BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 4.1, Problem 18ES

Textbook Problem

1 views

College Security A college apportions 40 security personnel among three education centers according to their enrollments. The following table shows the present enrolments at the three centers.

a. Use the Hamilton method to apportion the security personnel.

b. After one semester, the centers have the following enrolments,

Center A has an increased enrollment of 14 students, which is an increase of
*25* students, which is an increase of

To determine

**(a)**

Use the Hamilton method to apportion the security personnel.

**Given Information:**

Center | | | |

Enrollment | | | |

**Concept used:**

**Calculation:**

Since a college apportions

Therefore,

Now in Hamilton method divide each enrollment by standard divisor to get a quotient and standard quota

Center | Enrollments | Quotient | Standard quota | Number of Security personnel |

| | |

To determine

**(b)**

If the security personnel are reapportioned using the Hamilton method, will the population paradox occur? Explain.

Mathematical Excursions (MindTap Course List)

Show all chapter solutions

Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Give each state one representative. Use the...Ch. 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 - What is quota rule?Ch. 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 - College Security A college apportions 40 security...Ch. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Education The science division of a college...Ch. 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 - 25. The population of Louisiana increased 1.4%...Ch. 4.1 - House of Representatives Currently. the U.S. House...Ch. 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 - 32. According to the 2010 census, what is the...Ch. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Deriving the Huntington-Hill Number The...Ch. 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 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Suppose the Borda method used in Exercise 1 of...Ch. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Suppose the assignment of points for first,...Ch. 4.2 - What is the difference between a majority and a...Ch. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Explain how the Borda Count method of voting...Ch. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - 5. Explain how the pairwise comparison voting...Ch. 4.2 - What does the Condorcet criterion say?Ch. 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 - Cartoons Use the Borda count method of voting to...Ch. 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 - Cell Phone Usage Use plurality with elimination to...Ch. 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 - Family Reunion The Nelson family is trying to...Ch. 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 - Baseball Uniforms Use the pairwise comparison...Ch. 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 - Does the winner in Exercise 2k satisfy the...Ch. 4.2 - Does the winner in Exercise 24c satisfy the...Ch. 4.2 - Does the winner in Exercise 17 satisfy the...Ch. 4.2 - Does the winner in Exercise 20 satisfy the...Ch. 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 - Approval voting is a system in which voters may...Ch. 4.2 - Restaurants Suppose you and three friends. David,...Ch. 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 - Using the data in Check Your Progress 3 on page...Ch. 4.3 - For the data in Check Your Progress 3 on page 215,...Ch. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Create a voting system with four members in which...Ch. 4.3 - Create a voting system with five members that...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...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 - 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 - 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 - Which, if any, of the voting systems in Exercises...Ch. 4.3 - Explain why it is impossible to calculate the...Ch. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Four voters. A, B. C, and D. make decisions by...Ch. 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 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Football The head coach in Exercise 23 has decided...Ch. 4.3 - Consider the weighted voting system { 60:4,56,58...Ch. 4.3 - 26. Consider the weighted voting system {...Ch. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - 28. a. In a weighted voting system, suppose that...Ch. 4.3 - Voter Intimidation and Tampering Consider the...Ch. 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 - Is the Hamilton apportionment method susceptible...Ch. 4 - Is the Jefferson apportionment method susceptible...Ch. 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 - Campus Election Four students are running for the...Ch. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Use the pairwise comparison method of voting to...Ch. 4 - Use the pairwise comparison method of voting to...Ch. 4 - Homecoming Queen Three high school students are...Ch. 4 - Homecoming Queen In Exercise I. suppose Cynthia L....Ch. 4 - Scholarship Awards A scholarship committee must...Ch. 4 - A weighted voting system for voters A, B, C, and D...Ch. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Calculate the Banzhaf power indices for voters A....Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Identify any dictator and all dummies for each...Ch. 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 - A weighted voting system for voters A, B, C, D....Ch. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Executives Preferences A company with offices...Ch. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Budget Proposal A committee must vote on which of...Ch. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...

Find more solutions based on key concepts

Show solutions In Exercises 15-22, find the equation of the specified line. Through (1,2) parallel to x2y=2

Finite Mathematics

Use the following factorization formulas involving cubes to factor each expression in Problems 49-56.
Factoriz...

Mathematical Applications for the Management, Life, and Social Sciences

Describe the set of points (x,y) such that x2+y2=0.

Applied Calculus

Using Rolle's Theorem In Exercises 11-26, determine whether Rolles Theorem can be applied to f on the closed in...

Calculus: Early Transcendental Functions

For the following set of scores: a. Construct a frequency distribution table. b. Sketch a histogram showing the...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13-30, sketch the areas under the ...

Understanding Basic Statistics

For Problems 51-78, simplify each of the numerical expressions. Objective 3 3+4685

Intermediate Algebra

New Users The number of registered users at OHaganBooks.com has increased substantially over the past few month...

Finite Mathematics and Applied Calculus (MindTap Course List)

Equations of Circles Find an equation of the circle that satisfies the given conditions. 90. Center (1, 4); rad...

Precalculus: Mathematics for Calculus (Standalone Book)

Find the radius of convergence and interval of convergence of the series. 43. n=02n(x3)nn+3

Calculus: Early Transcendentals

Find all values of r such that the parabolas y = 4x2 and x = c + 2y2 intersect each other at right angles.

Single Variable Calculus: Early Transcendentals, Volume I

Graph the particular solution and several other solutions. What characteristics do these solutions have in comm...

Multivariable Calculus

Suppose the amount of liquid dispensed by a certain machine is uniformly distributed with lower limit A = 8 oz ...

Probability and Statistics for Engineering and the Sciences

In Exercises 1921, describe the interval(s) on which the function is continuous. Explain why the function is co...

Calculus: An Applied Approach (MindTap Course List)

In Exercises 1-8, use the graph of the given function f to determine limxaf(x) at the indicated value of a, if ...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

2. Define the terms population, sample, parameter and statistic.

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the limit, if it exists. 29. limt0(1t1+t1t)

Single Variable Calculus

Determine whether the series is convergent or divergent. n=1n2n(1+2n2)n

Calculus (MindTap Course List)

SOC A researcher has gathered information from a random sample of 178 households. For each of the following var...

Essentials Of Statistics

Find the value of each trigonometric ratio rounded to four significant digits: cos16.9

Elementary Technical Mathematics

Divide the following fractions and reduce to lowest terms.
23.

Contemporary Mathematics for Business & Consumers

Prove that the statements in Exercises are true for every positive integer .
3.

Elements Of Modern Algebra

For Questions 1 through 4, fill in each blank with the appropriate word. To find the arc length for a central a...

Trigonometry (MindTap Course List)

If MNPQin O, explain why MNPQ is an isosceles trapezoid. HINT: Draw a diagonal.

Elementary Geometry For College Students, 7e

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Single Variable Calculus: Early Transcendentals

Construct a 33 matrix A having the property that A=AT. What special characteristic does A have?

Finite Mathematics for the Managerial, Life, and Social Sciences

Determining Convergence or Divergence In Exercises 45-58, determine the convergence or divergence of the series...

Calculus: Early Transcendental Functions (MindTap Course List)

If the measures of the angles of a quadrilateral are in the ratio of 3:4:5:6, find the measure of each angle.

Elementary Geometry for College Students

Slope Field In Exercises 49 and 50, use a computer algebra system to graph the slope field for the differential...

Calculus of a Single Variable

In Exercises 11 and 12, express the given fractions as equivalent fractions with the indicated denominators. 12...

Mathematics For Machine Technology

Which curve is simple but not closed?

Study Guide for Stewart's Multivariable Calculus, 8th

Use a Table of Integrals to evaluate .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Solve each absolute value inequality. Express the solution set in interval notation, and graph it. 3|3x12|5

College Algebra (MindTap Course List)

Is the number of square feet of living space a good predictor of a houses selling price? The following data sho...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Center of Mass of a Two-Dimensional System Find the center of mass of the given system of point masses. mi 3 2 ...

Calculus (MindTap Course List)

It has been demonstrated that students with high self-esteem tend to have higher grades than students with low ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Compensation for Sales Professionals Suppose that a local chapter of sales professionals in the greater San Fra...

Statistics for Business & Economics, Revised (MindTap Course List)

Path of a ObjectWhen t=0, an object is at the point (0,1) and has a velocity vector v(0)=i. It moves with an ac...

Multivariable Calculus

Explain the advantages and disadvantages of using random assignment as a method to prevent individual differenc...

Research Methods for the Behavioral Sciences (MindTap Course List)

A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle...

Introduction To Statistics And Data Analysis

Find the mistakes in the “proofs” shown in 15—19. 17. Theorem: For every integer k, if k0 then k2+2k+1 is compo...

Discrete Mathematics With Applications

The Roths bought a house for 432,500. They paid the sellers a 20 down payment and obtained a simple interest am...

Mathematics: A Practical Odyssey

If D is defined as in (9), then find eDt.

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Test the following hypotheses by using the χ2 goodness of fit test.
H0: pA = .40, pB = .40, and pC = .20
Ha: Th...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Graphing an Exponential Function In Exercises 17-24, use a graphing utility to construct a table of values for ...

College Algebra

Drug-Resistant Gonorrhea. Each year, more than 2 million people in the United States become infected with bacte...

Essentials Of Statistics For Business & Economics

Reminder Round all answers to two decimal places unless otherwise indicated. Marginal Tax RateLet T(I) denote t...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)