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The questions shown in your image are about graph theory and optimization techniques such as the minimal-spanning tree and shortest-route techniques. Let's break them down:

1. **Question 1**: "In the minimal-spanning tree technique, it is necessary to start at the last node in the network."
   - **Answer**: False. In the minimal-spanning tree (MST) technique, the starting node can be any node. The goal is to connect all nodes while minimizing the total edge weight without forming cycles, and the starting point does not affect the final result.

2. **Question 2**: "The minimal-spanning tree technique determines the path through the network that connects all the points while minimizing total distance."
   - **Answer**: True. The MST technique focuses on connecting all nodes in a graph while ensuring the minimum total edge weight (distance, cost, etc.), making it true.

3. **Question 3**: "Transportation companies would definitely be interested in the shortest-route technique to optimize travel."
   - **Answer**: True. The shortest-route technique (like Dijkstra's or Bellman-Ford algorithms) finds the shortest path between two points, which is highly useful for transportation companies to minimize travel distances or times.

Let me know if you'd like more details or explanations! Here are some related questions for further exploration:

1. What algorithms are commonly used to find minimal-spanning trees?
2. How does Dijkstra’s algorithm differ from the minimal-spanning tree algorithm?
3. Can the minimal-spanning tree algorithm be applied to directed graphs?
4. What real-world applications utilize the minimal-spanning tree technique?
5. How do transportation networks use shortest-path algorithms for logistics optimization?

**Tip**: When dealing with graph problems, it's important to understand whether you are minimizing the path between two specific points (shortest-route) or trying to connect all nodes with minimum weight (MST).

The questions shown in your image are about graph theory and optimization techniques such as the minimal-spanning tree and shortest-route techniques.

Explore how the minimal-spanning tree technique connects all points in a network with minimum total distance and why transportation companies use the shortest-route technique to optimize travel. Learn about graph theory applications and algorithms suitable for college-level studies.

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