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Question: a) Devise a greedy algorithm that determines the fewest lecture halls needed to accommodate n talks given the starting and ending time for each talk.
b) Prove that your algorithm is optimal.
Suppose we have s men m1, m2,...,ms and s women w1,w2,...,ws. We wish to match each person with a member of the opposite gender. Furthermore, suppose that each person ranks, in order of preference, with no ties, the people of the opposite gender. We say that a matching of people of opposite genders to form couples is stable if we cannot find a man m and a woman w who are not assigned to each other such that m prefers w over his assigned partner and w prefers m to her assigned partner.
Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 4.8t0.8 - 3.1t + 19, with t ≥ 0, m in grams, and t in seconds.
Define a pushdown automaton. Explain how pushdown automata are used to recognize sets. Which sets are recognized by pushdown automata? Provide an outline of a proof justifying your answer.
Determine which ordered pair is a solution of the system -2x - y^2 = 4 -3x + y = 10
The highest average cost of 30-second commercial in October,2002 was $455,700. How much worth per second?
CRIME RATES The number of major crimes committed in Bronxville between 2000 and 2007 is approximated by the function.
What is the better investment and by how much: putting $300 a month into an RRSP that pays 6% compounded monthly or putting $3600 at the end of each year into an RRSP that pay 8% compounded annually?
Given the vertex pairs associated to the edges of a multigraph, determine whether it has an Euler circuit and, if not, whether it has an Euler path. Construct an Euler path or circuit if it exists.
Perform a break even analysis showing an algebraic statement of:
Find the demand functions x∗(p, m) and y∗(p, m). Find the partial derivatives of the demand functions with respect to p and m, and check their signs. How does the optimal expenditure on the good x vary with p? (That is, compute the elasticity of px∗ ..
Discuss the locations of the mean, median and mode for a normal, left-skewed and right-skewed distributions.
Calculate the first ten terms of the resulting sequence starting from x1 = 0.5. Find all equilibrium solutions. What do you notice about how rapidly the allele disappears?
question the surface areas of two similar cylinders are 6pift2 and 54pift2. the volume of the smaller cyllinder is
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