Thinking Mathematically, Books A La Carte Edition Format: Unbound (saleable)
7th Edition
ISBN: 9780134686516
Author: Blitzer, Robert F.
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.4, Problem 3E
The table shows the populations of three states in a country with a population of 20,000, Use Hamilton’s method to show that the Alabama paradox occurs if the number of seats in congress is increased from 40 to 41.
| State | A | B | C | Total |
| Population | 680 | 9150 | 10,170 | 20,000 |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
T3.2: Prove that if the Graceful Tree Conjecture (every tree has a graceful labeling) is true and T' is
a tree with m edges, then K2, decomposes into 2m - 1 copies of T.
Hint - Delete a leaf to get 7" and apply the decomposition of K2(m-1)+1 = K2m-1 into T'. Then
explain how the decomposition allows the pendant edge to be added to a new vertex to obtain a
decomposition of K2m into copies of T.
Use the matrix tree theorem to determine the number of spanning trees of the graphs Kr∨sK1.These are the graphs formed by by adding all edges between a complete graph on r vertices and atrivial graph (no edges) on s vertices.
The maximum capacity spanning tree problem is as follows for a given graph G = (V, E) withcapacities c(uv) on the edges. The capacity of a tree T is defined as the minimum capacity of anedge in T. The maximum capacity spanning tree problem is to determine the maximum capacity ofa spanning tree.(i) Describe how to modify the input graph to find a maximum weight spanning tree making use ofa minimum weight spanning tree algorithm.(ii) Show that a maximum (weight) spanning tree is also a maximum capacity spanning tree.(iii) Is the converse of part (ii) true? That is, is it true that a maximum capacity spanning tree is alsoa maximum spanning tree? Either give counterexamples (of all sizes) or a proof.(iv) Prove the following max-min result. The maximum capacity of a spanning tree is equal to theminimum bottleneck value of a cut. For a subset U ⊆ V , the cut [U, V − U] is the set of edgesbetween U and V − U. The bottleneck value of a cut [U, V − U] is the largest capacity among theedges of…
Chapter 13 Solutions
Thinking Mathematically, Books A La Carte Edition Format: Unbound (saleable)
Ch. 13.1 - CHECK POINT 1 Four candidates are running for...Ch. 13.1 - CHECK POINT 2 Table 13.2 on page 841 shows the...Ch. 13.1 - Prob. 3CPCh. 13.1 - Prob. 4CPCh. 13.1 - CHECK POINT 5 Table 13.2 on page 841 shows the...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...
Ch. 13.1 - Prob. 6CVCCh. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Prob. 8CVCCh. 13.1 - In Exercises 1-2, the preference ballots for three...Ch. 13.1 - In Exercises 1-2, the preference ballots for three...Ch. 13.1 - In Exercises 3-4, four students are running for...Ch. 13.1 - Prob. 4ECh. 13.1 - Your class is given the option of choosing a day...Ch. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - 8. The travel club members are voting for the...Ch. 13.1 - Four professors are running for chair of the...Ch. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Use the preference table shown in Exercise 8....Ch. 13.1 - Prob. 13ECh. 13.1 - Use the preference table shown in Exercise 10. Who...Ch. 13.1 - Use the preference table shown in Exercise 7....Ch. 13.1 - Use the preference table shown in Exercise 8....Ch. 13.1 - Use the preference table shown in Exercise 9. Who...Ch. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - In Exercises 19-22, suppose that the pairwise...Ch. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Use the preference table shown in Exercise 9. Who...Ch. 13.1 - Prob. 26ECh. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - Prob. 28ECh. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - The programmers at the Theater Channel need to...Ch. 13.1 - 35. Five candidates. A, B, C, D, and E, are...Ch. 13.1 - Prob. 36ECh. 13.1 - Prob. 37ECh. 13.1 - Three candidates, A, B, and C, are running for...Ch. 13.1 - What is a preference ballot?Ch. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - 42. Describe the Borda count method. Is it...Ch. 13.1 - What is the plurality-with-elimination method? Why...Ch. 13.1 - What is the pairwise comparison method? Is it...Ch. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.1 - Make Sense? In Exercises 49-52, determine whether...Ch. 13.1 - Make Sense? In Exercises 49-52, determine whether...Ch. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - In Exercises 53-56, construct a preference table...Ch. 13.1 - Prob. 55ECh. 13.1 - In Exercises 53-56, construct a preference table...Ch. 13.1 - 57. Research and present a group report on how...Ch. 13.1 - Research and present a group report on how voting...Ch. 13.2 - CHECK POINT I The 14 members of the school board...Ch. 13.2 - Prob. 2CPCh. 13.2 - CHECK POINT 3 An election with 120 voters and...Ch. 13.2 - Prob. 4CPCh. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Prob. 4CVCCh. 13.2 - Prob. 5CVCCh. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Voters in a small town are considering four...Ch. 13.2 - 2. Fifty-three people are asked to taste-test and...Ch. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - A town is voting on an ordinance dealing with...Ch. 13.2 - A town is voting on an ordinance dealing with...Ch. 13.2 - 7. The following preference table gives the...Ch. 13.2 - Prob. 8ECh. 13.2 - 9. Members of the Student Activity Committee at a...Ch. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - Prob. 14ECh. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Describe the majority criterion.Ch. 13.2 - Describe the head-to-head criterion.Ch. 13.2 - Describe the monotonicity criterion.Ch. 13.2 - 23. Describe the irrelevant alternatives...Ch. 13.2 - 24. In your own words, state Arrow’s Impossibility...Ch. 13.2 - Prob. 25ECh. 13.2 - Is it possible to have election results using a...Ch. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Make Sense? In Exercises 28-31, determine whether...Ch. 13.2 - Prob. 30ECh. 13.2 - Make Sense? In Exercises 28-31, determine whether...Ch. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Citizen-initiated ballot measures often present...Ch. 13.3 - CHECK POINT 1 The Republic of Amador is composed...Ch. 13.3 - CHECK POINT 2 Refer to Check Point 1 on page 865....Ch. 13.3 - Prob. 3CPCh. 13.3 - Prob. 4CPCh. 13.3 - Prob. 5CPCh. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Prob. 4CVCCh. 13.3 - Prob. 5CVCCh. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - A university is composed of five schools. The...Ch. 13.3 - Prob. 6ECh. 13.3 - 7. A small country is composed of five states. A,...Ch. 13.3 - 8. A small country is comprised of four states, A,...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - The police department in a large city has 180 new...Ch. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - 15. Twenty sections of bilingual math courses,...Ch. 13.3 - Prob. 16ECh. 13.3 - A rapid transit service operates 200 buses along...Ch. 13.3 - Refer to Exercise 11. Use Webster’s method to...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - The table shows the 1790 United States census. In...Ch. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - 27. Describe how to find a standard divisor.
Ch. 13.3 - 28. Describe how to determine a standard quota for...Ch. 13.3 - Prob. 29ECh. 13.3 - Prob. 30ECh. 13.3 - Describe the apportionment problem.Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Explain why Hamilton’s method satisfies the quota...Ch. 13.3 - Prob. 35ECh. 13.3 - Suppose that you guess at a modified divisor, d,...Ch. 13.3 - Describe the difference between the modified...Ch. 13.3 - In allocating congressional seats, how does...Ch. 13.3 - 39. How are modified quotas rounded using...Ch. 13.3 - Why might it take longer to guess at a modified...Ch. 13.3 - In this Exercise Set, we have used apportionment...Ch. 13.3 - Prob. 42ECh. 13.3 - Make Sense? In Exercises 42-45, determine whether...Ch. 13.3 - Make Sense? In Exercises 42-45, determine whether...Ch. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - A small country is composed of three states, A, B,...Ch. 13.3 - Prob. 50ECh. 13.3 - Research and present a group| report on a brief...Ch. 13.4 - CHECK POINT I Table 13.42 shows the populations of...Ch. 13.4 - CHECK POINT 2 A small country has 100 seats in the...Ch. 13.4 - Prob. 3CPCh. 13.4 - Prob. 1CVCCh. 13.4 - Prob. 2CVCCh. 13.4 - Prob. 3CVCCh. 13.4 - Prob. 4CVCCh. 13.4 - 1. The mathematics department has 30 teaching...Ch. 13.4 - 2. A school district has 57 new laptop computers...Ch. 13.4 - 3. The table shows the populations of three states...Ch. 13.4 - The table at the top of the next column shows the...Ch. 13.4 - A small country has 24 seats in the congress,...Ch. 13.4 - Prob. 6ECh. 13.4 - 7. A town has 40 mail trucks and four districts in...Ch. 13.4 - 8. A town has five districts in which mail is...Ch. 13.4 - A corporation has two branches A and B. Each year...Ch. 13.4 - 10. A corporation has three branches, A, B, and C...Ch. 13.4 - Prob. 11ECh. 13.4 - a. A country has three states, state A, with a...Ch. 13.4 - 13. In Exercise 12, use Jefferson’s method with ...Ch. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - What is the new-states paradox?Ch. 13.4 - 17. According to Balinski and Young’s...Ch. 13.4 - Make Sense? In Exercises 18-21, determine whether...Ch. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Make Sense? In Exercises 18-21, determine whether...Ch. 13.4 - Give an example of a country with three states in...Ch. 13 - 1. The 12 preference ballots for four candidates...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - Prob. 6RECh. 13 - In Exercises 6-9, the Theater Society members are...Ch. 13 - In Exercises 6-9, the Theater Society members are...Ch. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - In Exercises 10-13, four candidates, A, B, C, and...Ch. 13 - In Exercises 14-16, voters in a small town are...Ch. 13 - In Exercises 14-16, voters in a small town are...Ch. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Use the following preference table to solve...Ch. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Use the following preference table, which shows...Ch. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - In Exercises 37-40, a country is composed of four...Ch. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - A country has 100 seats in the congress, divided...Ch. 13 - Prob. 43RECh. 13 - Is the following statement true or false? There...Ch. 13 - Prob. 1TCh. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Prob. 8TCh. 13 - Prob. 9TCh. 13 - Prob. 10TCh. 13 - Prob. 11TCh. 13 - Prob. 12TCh. 13 - Prob. 13TCh. 13 - Prob. 14TCh. 13 - Prob. 15TCh. 13 - Prob. 16TCh. 13 - In Exercises 16-24, an HMO has 10 doctors to be...Ch. 13 - Prob. 18TCh. 13 - Prob. 19TCh. 13 - Prob. 20TCh. 13 - Prob. 21TCh. 13 - Prob. 22TCh. 13 - Prob. 23TCh. 13 - Prob. 24TCh. 13 - Prob. 25T
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
- 1) Find The inverse The domain of m(x) = tion and of the function The inverse function 3- √x-aarrow_forwardProve that the following version of a greedy algorithm produces a minimum spanning tree in aweighted graph. Start with a vertex v as the initial tree and at each stage add an edge with minimumweight having exactly one end in the current tree. Stop when all vertices have been addedarrow_forwardb. According to the analyst, what is the probability that the confidence score is not 1? 11. Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.10 B 3 0.30 C 2 0.40 D 1 0.10 F O 0.10 a. Depict the probability distribution graphically. Comment on whether or not the probability distribution is symmetric. b. Convert the probability distribution to a cumulative probability distribution. C. What is the probability of earning at least a B in Professor Sanchez's course? d. What is the probability of passing Professor Sanchez's course? 2. Professor Khurana expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5% chance that she may not be able to fund any student, there is an 80% chance that she will be able to fund two students. a. What hat is the proarrow_forward
- Graph the following function. Please also graph the asymptote. Thank you.arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forwardTwo cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forward
- An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ Noarrow_forwardAt a local college, for sections of economics are taught during the day and two sections are taught at night. 70 percent of the day sections are taught by full time faculty. 20 percent of the evening sections are taught by full time faculty. If Jane has a part time teacher for her economics course, what is the probability that she is taking a night class?arrow_forward4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License