounces of water into the big cup? If so, carefully explain your method; if not, carefully explain why not?

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2. Suppose we had a room filled with 370 people. Will there be at least two people who have the same birthday (year of birth excluded)? Please explain what principle you used to give your answer, we discussed this in Week 1.

3. The store is selling lemons at 2 for $1. Each yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make a 9-inch lemon pie requiring ½ cup of lemon juice? Be sure to show all of your work!

4. Convert the base 10 number 1,204 to Mayan notation. Show your calculations used to get your answers.

5. Calculate the length between the ship and the lighthouse in the following image. Be sure to show all of your work!

6. Name a shape of constant width other than a circle. Describe, in your own words, the meaning of “constant width.”

7. The homeowner’s association is deciding a new set of neighborhood standards for architecture, yard maintenance, etc. Four options have been proposed. The votes are:
Number of voters
8
9
11
7
7
5
1st choice
B
A
D
A
B
C
2nd choice
C
D
B
B
A
D
3rd choice
A
C
C
D
C
A
4th choice
D
B
A
C
D
B

a. How many voters voted in this election?

b. How many votes are needed for a majority?

c. How many votes are needed for a plurality?

d. Find the winner under the plurality method.

e. Find the winner under the Instant Runoff Voting method.
Number of voters
8
9
11
7
7
5
1st choice
B
A
D
A
B
C
2nd choice
C
D
B
B
A
D
3rd choice
A
C
C
D
C
A
4th choice
D
B
A
C
D
B

8. A state with five counties has 50 seats in their legislature. Using Hamilton’s method, apportion the seats based on the 2010 census. You can use Excel to complete this. I sent the Excel example for the 2000 population via Announcements in Canvas. You can also use Google Sheets. Please include the sheets or excel file when you submit the exam.
County
2010 Population
Jefferson
60,000
Clay
31,200
Madison
72,400
Jackson
81,600
Franklin
118,400

9. BONUS: You can replace any question on the exam if you want to geek out on Excel like I did to find the apportionment of the five counties using the Huntington-Hill Method. Note, you will have to divide by a smaller divisor because you are short on seats after applying the Huntington-Hill Method once. It took me a few times to get the right one, but if you use Excel, it’s kind of a fun game.
County
2010 Population
Jefferson
60,000
Clay
31,200
Madison
72,400
Jackson
81,600
Franklin
118,400

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