Find a spanning tree in the following graph.  Draw your spanning tree on your paper. (Count and write how many vertices and edges your spanning tree has here, and make sure to include your spanning tree in your File Upload to receive full credit.)  

Consider the following graph. Find the degree of the vertices  and . Find a walk of length 4 that begins at vertex  and \newline ends at vertex . (Write your final answers here, and make sure to include your work in your File Upload to receive full credit.)

Identify the sampling technique used to obtain a sample in each in the following situations. Every  box of cereal on the production line is inspected for quality control. To determine the average number of computers per household, each household in 4 of the 12 local counties were sent a survey regarding computer ownership.

Let be a tree with internal vertices of degree 5, 3, 3, 4, 2, and 2. How many leaves does  have? (Write your final answer here, and make sure to include your work in your File Upload to receive full credit.)

In the following graph, the vertices represent European cities and the weights on the edges represent the number of hours needed to fly in an airplane from one city to the next.  Find the minimum weight of a minimum weight spanning tree for the graph.

If a restaurant normally charges $15 for an all-you-can-eat buffet, the buffet should include entrées from the a la carte menu that sell for $18 or less as the buffet has a lower labor cost.

Some casual all-you-can-eat buffet operations place the entrées before the appetizers in the hopes that guests will fill up on entrées and just skip the appetizers entirely.

The fundamental “error” that the error theory seeks to debunk is the idea that

Which of the following claims would an error theorist not accept?

A categorical reason is a reason that applies to us