Question 1

Round the following to whole percentages using the Webster method: 36.3% + 11.7% + 7.9% + 5.6% + 10.4% + 28.1% = 100%

Accepted Answer

A)  36 + 11 + 8 + 6 + 11 + 28 
B)  36 + 12 + 8 + 6 + 10 + 28 
C)  37 + 12 + 8 + 5 + 9 + 28 
D)  37 + 11 + 8 + 6 + 9 + 28 
A)  36 + 11 + 8 + 6 + 11 + 28 
B)  36 + 12 + 8 + 6 + 10 + 28 
C)  37 + 12 + 8 + 5 + 9 + 28 
D)  37 + 11 + 8 + 6 + 9 + 28

Question 2

Which of the following is a true statement?

Accepted Answer

A)  Jefferson's method of apportionment is not biased with respect to a state's population. 
B)  Jefferson's method of apportionment is biased toward states with smaller populations. 
C)  Jefferson's method of apportionment is biased toward states with larger populations. 
A)  Jefferson's method of apportionment is not biased with respect to a state's population. 
B)  Jefferson's method of apportionment is biased toward states with smaller populations. 
C)  Jefferson's method of apportionment is biased toward states with larger populations.

Question 3

A town board has 10 members, divided among three regions of the town using the Hamilton method of apportionment. The regions and their populations are given below. Find the difference in representative share for the North and South regions. $$\begin{array} { l c } 
\text { Region } & \text { Population } \
\text { North } & 13,400 \
\text { Central } & 21,900 \
\text { South } & 8700
\end{array}$$

Accepted Answer

The answer of A town board has 10 members, divided...

Question 4

A state has four districts with the populations shown below. The House of Representatives has 20 seats that are to be apportioned using the Jefferson method. Find the apportionment for each district. $$\begin{array} { c c } 
\text { District } & \text { Population } \
\text { A } & 87,000 \
\text { B } & 56,000 \
\text { C } & 72,000 \
\text { D } & 35,000
\end{array}$$

Accepted Answer

A)  6, 5, 6, 3 
B)  7, 4, 5, 4 
C)  6, 4, 6, 4 
D)  7, 4, 6, 3 
A)  6, 5, 6, 3 
B)  7, 4, 5, 4 
C)  6, 4, 6, 4 
D)  7, 4, 6, 3

Question 5

A small county has populations in three regions as shown below. They have apportioned 15 seats on the county council and obtained the apportionment for each region shown below. Find the relative difference in district population between the Parkview and Hillside regions. $$\begin{array} { l c c } 
\text { Region } & \text { Population } & \text { Apportionment } \
\text { Parkview } & 43,000 & 6 \
\text { Hillside } & 32,800 & 5 \
\text { Riverdale } & 24,200 & 4
\end{array}$$

Accepted Answer

A)  9.25% 
B)  8.47% 
C)  1.85% 
D)  1.41% 
A)  9.25% 
B)  8.47% 
C)  1.85% 
D)  1.41%

Question 6

Suppose a country has four states with the populations shown below and a parliament with 30 seats. Use the Jefferson method of apportionment to apportion the seats between the states. $$\begin{array} { c c } 
\text { State } & \text { Population } \
\text { A } & 182,575 \
\text { B } & 243,170 \
\text { C } & 322,115 \
\text { D } & 252,140
\end{array}$$

Accepted Answer

A)  5, 7, 10, 8 
B)  6, 7, 9, 8 
C)  5, 7, 11, 7 
D)  6, 8, 8, 8 
A)  5, 7, 10, 8 
B)  6, 7, 9, 8 
C)  5, 7, 11, 7 
D)  6, 8, 8, 8

Question 7

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district. $$\begin{array} { c c } 
\text { District } & \text { Population } \
\text { A } & 43,000 \
\text { B } & 32,800 \
\text { C } & 24,200
\end{array}$$

Accepted Answer

A)  5, 3, 3 
B)  5, 4, 2 
C)  6, 3, 2 
D)  4, 4, 3 
A)  5, 3, 3 
B)  5, 4, 2 
C)  6, 3, 2 
D)  4, 4, 3

Question 8

Use the Hill-Huntington method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below. $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { North } & 30,000 \
\text { Central } & 10,100 \
\text { South } & 34,900
\end{array}$$

Accepted Answer

North 5
Ce

Question 9

The Anysville Transit System (ATS) has four bus routes, as identified below: $\begin{array}{l}

\begin{array}{cc} 
\text { Route }&\text { Average passengers }\
& \text { per day } \
1 & 682 \
2 & 2383 \
3 & 857 \
4 & 1425
\end{array}
\end{array}$
The ATS is replacing the entire old bus fleet with 25 new buses. Use the Hill-Huntington method to determine how many buses each route should get.

Accepted Answer

A)  4, 14, 8, 9 
B)  4, 15, 7, 9 
C)  4, 16, 6, 9 
D)  4, 16, 5, 10 
A)  4, 14, 8, 9 
B)  4, 15, 7, 9 
C)  4, 16, 6, 9 
D)  4, 16, 5, 10

Question 10

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Find the apportionment for the Boxwood district. $$\begin{array} { l c } 
\text { District } & \text { Population } \
\text { Applewood } & 8280 \
\text { Boxwood } & 4600 \
\text { Central } & 5220
\end{array}$$

Accepted Answer

A)  2 
B)  3 
C)  1 
D)  4 
A)  2 
B)  3 
C)  1 
D)  4

Question 11

Use the following information to answer the Questions:
A senate of 20 faculty members represents three departments: math, statistics, and applied math. The seats are to be apportioned according to the numbers of students in each department, which are as follows: $\begin{array}{lccc}
  \text { Math} &97\
  \text { Statistics} && 83\
  \text { Applied math} &134\
\end{array}$

-In d'Hondt's method, who gets the first seat?

Accepted Answer

A)  math 
B)  statistics 
C)  applied math 
A)  math 
B)  statistics 
C)  applied math

Question 12

A country has three states and a national senate with 10 seats. The state populations and the apportionment of the senate seats are shown below. Find the relative difference in district population of states A and B. $$\begin{array} { c c c } 
\text { State } & \text { Population } & \text { Seats } \
\text { A } & 69,000 & 5 \
\text { B } & 43,500 & 3 \
\text { C } & 37,500 & 2
\end{array}$$

Accepted Answer

A)  4.83% 
B)  1.61% 
C)  1.01% 
D)  5.07% 
A)  4.83% 
B)  1.61% 
C)  1.01% 
D)  5.07%

Round the following to whole percentages using the Webster method: 36.3% + 11.7% + 7.9% + 5.6% + 10.4% + 28.1% = 100%

Which of the following is a true statement?

A town board has 10 members, divided among three regions of the town using the Hamilton method of apportionment. The regions and their populations are given below. Find the difference in representative share for the North and South regions. Region Population North 13,400 Central 21,900 South 8700

A state has four districts with the populations shown below. The House of Representatives has 20 seats that are to be apportioned using the Jefferson method. Find the apportionment for each district. District Population A 87,000 B 56,000 C 72,000 D 35,000

Suppose a country has four states with the populations shown below and a parliament with 30 seats. Use the Jefferson method of apportionment to apportion the seats between the states. State Population A 182,575 B 243,170 C 322,115 D 252,140

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district. District Population A 43,000 B 32,800 C 24,200

Use the Hill-Huntington method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below. District Population North 30,000 Central 10,100 South 34,900

The Anysville Transit System (ATS) has four bus routes, as identified below: Route Average passengers per day 1 682 2 2383 3 857 4 1425 The ATS is replacing the entire old bus fleet with 25 new buses. Use the Hill-Huntington method to determine how many buses each route should get.

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Find the apportionment for the Boxwood district. District Population Applewood 8280 Boxwood 4600 Central 5220

A country has three states and a national senate with 10 seats. The state populations and the apportionment of the senate seats are shown below. Find the relative difference in district population of states A and B. State Population Seats A 69,000 5 B 43,500 3 C 37,500 2

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Exam 14: Apportionment

Round the following to whole percentages using the Webster method: 36.3% + 11.7% + 7.9% + 5.6% + 10.4% + 28.1% = 100%

Which of the following is a true statement?

A town board has 10 members, divided among three regions of the town using the Hamilton method of apportionment. The regions and their populations are given below. Find the difference in representative share for the North and South regions. Region Population North 13,400 Central 21,900 South 8700

A state has four districts with the populations shown below. The House of Representatives has 20 seats that are to be apportioned using the Jefferson method. Find the apportionment for each district. District Population A 87,000 B 56,000 C 72,000 D 35,000

Suppose a country has four states with the populations shown below and a parliament with 30 seats. Use the Jefferson method of apportionment to apportion the seats between the states. State Population A 182,575 B 243,170 C 322,115 D 252,140

A county has three districts with the populations shown below. The 11 seats on the county council are to be apportioned using the Jefferson method. Find the apportionment for each district. District Population A 43,000 B 32,800 C 24,200

Use the Hill-Huntington method of apportionment to distribute 12 seats on a city council to three districts with the populations shown below. District Population North 30,000 Central 10,100 South 34,900

The Anysville Transit System (ATS) has four bus routes, as identified below: Route Average passengers per day 1 682 2 2383 3 857 4 1425 The ATS is replacing the entire old bus fleet with 25 new buses. Use the Hill-Huntington method to determine how many buses each route should get.

A county is divided into three districts with the populations shown below. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Find the apportionment for the Boxwood district. District Population Applewood 8280 Boxwood 4600 Central 5220

A country has three states and a national senate with 10 seats. The state populations and the apportionment of the senate seats are shown below. Find the relative difference in district population of states A and B. State Population Seats A 69,000 5 B 43,500 3 C 37,500 2

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

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