# Project #67840 - Quiz 6

1  of 20
Determine whether the graph is connected or disconnected.

 Connected Disconnected
2  of 20
Find the standard divisor for the given situation.

A school district receives a grant to purchase 39 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table:

 30.59 31.9 34.82 40.23
3  of 20
The mathematics department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S):

A second election is then held resulting in the following preference table:

If the plurality with elimination method is used to determine the winner, is the montonicity criterion satisfied?
 Yes No
4  of 20
Determine whether the graph is connected or disconnected.
 Connected Disconnected
5  of 20
A country with two states has 16 seats in the legislature. The population of each state (in thousands) is as follows:

Does the new-states paradox occur using Hamilton's method of apportionment?
 Yes No
6  of 20
Determine whether the graph is connected or disconnected.

 Connected Disconnected
7  of 20
For the floor plan below, is it possible to find a circuit that passes through each doorway exactly one time?

 Yes No
8  of 20
A condominium association is holding an election for president of the board of directors. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Abbott (A), Blake (B), Cleary (C), and Downs (D):

Determine the winner using the plurality method and whether the winner received a majority of first-place votes.
 Abbott; Yes Abbott; No Cleary; Yes Cleary; No
9  of 20
For the following floor plan, is it possible to find a route that begins in one room, passes through each doorway exactly once, and ends in the starting room?

 Yes No
10  of 20
The mathematics department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S):

If the plurality method is used to determine the winner and Clark drops out, is the irrelevant alternatives criterion satisfied?
 Yes No
11  of 20
A condominium association is holding an election for president of the board of directors. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Abbott (A), Blake (B), Cleary (C), and Downs (D):

If the plurality method if used to determine the winner and Downs drops out, is the irrelevant alternatives criterion satisfied?
 Yes No
12  of 20
Find two different Hamilton circuits for the given graph.

 A → B → E → D → A  //  A → C → E → B → C → D → A A → B → E → D → C → A  //  A → C → D → E → A → B A → B → E → D → C → A  //  A → D → C → E → B → A The graph does not have two different Hamilton circuits.
13  of 20
Martinson Company is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference table:

Determine the winner using the pairwise comparison method.
14  of 20
A university has 21 scholarships to be apportioned among the engineering students based on the enrollment in each department. There are three departments: mechanical engineering (M), electrical engineering (E), and civil engineering (C). The number of students in each department is given in the following table:

Find the modified quota for the civil engineering department using the divisor 27.
 5.47 5.52 5.67 5.72
15  of 20
A school district receives a grant to purchase 55 new computers to be apportioned among the 6 schools in the district based on the student population of each school. The student populations are given in the following table:

Find the modified quota for school B using the divisor 28.5.
 7.4 7.52 7.55 7.63
16  of 20
Using the following graph, find an Euler path that starts with vertex B.

 B → A → C → D B → A → D → C B → A → D → C → A → B No Euler path exists.
17  of 20
The Spanish department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Cortazar (C), Jimenez (J), and Soto (S):

If the Borda count method is used to determine the winner, is the majority criterion satisfied?
 Yes No
18  of 20
Find two different Hamilton paths for the given graph.

 A → B → C → A → D  //  A → C → B → A → D C → B → A → D  //  D → B → A → C D → A → C → B  //  D → A → B → C The graph does not have two different Hamilton paths.
19  of 20
Which fairness criterion is always satisfied by the plurality with elimination method?
20  of 20
Using the following graph, find an Euler circuit that begins and ends with vertex A.

 A → B → C → D → B → A A → B → C → D → B → E → A A → B → C → D → E → A → B No Euler circuit exists.

 Subject Mathematics Due By (Pacific Time) 04/30/2015 12:00 am
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