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(Steiner Tree Problem Heuristic) We are given a connected graph G with a nonnegative weight aij for each arc (i, j) ∈ A. We assume that if an arc (i, j) is present, the reverse arc (j, i) is also present, and aij = aji. Consider the problem of finding a tree in G that spans a given subset of nodes S and has minimum weight over all such trees. (a) Let W∗ be the weight of this tree. Consider the graph I(G), which has node set S and is complete (has an arc connecting every pair of its nodes). Let the weight for each arc (i, j) of I(G) be equal to the shortest distance in the graph G from the node i ∈ S to the node j ∈ S. Let T be a minimum weight spanning tree of I(G). Show that the weight of T is no greater than 2W
A recent survey of 150 executives at Elvers Industries, a large insurance and financial firm located in the Southwest, reported the number of pounds by which the executives were overweight. Compute the mean and the standard deviation.
One state lottery has 500 prizes of $1, 75 prizes of $15, 15 prizes of $100, 5 prizes of $450, 2 prizes of $1225, and 1 prize of 2500. Assume that 28,000 lottery tickets are issues and sold for $1. What is the lottery's expected profit per ticket?
Define validity and reliability. How can we insure our data is both reliable and valid? Which of these two do you think is the more important? Provide examples to support your reasoning.
The New York Times ran a story headlined "Study Shows Marathons Aren't Likely To KillYou," claiming that the risk of dying on a marathon is twice as high if you drive it than if you run it. The underlying study (Redelmeier and Greenwald 2007) esti..
the mean drying time of a brand of spray paint is known to be 90seconds. the research division of the company that
Findout the normal model for the given proportions. The professor has every student toss a coin 50 times also calculated the proportion
Use the central limit theorem to find the probability that the average number of moths in 30 traps is greater than 0.6. Give your answer to four decimal places.
How large a sample should she check in order to be 93 percent confident that the true proportion is estimated to within 0.014?
Assuming that the standard deviation is known to be 121.8Ib use 0.05 significance level to test the claim that the population mean of all such bear weights is greater than 150 Ib
Probability the second truck is available is .50, and the probability that both trucks are available is .30. What is the probability neither truck is available?
Using the SPSS, calculate a simultaneous multiple regression with SES, age, and optimism as the independent variables and longevity as the dependent variable.
Hugh's Repair Shop specializes in repairing German and Japanese cars. The shop has two mechanics. One mechanic works on only German cars and the other mechanic works on only Japanese cars.
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