Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 2EE
Find the apportionment that would have resulted if the Hamilton method had been used.
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The 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.
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RECh. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
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- The 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. Number of Number of teachers students Fifth grade 21 639 Sixth grade 23 699 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. O fifth grade sixth grade (b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. fifth grade sixth grade How does this result compare with the result in part (a)? same result different resultarrow_forwardQUESTION 1. APPORTIONMENT. Five city police departments are asking the FBI for urgent assistance. They want experienced special agents to come to their cities and work with them on their hardest cases. The director of the FBI has 44 special agents he can send. He decides to allocate agents in accord with the population of the cities, using the Alexander Hamilton method for apportionment. The cities and populations are: Chicago: 2,907,000 Houston: 2,560,000 Philadelphia: 1,750,000 Phoenix: 1,453,000 San Diego: 1,230,000 How many FBI agents are assigned to each city? (Show the calculations.)arrow_forwardWhich apportionment paradox may be produced by the Adams' method but not the Webster method?arrow_forward
- The 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_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. Number of Teachers Number of Students Fifth Grade 20 576 Sixth Grade 23 726 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. fifth gradesixth grade (b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. fifth gradesixth grade How does this result compare with the result in part (a)? same resultdifferent resultarrow_forwardIf 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.arrow_forward
- The 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. Number of Teachers Number of Students Fifth Grade 20 576 Sixth Grade 23 726 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. fifth grade sixth gradearrow_forwardA Father of four children plans to distribute 40 ampao among his children based on the hours they study their subjects. If he uses the Hamilton method, what will be the fairway to divide the ampao? Child 1 Child 2 Child 3 child 4 Total Minutes worked 40 50 170 20 280 Standard Quota Lower Quota Final apportionment Allocationarrow_forwardIn the controversial election of 1876, Republican Rutherford B. Hayes ran against Democrat Samuel J. Tilden. Tilden won the popular vote with 4,300,590 votes, whereas Hayes received 4,036,298 votes. Rutherford B. Hayes became president according to an unconstitutional apportionment of votes. If the population of one state was 4,382,759 and the total population was 38,115,641, find the state quota if the House size was 294. Any state with a remainder above 0.438464 would be given an additional representative. Should the state have received an additional representative? The state quota was (Round to three decimal places as needed.) Should the state have received another representative? Yes Noarrow_forward
- The Republic of Amador is composed of five states, A, B, C, D, and E. According to the country's constitution, the Congress will have 200 seats, divided among the five states according to their respective populations. State C D E Population |(in thousands) 1112 1118 1320 1515 4935 Use Adam's method with d = 50.6 to apportion the %3D 200 congressional seats for state A and E. Seats for state A = Seats for state E =arrow_forwardIn the controversial election of 1876, Republican Rutherford B. Hayes ran against Democrat Samuel J. Tilden. Tilden won the popular vote with 4,300,590 votes, whereas Hayes received 4,036,298 votes. Rutherford B. Hayes became president according to an unconstitutional apportionment of votes. If the population of one state was 4,383,359 and the total population was 48,115,641, find the state quota if the House size was 289. Any state with a remainder above 0.438464 would be given an additional representative. Should the state have received an additional representative? The state quota was ?arrow_forward
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