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Let f, g : [a, b] → R be two continuous functions. If f(x) > g(x) for all x ∈ [a, b], then there exists a number c > 0 such that f(x) ≥ g(x) + c for all x ∈ [a, b].
How should I go about this problem? I have a gut feeling that the IVT can be used in some way. Maybe making a function h = f - g and using that somehow?
Consider the weighted MIN-VC, where every vertex has been assigned a positive integer weight, and the task is to minimize the overall weight of the vertex cover. Express this optimization problem as 0/1-LP.
A loaf of bread weighing 500 grams is sold at 23 dollars including VAT 18%.What should be the price of a loaf weighing 400 grams and VAT fixed at 16%.
Suppose that you are dealt a hand of 9 cards from a standard deck of 52 playing cards. What is the probability that you are dealt exactly 3 kings? What is the probability that you are dealt 9 cards of the same suit?
If order of the draw were important in a lottery, what would be the effect on odds of winning, if any? Explain. Find Probability and data representation
a motorboat travels 332 in 4 hoursgoing upstream 555 and in 5 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?
Find the coordinates
question 1a the following data represent the number of years patients survived after being diagnosed with terminal
Define the unknown quantities in terms of one variable. Translate the question into an equation. Solve the equation, showing all work.
Discuss the advantages of using the formulas, any difficulties in using them, and whether computers are used with them.
A car rental agency rents 220 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income..
By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possible situation.
Let M be a matching in a bipartite graph G.Derive the marriage theorem from Konig’s theorem.Let G and H be defined as for the third proof of Halls theorem.
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