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(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph. (b) Let G be a non directed graph with L2 edges. If G has 6 vertices every of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have? (c) Explain the truth value for each of the following statements: (i) 4 + 3 = 6 AND 3 + 3 = 6(ii) 5 + 3 = 8 OR 3 + 1 = 5(d) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function. (e) Show the sufficient conditions of Dirac and Ore for a graph to be Hamiltonian. Give an instance of a graph that does not satisfy Dirac's condition, but satisfies Ore's condition. (f) Measure -25 + 75 using 2's complement.
If a triangular sail has a horizontal length of 30 ft and a vertical height of 83 ft , Determine the area of the sail? a. 1,245 ft 2 b. 1,155 ft 2 c. 201 ft 2 d. 2,4
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The set of whole numbers also does not satisfy all our requirements as on observation, we find that it does not include negative numbers like -2, -7 and so on. To
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Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II. Their rankings in the two tests were as:
Find the volume of a right circular cylinder: Calculate the volume and surface area of a right circular cylinder along with r = 3" and h = 4". Solution: V = πr 2
The longer base of a trapezoid is three times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the t
Five cards - the ten, jack, queen, king and ace, are well shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is
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