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
Concept explainers
Question
Chapter 15.3, Problem 22E
To determine
Why the modified divisor is always found by slowly increasing value of standard divisor.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Now the city expands to cover a new district called district C. As a result, the city hires
10 new police officers to cover the new district. This brings the total number of officers
to 50. The total population of the city is shown in the table. Complete the table using
Hamilton's method to apportion the police offices for the populations after 2000. Round
all standard quotas and the divisor to 7 decimal places if needed. You can use a
spreadsheet to help you figure out an answer or calculate using a calculator.
Find the divisor. Enter your answer in the space provided below.
Divisor:
Population
2000
Initial Quotas
Final Quotas
State
Standard
Quotas
А
6,550
11,520
4,698
22,768
B
C
Total
21.)
7.) Did a new state paradox occur? Explain your answer.
Write your response below:
If after apportionment, the total seats apportioned exceeds the total possible apportionment, What must be
done to the standard divisor to lower the seats apportioned?
It should not be changed.
O It cannot be determined.
O It must be decreased.
O It must be increased.
A 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: 522
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
- How many six-digit license plates can be made if no plate begins with 0 or 1?arrow_forwardTo allocate annual bonuses, a manager must choose his top four employees and rank them first to fourth. In how many ways can he create the ‘Top- Four” list out of the 32 employees?arrow_forwardSuppose 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_forward
- The table shows the county's populations after a 2020 census. Complete the table using Hamilton's method to apportion the 30 seats for the populations after 2000. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Find the divisor. Enter your answer in the space provided below. Divisor: State Population Standard Initial Quotas Final Quotas 2000 Quotas 43,913 72,543 168,244 284,700 А B C Totalarrow_forwardA country consists of 20 states. There are 386 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. Seats: 386 Hamilton Jefferson's Modified Modified Lower Quotas Disadvantage Jefferson State Population Standard Initial Benefit and Quotas Quota without Quotas decimal A 538,723 61,837 C 346,146 448,119 D E 500,521 F 89,678 G 221,803 H 314,404 I 41,754 J 373,154 K 94,310 399,190 M 297,083 391,098 163,551 218,689 Q 329,896 R 77,150 S 113,753 T 101,301 Total 5,122,220arrow_forwardA company has four divisions with 560, 1230, 1490, and 1760 people, respectively. A total of 18 IT workers must be allocated to each division according to their size. Complete parts (a) through (d) to find the apportionment using the Hill-Huntington method. Find the standard divisor. Find the standard quota and modified standard quota for each division. Using a modified standard divisor of 275, find the modified quota for each division. Find the geometric mean for each division. Show the rounded quota (according to the Hill-Huntington method) for each division and the final apportionment of IT workers. PLEASE WATCH GRAMMAR, PUNCTUATION, AND HAVE CLEAR FORMATTING. Thank you.arrow_forward
- Consider a fictional country with a population of 430,665 that is divided into 5 provinces, as shown in the table below. The country's constitution provides for 13 representatives to the lower house of the legislature. These representatives are allocated on the basis of province population. Use the Jefferson Apportionment Plan to find the number of representatives for each province by completing the table. Use modified standard divisor 30,000. Round values in the Quotient column to the nearest hundredth. Province Population Quotient Number of Representatives Kennebec 61,229 South Bay 38,832 North Island 94,721 Lakeland 167,386 Montbleu 68,497arrow_forwardThe following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or sixth grade. Fifth grade Sixth grade Number of teachers 21 22 Number of students 649 730 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. O fifth grade O sixth grade (b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. O fifth grade O sixth grade How does this result compare with the result in part (a)? O same result O different resultarrow_forwardPlease help with darrow_forward
- Twenty sections of bilingual math courses, taught in both English and Spanish, are to be offered in introductory algebra, intermediate algebra, and liberal arts math. The preregistration figures for the number of students planning to enroll in these bilingual sections are given in the following table. Use Webster's method with d = 29.6 to determine how many bilingual sections of each course should be offered. Course Introductory Algebra| Intermediate Algebra Liberal Arts Math Enrollment 139 271 182 ..... Course Introductory Algebra Number of Apportioned Sections 5 (Type an integer.) Course Intermediate Algebra Number of Apportioned Sections (Type an integer.)arrow_forwardPlease help with letter aarrow_forwarda rapid transit service operates 196 trains along five routes, A, B, C, D, and E. the number of trains assigned to each route is based on the average number of daily passengers per route given in the following table. use websters method to apportion the trains. (hint: a modified divisor between 50 and 60 will work.) please find each onearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY