1-14 in attached file

Math 128 Topi cs in Liberal Arts Mathematics Fall 2020 Midterm Examin ation 1 Answer each question by showing all of your work and stating your a n swer. You may print this test and work directly on it or y ou may work on your own paper. Throughout the entire test time, you are only allowed access to your notes, your textbook , your home work , and your calculator. Y o u m ay not use any other re sources, electronic or otherwise. 1. XYZ Corporation is predi cting $ 252 M in revenue in 202 0. It ori ginally had $ 3 10 M in revenue in 2019. What is the p er cent increase/decrease in revenue? 2. A n internet provider can lay down new fiber optic cable at a cost of $470 , 00 0 per kil om eter . If 1 mile = 1.6 1 kilometers, how much does it cost to lay down 20 miles of cable? 3. If the speed of light is 186,000 miles per second , how far does light travel in one day? 4. Determine the degree of each vertex of the graph: 5. U sing the mileage chart, const ruct a graph showing the mileage between Chic ago , Houston, Los Angeles (L) , New York (N), and Washington 6. State the theorem that tells you how to determine if a graph has an Euler circuit, an Euler path, or neither. 7. With a few sentences, d escribe a practical , real - life situation where using a graph and graph th eory would be useful. 8. Determine if the following gr aph has an Euler cir cui t. If it has one , list the Euler circuit starting at A. 9. Determine if the following graph has a Hami lton circuit. If it does, list it starting at A. 10. Determine whether this graph has an Euler path, a Hamilton path, both types, or neither type. Y o u do not have to state the path. 11. Complete the Eulerization of this graph with as few add ed edges as possible. 12. Determine an itinerary for a traveling sale sperson by using the Nearest Neighbor Algori thm on this graph. Assume t hat A is home. What is the total cost? 13. U se the C hea pest Link Algorithm to d etermine an itinerary for the graph below. Assume that A is home. What is the total cost? 14. Determine the minimum cost spanning tree for the graph. What is the total cost?