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1. For an acyclic network G with a specified source node s, outline an algorithm that enumerates all distinct directed paths from the source node to every other node in the network. The running time of your algorithm should be proportional to the total length of all the paths enumerated (i.e., linear in terms of the output length.)
2. In an undirected connected graph G = (N, A), an Euler tour is a walk that starts at some node, visits each arc exactly once, and returns to the starting node. A graph is Eulerian if it contains an Euler tour. Show that in an Eulerian graph, the degree of every node is even. Next, show that if every node in a connected graph has an even degree, the graph is Eulerian. Establish the second result by describing an O(m) algorithm for determining whether a graph is Eulerian and, if so, will construct an Euler tour. (Hint: Describe an algorithm that decomposes any graph with only even-degree nodes into a collection of arc-disjoint cycles, and then converts the cycles into an Euler tour.)
What is the impact of the variable you added? Is it statistically significant? Explain your answer in a sentence or two. Did this affect the output from the "baseline" regression
Assume that output per unit of labor is related to the capital-labor ratio by yt = r log(kt); and that saving is a fixed proportion, s, of output.
Explain how you created the differing impressions (what strategies you used). See strategies #2-5 on pages 47-48 for help with this. (Remember, you may not use strategy #1.) Cite specific examples of each strategy you used.
Its rent is $80,000 per year. What is the marginal cost of a blood draw? What principle does your calculation illustrate?
Suppose that the demand for Federal funds curve is such that the quantity of funds demanded changes by $160billion for each 1 percent change in the Federal funds interest rate. Also, assume that the current Federal funds rate is at the 3 percent r..
Bank North advertises, "We pay 6.5%, compounded daily." Bank South advertises, "We pay 6.5%, compounded continuously." If you deposit $10,000 with Bank South for one year, how much additional interest will you receive
Desperate David devours (consumes) only donuts and dumplings. Every donut costs $1.00 and every dumpling costs $1.50. His monthly budget for these items is $100. His mom makes dumplings at home at gives him 30 dumplings free every month.
Suppose that the government is committed to providing welfare eligibility to every family below the poverty line. If this government wishes to keep total spending to a minimum, which of the two views should it support?
The price of scarves is $9, the hourly wage is $24, and each scarf requires $1 worth of material. The following table shows the relationship between the number of workers and the output of scarves.
Suppose the demand curve for a monopolist is QD=500-P and the marginal revenue function as MR=500- 2Q The monopolist has a constant marginal and average total cost of $50 per unit
The mean gross annual incomes of certified welders are normally distributed with the mean of $23,577 and a standard deviation of $2,358. The ship building association wishes to find out whether their welders earn more or less than $23,577 annually..
Aunt Jane's Fitness Center is planning to utilize price discrimination to set its family and corporate rates. For a family membership, it's estimated demand curve is Qf = 984 - 20Pf For the corporate market its estimated demand curve is Qc = 2,070..
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