Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 15.3, Problem 19E
To determine
To calculate: A population profile for 5 states with a total population of 1000 for which Hamilton, Jefferson and Webster method are same, and modified divisors for the Jefferon and Webster apportionments are equal to standard divisor.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Use Webster's method of apportionment to solve the following problem.
2. Suppose a nation has 5 states, with populations shown in the chart below. The
representative body had 150 seats.
Find:
• the standard divisor,
the modified divisor, and
• the distribution of representatives to each state.
Then complete the table. Round all standard and modified quotas to 7 decimal places if
needed.
You can use a spreadsheet to help you figure out an answer or calculate using a
calculator.
Representative Seats
State
A
B
C
Total
Standard Divisor
Modified Divisor
150
Population
1,895,500
1,234,500
845,200
399.120
500.680
4,875,000
Standard Rounded Modified Modified
Quotas Quotas Rounded
Quotas
Quotas
Use Huntington-Hill's method of apportionment to solve the following problems.
3. Suppose a nation has 4 states, with populations shown in the chart below. The
representative body had 80 seats.
a.) Find the standard divisor and the distribution of representatives to each state using the
Huntington-Hill method of apportionment. Round the standard quotas to 7 decimal places
if needed. You can use a spreadsheet to help you figure out an answer or calculate using a
calculator.
Representative
Seats
State
D
Total
Standard
Divisor
80
Population Standard
Quotas
100
200.650
324.150
875,400
456,200
1,856,400
Round
Down
Round Geometric
Up
Mean
Huntington-
Hill's
Method
b.) Find the modified divisor and the distribution of representatives to each state using the
Huntington-Hill method of apportionment. Round the modified quotas to 7 decimal places if
needed. You can use a spreadsheet to help you figure out an answer or calculate using a
calculator.
I just need the bottom part answered.
Chapter 15 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding down for the standard quotas. 10 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 35,000 22,000 15,000 46,000 118,000arrow_forwardb.) Find the modified divisor and the distribution of representatives to each state using the Huntington-Hill method of apportionment. Round the modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator.arrow_forwardConsider the desired number of seats and the populations given below. 12 seats Population 1st Precinct 33,000 25,000 2nd Precinct 3rd Precinct 12,000 4th Precinct 49,000 TOTAL 119,000 (a) Find the standard divisor. (Round your answers to two decimal places.) (b) Find the standard quota for each precinct. (Round your answers to two decimal places.) 1st Precinct 2nd Precinct 3rd Precinct 4th Precinct (c) Find the total of the standard quotas, rounding the standard quotas down. (d) Find a modified divisor that will give modified quotas to produce the desired number of seats when the standard quotas are rounded down.arrow_forward
- A country is made up of four regions A, B, C, and D. The population of each region, in thousands, is given in the following table. According to the country's constitution, the congress will have 40 seats divided among the four regions according to their respective populations. Find the standard quota for each region. Round to the nearest hundredth. Region A B C D Total Population (in thousands) 512 630 483 615 2.240 OA. A, 9.14; B, 11.25; C, 8.63; D, 5.31 OB. A, 9.14; B, 11.82; C, 8.63; D, 10.98 OC. A, 9.14; B, 11.25; C, 6.23; D. 10.98 OD. A, 9.14; B, 11.25; C, 8.63; D, 10.98 www.arrow_forwardOf the 15 states in the Union when the issue of apportionment for the House of Representatives was first taken up in 1794, let's consider Kentucky, which had a population of 72677, and New Jersey, which had a population of 184139. The total population as of the 1790 census was 3893874 individuals, and the size of the House of Representatives was 105. (a) What was the standard quota for Kentucky? Include at least three decimal places of accuracy. Standard quota: (b) What was the standard quota for New Jersey? Include at least three decimal places of accuracy. Standard quota: (c) What is the standard divisor for this apportionment exercise? Include at least one decimal place.Standard divisor:arrow_forwardWhich one of the apportionment methods studied does not violate the quota rule? Group of answer choices Hamilton's Method Jefferson's Method Adam's Method Webster's Methodarrow_forward
- Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: the standard divisor, the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculatorarrow_forwardUse Huntington-Hill's method of apportionment to solve the following problems. 3 Suppose a nation has 4 states, with populations shown in the chart below. The representative body had 80 seats 7 Find the standard divisor and the distribution of representatives to each state using the Huntington-Hill method of apportionment. Round the standard quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator.arrow_forwardAs part of a "green" initiative, California wants to apportion 150 new electric vehicles to its university system campuses. Given the following table, use the Hamilton method to determine how many of the vehicles should be apportioned to the Los Angeles campus based on the number of students. Student Enrollment in the University of California System Enrollment Full Time Equivalent (FTE) 37,221 28,292 20,956 4689 15,012 4597 Campus Los Angeles Riverside Santa Cruzarrow_forward
- Please show working outs.arrow_forwardUse Huntington-Hill's method of apportionment to solve the following problems. 3. Suppose a nation has 4 states, with populations shown in the chart below. The representative body had 80 seats. a.) Find the standard divisor and the distribution of representatives to each state using the Huntington-Hill method of apportionment. Round the standard quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats 80 State Population Standard Round Round Geometric Huntington- Hill's Quotas Down Up Mean Method A 200,650 324,150 C 875,400 D 456,200 Total 1,856,400 Standard Divisorarrow_forwardA country consists of 20 states. There are 522 seats in the Congress which are to be apportioned among the 20 states to their respective population. The following table shows the population of the 20 states. Use a spreadsheet program to answer the following questions. Round all standard quotas, modified quotas, and the divisor to 5 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Stat Populati Standa Adams' Webste Modifi Modifi Adams' Webste Advantage on rd S r's ed ed S r's or e Quotas Rounde Rounde Quotas Quotas Modifi Modifi Disadvant d Up Quotas Quotas Adam Webste Rounde Rounde d for for ed ed age A 413,875 B 500,032 397,004 D 360,874 E 193,993 F 131,279 G 76,121 H 297,022 I 94,239 J 423,566 K 565,883 L 473,525 M 399,170 N 403,576 100,904 P 73,143 Q 360,997 R 410,181 S 456,755 T 139,361 Tota 6,271,50 Seats: 522arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY