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mathematics
survey of mathematics
Questions and Answers of
Survey of Mathematics
Suppose that the plurality method is used on the following preference table. If C drops out, is the irrelevant alternatives criterion satisfied? Explain. Number of Votes First 3 B A Second Third A B B
Suppose that the plurality method is used on the following preference table. If B drops out, is the irrelevant alternatives criterion satisfied? Explain Number of Votes First Second 4 A B B Third B A
Twenty-five people are surveyed in the Mall of America and asked to taste and rank four different brands of coffee. The preference table below shows the rankings of the 25 voters. Suppose that the
Twenty-one people are asked to taste test and rank three different brands of grape jelly. The preference table below shows the rankings of the 21 voters. Suppose that the plurality with elimination
The planning committee of Tulsa Community College is considering three proposals, A, B, and C, for the design of a new technology building for the college. The nine members of the planning committee
The administration at Erie Community College is considering three possible areas of improvement to the school’s residence halls: parking (P), security (S), and lounge areas (L). The nine members of
The children in Ms. Cohn’s seventh-grade class are voting on a theme for their class party. Their choices are beach (B), the world (W), superheroes (S), or rock and roll (R). The results are shown
The board of directors at The Limited is considering three different administrative restructuring plans, A, B, and C. The 11 members of the board of directors rank the plans according to the
In many corporations and professional societies, the members of the board of directors are elected by a method called approval voting. With approval voting, a voter does not cast a ranked ballot.
Suppose that 15 voters rank four candidates.(a) What is the total number of points awarded to candidates using the Borda count method?(b) Suppose that using the Borda count method, candidate A
Suppose that 20 voters rank three candidates.(a) What is the total number of points awarded to the candidates using the Borda count method? (b) Suppose that, using the Borda count method,
The results of a swim meet between the Comets (C), Rams (R), Warriors (W), and Tigers (T) are shown in the preference table below. Notice, for example, that in the sprint competition, the Comets (C)
Friskies Cat Food is looking for a new cat for the cover of their 2016 calendar. Four cats are finalists: A, B, C, and D. They are ranked first, second, third, and fourth in each of the following
A ski club is having an election for president. There are three candidates and 15 voters. Each voter casts a ballot listing his or her preferences for the candidates. Just before the winner is to be
Describe one way other than flipping a coin to settle a tied election.
Describe a benefit of the Borda count method over the plurality method.
The Wizards Computer Club is ordering five new computers. To obtain a discount price, the club has decided that all five should be the same brand. The choices they are considering are Mac (M),
The flowers in a garden at a resort need to be replaced. The choices for the flowers are Geraniums (G), Impatiens (I), Petunias (P), and Zinnias (Z). The head gardener holds an election in which all
The programmers at the Retro-Vision cable television station are deciding which classic TV show should lead their prime-time programming. Their choices are Friends(F), Seinfeld(S), Mash(M), and
The board of directors of Precision Optics is holding an election to decide which contractor should be hired to build an expansion to its corporate head-quarters. The 15 members of Precision
Determine the winner using the plurality with elimination method if the candidate with the most last-place votes is eliminated at each step.The 11 members of the Henrietta Town Board must decide
Determine the winner using the pairwise comparison method.The 11 members of the Henrietta Town Board must decide where to build a new post office. Their three choices are Lehigh Road (L), Erie Road
Determine the winner using the plurality with elimination method.The 11 members of the Henrietta Town Board must decide where to build a new post office. Their three choices are Lehigh Road (L), Erie
Determine the winner using the Borda count method.The 11 members of the Henrietta Town Board must decide where to build a new post office. Their three choices are Lehigh Road (L), Erie Road (E), and
Determine the winner using the plurality method.The 11 members of the Henrietta Town Board must decide where to build a new post office. Their three choices are Lehigh Road (L), Erie Road (E), and
Another way to determine the winner if the plurality with elimination method is used is to eliminate the candidate with the most last-place votes at each step. Using the preference table given above,
Determine the winner using the plurality with elimination method.The 12 members of the executive committee of the Student Senate must vote for a student representative for the college board of
Determine the winner using the pairwise comparison method.The 12 members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from
Determine the winner using the plurality method.The 12 members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among
Determine the winner using the Borda count method.The 12 members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among
Determine the winner using the pairwise comparison method.The National Football League (NFL) is considering four cities for expansion: San Antonio (S), Los Angeles (L), Honolulu (H), and Toronto (T).
Determine the winner using the plurality with elimination method.The National Football League (NFL) is considering four cities for expansion: San Antonio (S), Los Angeles (L), Honolulu (H), and
The National Football League (NFL) is considering four cities for expansion: San Antonio (S), Los Angeles (L), Honolulu (H), and Toronto (T). The 32 current owners rank the four candidates
Determine the winner using the plurality method.The National Football League (NFL) is considering four cities for expansion: San Antonio (S), Los Angeles (L), Honolulu (H), and Toronto (T). The 32
The Wilson family is trying to decide whether to go to Washington, D.C. (W), Orlando (O), or Virginia Beach (V) on their summer vacation. The two parents, five children, and two
Determine the winner using the pairwise comparison method.The Wilson family is trying to decide whether to go to Washington, D.C. (W), Orlando (O), or Virginia Beach (V) on their summer vacation. The
Determine the winner using the plurality method.The Wilson family is trying to decide whether to go to Washington, D.C. (W), Orlando (O), or Virginia Beach (V) on their summer vacation. The two
Determine the winner using the Borda count method.The Wilson family is trying to decide whether to go to Washington, D.C. (W), Orlando (O), or Virginia Beach (V) on their summer vacation. The two
Determine the winner using the pairwise comparison method.Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a canoe
Determine the winner using the plurality with elimination method.Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a
Determine the winner using the Borda count method.Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a canoe (C).
Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a canoe (C). Each employee ranks the three
Is there a majority winner?Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a canoe (C). Each employee ranks the
How many employees voted?Employees of Brighton Summer Camp are choosing a new logo for their summer camp brochure. The choices are a sun (S), a lake (L), and a canoe (C). Each employee ranks the
Eight voters are asked to rank three brands of yogurt: Dannon (D), Breyers (B), and Columbo (C). The eight voters turn in the following ballots showing their preferences in order: Make a preference
Nine voters are asked to rank three brands of potato chips: Pringles (P), Lay’s (L), and Kettle (K). The nine voters turn in the following ballots showing their preferences in order:Make a
Five candidates are running for president of the Student Senate. They receive the following votes:(a) Determine the winner using the plurality method. (b) Did this candidate receive a majority
Three candidates are running for mayor of Austin. They receive the following votes: a) Determine the winner using the plurality method. b) Did this candidate receive a majority of votes? Li 102,503
Fill in the blank with an appropriate word, phrase, or symbol(s).The voting method that may involve a series of elections until a candidate receives a majority of the votes is called the
Fill in the blank with an appropriate word, phrase, or symbol(s).The voting method in which each candidate is compared with each of the other candidates is called the _____________ method.
Fill in the blank with an appropriate word, phrase, or symbol(s).In the Borda ________________ voting method, the candidates are ranked from most favored to least favored.
Fill in the blank with an appropriate word, phrase, or symbol(s).The voting method in which each voter votes for one candidate and the candidate receiving the most votes is declared the winner is
Fill in the blank with an appropriate word, phrase, or symbol(s).When there are four candidates, the number of comparisons needed with the pairwise comparison method is ________________.
Fill in the blank with an appropriate word, phrase, or symbol(s).When using the pairwise comparison method, the number of comparisons, c, needed when there are n candidates is determined by the
Fill in the blank with an appropriate word, phrase, or symbol(s).A table that summarizes the results of an election is called a(n) _________ table.
Fill in the blank with an appropriate word, phrase, or symbol(s).A candidate who receives more than 50% of the votes in an election is said to have a(n) ____________ of votes.
If the new irrigation materials cost $1.25 per foot, what would be the cost of installing the system determined in part (a)?Use the following information.Daniel is planning a new irrigation system
Determine the minimum-cost spanning tree that reaches each valve.Use the following information.Daniel is planning a new irrigation system for his yard. His current system has valves already in place
Determine the minimum-cost spanning tree for the following graph. B 3 37 11 19 17 13, 23 41 31
Determine a spanning tree for the graph shown below. D Н/ K
Use a tree to show the parent–child relationships in the following family. Beth has three children: Kevin, Darrell, and Teri. Kevin has one child, Chris. Darrell has two children: Michelle and
Use the nearest neighbor method to approximate the optimal route for Doug to visit each company and return to Champs Sports. What is the cost of this route?Use the following information.Doug is a
Use the brute force method to determine the least expensive route for Doug to visit each company and return to Champs Sports. What is the cost of this route?Use the following information.Doug is a
Represent this traveling salesman problem with a complete weighted graph showing the prices of flights on the appropriate edges.Use the following information.Doug is a purchasing agent for Champs
Tamiko is campaigning in Arizona for the U.S. Senate. Tamiko lives in Yuma and she wishes to travel to the following cities: Flagstaff, Phoenix, Tombstone, Tucson, and Winslow. How many different
Draw a complete graph with five vertices.
In the following graph, determine a Hamilton circuit. B D Н K
In the following graph, determine a Hamilton path. A D B E C F G
Use Fleury’s algorithm to determine an Euler circuit in the following graph. B De G Н
Is it possible for a person to walk through each doorway in the house, whose floor plan is below, without using any of the doorways twice? If so, indicate in which room the person may start and where
In the following graph, determine an Euler circuit. B Н
In the following graph, determine an Euler path. B
Draw a disconnected graph.
The drawing below shows the floor plan of Carol Ann’s Photography Studio. Construct a graph to represent the studio using the letters shown to label the vertices. Use the letter O to label the
Represent the map below as a graph where each vertex represents a country and each edge represents a common border between the countries. BURKINA FASO SIERRA LEONE GHANA IVORY COAST LIBERIA TÖGO
Create a graph with seven vertices, a bridge, and a loop.
Lucille wants to install an irrigation system to water all six of her flowerbeds in her backyard. The drawing shows the location of each flowerbed and the distance between them in feet.(a) Represent
Determine the minimum-cost spanning tree for the following graph. B 3 18 9. 21 15 24 12 27
Determine two different spanning trees for the following graph. B C• PE
Use a tree to show the supervisory relationships in the Hulka Consulting Corporation. Hulka is president. Winger and Ziskey are vice presidents who work for Hulka. Markowicz, Oxburger, and Soyer are
Jennifer is the sales manager for AT&T for the state of Missouri. There are major sales offices in Columbia, Kansas City, St. Joseph, St. Louis, and Springfield. The distances in miles between
Lance is searching for a new job. He lives in Portland, Oregon, and has interviews in Des Moines, Iowa; Charleston, West Virginia; and Montgomery, Alabama. The costs of the one-way flights between
The American League Eastern Division has the following teams: Baltimore Orioles, Boston Red Sox, New York Yankees, Tampa Bay Rays, and Toronto Blue Jays. How many different possible ways could a
Draw a complete graph with five vertices.
Determine two different Hamilton circuits in the following graph. B D |н G K
Determine two different Hamilton paths in the following graph. B D Н K
Use Fleury’s algorithm to determine an Euler circuit in the following graph. B Н K L
Use Fleury’s algorithm to determine an Euler path in the following graph. B D' G
(a) Can a police officer walk each street shown in the figure below without walking any street more than once? Explain.(b) If yes, where would the police officer have to start the walk? Alvarez Ave.
(a) The drawing below shows the floor plan of a single-story house. Construct a graph that represents the floor plan. (b) Is it possible for a person to walk through each doorway in the house
Consider the following map.(a) Represent the map as a graph. (b) Determine (state yes or no) whether the graph has an Euler path. If yes, give one such Euler path. (c) Determine (state yes
Determine an Euler circuit that begins with vertex E.Use the following graph. A B G
Determine an Euler circuit that begins with vertex A.Use the following graph. A B G
Determine an Euler path that begins with vertex F.Use the following graph. A B св D G Н
Determine an Euler path that begins with vertex C.Use the following graph. A B св D G Н
Identify any bridges in the graph below. B G JE Н
Determine whether the graph shown is connected or disconnected. B G
Determine whether the graph shown is connected or disconnected. B D
The drawing below shows the floor plan of Raintree Montessori School. Construct a graph to represent the school using the letters shown to label the vertices. Use the letter O to label the vertex
Represent the map as a graph where each vertex represents a state and each edge represents a common border between the states. WA OR ID CA NV UT AZ
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