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Question: Prove that every nontrivial tree has at least two vertices of degree 1 by filling in the details and completing the following argument: Let T be a nontrivial tree and let S be the set of all paths from one vertex to another of T. Among all the paths in S, choose a path P with the most edges. (Why is it possible to find such a P?) What can you say about the initial and final vertices of P? Why?
Composition of Functions and Isomorphisms, I can't prove the following statements about functions f:A->B and g:B->C, 1. If gof is one-to-one then so is f.
determine the depreciation for each of the first two years (a) by the straight-line method and (b) by the double-declining-balance method.
Essay Question Explain how your answers (both incorrect and correct) to the Quick Preview shaped your perspective and how your perspectives affect customer service and long-term market strategy.
A plane heads on a bearing of 210* at 500 mph; the winds at the cruising altitude are 75 mph from the southwest to the north east.
Let F be a field and f(x), p(x) ∈ F[x] with p(x) 6= 0. Then there exist unique polynomials q(x) and r(x) such that f(x) = q(x)p(x) + r(x) with r(x) = 0 or deg r(x) deg p(x).
The cross section of a large circular conduit has seven smaller equal circular conduits within it. The conduits are tangent to each other as shown in Fig.
A stone is thrown straight up from the edge of a roof, 950 feet above the ground, at a speed of 16 feet per second.
Compare and contrast leadership development interventions with career development interventions? In what areas and activities might they overlap?
Math 104: Homework 6. Determine the interior and closure of the following subsets of R: A = {1/n: n ∈ N}, B = [0, 1] ∪ Q
An account has been dormant for many years earning interest at the constant rate of 4% per year. Now the amount is $100 000. How much was in the account.
plot on the same graph the density φ(x) = normal (x, µ(S25), σ(S25)). How well does the normal density fit your bar graph in each case?
you place 5000 in a saving account earning 2.50 interest compounded annually. how much will you have at the end of four
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