for All Practical Purposes: Mathematical Literacy in Today's World Tenth Edition Test Bank

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Chapter 1: Urban ServicesFree-ResponsePage30Format:ShortAnswer1.On a graph that represents six cities and the roads between them, the valence of vertexA is 4. What does this mean in real-world terms?Ans:If the valence of vertex A is four, it means there are four roads that lead to townA.Format:ShortAnswer2.A graph that represents six cities and the roads among them is connected. What doesthis mean in real-world terms?Ans:Any pair of two cities has at least one connecting path of roads.Format:ShortAnswer3.Describe the two conditions for a graph to have an Euler circuit.Ans:The graph must be connected and haveall valences even.Format:ShortAnswer4.Draw a graph representing four cities, A, B, C, and D, with a road that connects eachpair of cities given:AB, AC, BC, BD, CDAns:Format:ShortAnswer5.Draw a graph with vertices A, B, C, and D in which the valence of vertices A and D is3 and the valence of vertices B and C is 2.Ans:Answersmay vary. One solution is:

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Chapter 1 Free-ResponsePage31Format:ShortAnswer6.Draw a graph with vertices A, B, and C in which A has valence 4 and B and C havevalence 5.Ans:Format:ShortAnswer7.Draw a graph that has four vertices, with valences 1, 2, 3, and 4.Ans:Format:ShortAnswer8.Consider the path represented by the sequence of numbered edges on the graph below.Explain why the path isNOTan Eulercircuit.Ans:The path is notan Eulercircuit because it does not start and stop at the samevertex.

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Chapter 1 Free-ResponsePage32Format:ShortAnswer9.Consider the path represented by the sequence of numbered edges on the graph below.Explain why the path isNOTan Eulercircuit.Ans:The path is notan Eulercircuit because it does not cover every edge of the graph.Format:ShortAnswer10.Draw a graph with eight vertices, with the valence of each vertex being even, that doesNOThavean Eulercircuit.Ans:Answers may vary. One solution is:Format:ShortAnswer11.Explain why the graph shown below doesNOThavean Eulercircuit.Ans:The graph does not havean Eulercircuit because the valences of vertex B andvertex D are odd.

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Chapter 1 Free-ResponsePage33Format:ShortAnswer12.Explain why the graph shown below doesNOThavean Eulercircuit.Ans:The graph does not havean Eulercircuit because it is not connected.Use the following to answer Questions 13–16:Identifyan Eulercircuit on the following graphs by numbering the sequence of edges in theorder traveled.Reference:1-1Format:ShortAnswer13.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage34Reference:1-1Format:ShortAnswer14.Ans:Answers may vary. One solution is:Reference:1-1Format:ShortAnswer15.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage35Reference:1-1Format:ShortAnswer16.Ans:Answers may vary. One solution is:Use the following to answer Questions 17–22:Add wiggly edges to find an efficient eulerization of the following graphs.Reference:1-2Format:ShortAnswer17.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage36Reference:1-2Format:ShortAnswer18.Ans:Answers may vary. One solution is:Reference:1-2Format:ShortAnswer19.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage37Reference:1-2Format:ShortAnswer20.Ans:Answers may vary. One solution is:Reference:1-2Format:ShortAnswer21.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage38Reference:1-2Format:ShortAnswer22.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage39Format:ShortAnswer23.The map below gives the territory of a parking control officer. The dots representmeters that must be checked. Draw the graph that would be useful for finding anefficient route.Ans:

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Chapter 1 Free-ResponsePage40Format:ShortAnswer24.For the street network shown below, draw a graph that would be useful for routing agarbage truck. Assume all streets are two-way and that passing once down the street issufficient for collecting trash from both sides.Ans:

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Chapter 1 Free-ResponsePage41Format:ShortAnswer25.Findan Eulercircuit on the graph on the left and use it to find a circuit on the graph onthe right that reuses one edge.Ans:Answers may vary. One solution is:Format:ShortAnswer26.Findan Eulercircuit on the graph on the left and use it to find a circuit on the graph onthe right that reuses four edges.Ans:Answers may vary. One solution is:

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Chapter 1 Free-ResponsePage42Format:ShortAnswer27.Findan Eulercircuit on the graph on the left and use it to find a circuit on the graph onthe right that reuses three edges.Ans:Answers may vary. One solution is:Format:ShortAnswer28.Findan Eulercircuit on the graph on the left and use it to find a circuit on the graph onthe right that reuses three edges.Ans:Answers may vary.One solution is:

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Chapter 1 Free-ResponsePage43Format:ShortAnswer29.Why would a city street department want its snowplow operator’s path to followanEulercircuit if possible?Ans:If the snowplow operator followedan Eulercircuit, he would end his route at thecity garage where he started. Also, no time or gas would be wasted travelingdown streets that were already plowed.Format:ShortAnswer30.Give three real-world applications in which a worker would want to findan Eulercircuit on a street network.Ans:Answers may vary. Some situations include:Plowing snowPainting lines down the center of streetsCollecting trashChecking gutters on the corners of all streetsChecking parking meters along the edge of all streetsDelivering mail to all houses on all streetsFormat:ShortAnswer31.Draw a connected graph with seven vertices where each vertex has valence 4.Ans:Answers will vary. One solution is:

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Chapter 1 Free-ResponsePage44Format:ShortAnswer32.Draw a graph with six vertices where the valences are 1, 2, 2, 3, 4, and 4.Ans:Answers will vary. One solution is:Format:ShortAnswer33.Findaneulerizationwith nine added edges for a 36–block rectangular street network.Ans:Format:ShortAnswer34.Draw a graph where every vertex has a valence of at least 2 but removing a single edgedisconnects the graph.Ans:Answers will vary. One solution is:

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