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Question: 1. Prove that for a planar graph with k components, |V(G)|-|E(G)|+|F(G)| = 1+k.
2. Prove that the Petersen graph (shown in Figure) is not planar.
3. Show that if every face of a planar graph has four edges, then |E(G)| = 2|V(G)| -4.
4. For which n is Kn planar and for which n is Kn non planar? Make and prove a conjecture.
the perimeter of a rectangular concrete slab is 94 feet and its area is 462 square feet. What ids the length of the longer side of the slab.
Suppose you want to collect a sample of certain size from a continuous population to satisfy given confidence level and margin of error. What formula do you use to determine the sample size if you know the population proportion?
A major league pitcher can throw a baseball in excess of 48.8 m/s. if a ball is thrown horizontally at this speed, how much will it drop by the time it reaches the catcher who is 15.7 m away from the point of release?
Nata spent $28 on 2 DVDS. At this rate,how much would 5 DVDS cost? At what rate did she spend her money
QUALITY CONTROL A sample of three transistors taken from a local electronics store was examined to determine whether the transistors were defective.
Investors at a theme park would like to estimate the unknown proportion (p) of visitors who have visited the theme park in the past five years. They would like to be 90% confident of achieving an accuracy of at least 0.04. How large a sample of vi..
Find the critical numbers of f. Find the open intervals on which the function is increasing or decreasing. Apply the First Derivative Test to identify the relative extremum.
A cup of coffee at 179 degrees is poured into a mug and left in a room at 66 degrees. After 7 minutes, the coffee is 133 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case)dT/dt=k(T-66).What is the t..
what is the probability that the oilfield will be purchased by Exxon?
To avoid creating a backlog, all cases must be handled by the end of December. Formulate a linear program that can be used to determine how many udges the city needs.
plane can travel 490 miles per hour with wind and 410 miles per hour against the wind, find the speed of the plane in still air.
1. In regression equations represented by Y = 2 + 3X, if value X =2 then predicted value of Y is 10. 2. Residual = Actual Value - Predicted Value 3. In a queuing system, percentage of time a server is busy is called the utilization factor for the ..
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