Podcast
Questions and Answers
Which activity has no immediate predecessors?
Which activity has no immediate predecessors?
What is the immediate predecessor of activity I?
What is the immediate predecessor of activity I?
Which activity does NOT lead directly to the finish?
Which activity does NOT lead directly to the finish?
What is a characteristic of a directed graph in this scenario?
What is a characteristic of a directed graph in this scenario?
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Which statement about the inverse of matrices is true?
Which statement about the inverse of matrices is true?
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In the Leslie matrix for the bird species, what does the element in the second row, first column represent?
In the Leslie matrix for the bird species, what does the element in the second row, first column represent?
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What is indicated by the zero values in the Leslie matrix regarding reproduction?
What is indicated by the zero values in the Leslie matrix regarding reproduction?
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How many of the following statements about square matrices are true: All square matrices have an inverse; the inverse could be the same as the transpose; the determinant must be non-zero for an inverse to exist; an identity matrix has an inverse?
How many of the following statements about square matrices are true: All square matrices have an inverse; the inverse could be the same as the transpose; the determinant must be non-zero for an inverse to exist; an identity matrix has an inverse?
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Considering the life span and reproduction of the bird species, how many offspring do females produce on average over their lifespan?
Considering the life span and reproduction of the bird species, how many offspring do females produce on average over their lifespan?
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What is the weight of the minimum spanning tree given that the edge weights are 15, 10, 8, 12, 9, and 7?
What is the weight of the minimum spanning tree given that the edge weights are 15, 10, 8, 12, 9, and 7?
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What is the minimum total time taken to complete the duties for Anthea, Bob, Cho, and Dario?
What is the minimum total time taken to complete the duties for Anthea, Bob, Cho, and Dario?
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How many edges does the planar graph represented by the adjacency matrix have?
How many edges does the planar graph represented by the adjacency matrix have?
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Based on the adjacency matrix, how many vertices are connected to vertex K?
Based on the adjacency matrix, how many vertices are connected to vertex K?
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If a new activity is added that connects to activities with the highest total time usage, what will be the impact on total project completion time?
If a new activity is added that connects to activities with the highest total time usage, what will be the impact on total project completion time?
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What is the maximum time taken by any one employee to complete their assigned duty?
What is the maximum time taken by any one employee to complete their assigned duty?
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In the planar graph with 5 vertices, if the number of edges is 10, how many faces are there according to Euler's formula?
In the planar graph with 5 vertices, if the number of edges is 10, how many faces are there according to Euler's formula?
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How do the completion times of Cho and Anthea for Duty 3 compare?
How do the completion times of Cho and Anthea for Duty 3 compare?
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What does element m21 in the matrix represent?
What does element m21 in the matrix represent?
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Which temperature is reported for Wednesday in week 1?
Which temperature is reported for Wednesday in week 1?
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How many days did the temperature reach 20 °C or higher in week 2?
How many days did the temperature reach 20 °C or higher in week 2?
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Which three letters change position when Q is multiplied by P?
Which three letters change position when Q is multiplied by P?
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Which location will have no birds remaining in the long term?
Which location will have no birds remaining in the long term?
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What is the average maximum temperature for week 1?
What is the average maximum temperature for week 1?
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Which day had the highest temperature recorded
Which day had the highest temperature recorded
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If the temperatures for week 2 are considered, what was the lowest recorded temperature?
If the temperatures for week 2 are considered, what was the lowest recorded temperature?
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What is the maximum flow capacity from entrance A to exit H using the given paths?
What is the maximum flow capacity from entrance A to exit H using the given paths?
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If the capacity from edge CD is increased by 5, what will be the new capacity of flow from entrance to exit?
If the capacity from edge CD is increased by 5, what will be the new capacity of flow from entrance to exit?
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Which edge currently has the smallest capacity limiting the flow from entrance to exit?
Which edge currently has the smallest capacity limiting the flow from entrance to exit?
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What would be the effect of reversing the direction of flow along edge FG?
What would be the effect of reversing the direction of flow along edge FG?
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If capacity along edge BH is increased to 15, what would be the total flow capacity from A to G?
If capacity along edge BH is increased to 15, what would be the total flow capacity from A to G?
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How many total paths can children take from A to exit H based on current edge capacities?
How many total paths can children take from A to exit H based on current edge capacities?
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Which edge alteration would provide the most significant capacity increase?
Which edge alteration would provide the most significant capacity increase?
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What is the significance of a cut in this network regarding flow management?
What is the significance of a cut in this network regarding flow management?
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Study Notes
Minimum Spanning Tree
- The graph has 7 vertices (points) and 8 edges (lines) connected between them
- The minimum spanning tree is the tree with the lowest total weight (sum of all the numbers)
- The minimum spanning tree is found by connecting all the vertices with the smallest possible weights
- The weight of the minimum spanning tree is 30
Employee Duty Allocation
- Anthea, Bob, Cho and Dario are assigned duties 1, 2, 3 and 4
- The manager tries to allocate duties to minimise the total time to complete all duties
- The minimum total time is 29 minutes
Graph Planarity
- The adjacency matrix represents a graph
- The matrix displays connection between vertices
- The number of faces in the graph is 7
Project Scheduling
- The project has 10 activities to be completed
- The project network is a directed graph
- The directed graph shows the dependencies of activities and their predecessors
- The graph represents a sequence of activities with arrows connecting predecessors to successors
- Option D correctly shows the project's activity dependencies using a directed graph
Flow Network
- The network shows one-way paths through a maze
- Paths are from the entrance (A) to exit (H)
- Network has vertices (intersections) and connecting edges (paths)
- The capacity of a cut is the sum of capacities of edges across the cut
- The minimum cut capacity is the smallest possible capacity of all cuts
- The minimum cut capacity is 23
- Increasing the capacity of edge GH to 16 would lead to the greatest increase in flow
Matrix Operations
- Element m21 is the temperature for Week 2, Monday
- Matrix P is a permutation matrix, and matrix Q is a column matrix
- Multiplying Q by P rearranges the letters in Q
- Letters e, a and s change position
Markov Chains
- The transition matrix T models movement of birds between locations
- The rows of the transition matrix represent the starting location
- The columns represent the ending location
- The long-term outcome is that the number of birds will decrease at locations M and N and increase at location O
Matrix Inverses
- There are 4 statements about true and false statements regarding matrix inverses
- Two of the statements are true
- Not all square matrices have inverses
- The inverse of a matrix could be the same as the transpose of that matrix, but not always
Leslie Matrices
- The Leslie matrix models population distribution of a species
- Each column of the matrix represents an age class
- Each row represents the rate of change for that age class
- The element in the second row, first column represents the survival rate from the first year to the second year
School Lunch Transitions
- The transition diagram shows the proportion of students moving between four locations
- Numbers on the edges represent the maximum number of students allowed to move along that edge per minute
- The entrance and exit nodes allow for students to enter and leave the system
- The network could be used to track the flow of students through the different locations
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Description
This quiz covers essential topics in graph theory, including minimum spanning trees and graph planarity, as well as practical applications in project scheduling. Explore concepts such as duty allocation and project dependencies to deepen your understanding of efficient graph utilization.
