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Prove that for all positive integers n > 1, the inequality 2^n < 2nCn (2n choose n) holds.
The hint given is: create a one-to-one function f : P → Q between particular sets of sizes |P| = 2n, |Q| = 2nCn. This will prove |P|≤|Q|.
a) Express the problem as a linear programming model. b) Graph the problem and indicate the optimal solution on the graph.
a rectangle carpet has a perimeter of 246 inches. the length of the carpet is 89 inches more than the width. what are the dimensions of the carpet?
For each object, its SA, and some dimensions are given. Calculate the dimension indicated by the variable.right square pyramid SA = 132 cm square and base is 6 cm on each side
Prove that a ≡ b (mod n) if and only if n|(a - b); that is, check that the condition given in Definition 5.3.1 is correct.
At the start of lifting the bucket it contains 25 kg of water but slowly loses water at a constant rate so that at the top, half of the water is in the bucket. How much work is required to pull the bucket up the 100 m?
How large is the sample space for all ways the three teams can be chosen when the number of employees on each project are as follows.
a sample of 10 adult men gave the following data on their heights and weights.height inchesx62626365666768687072weight
At a certain screening with full attendance, there were half as many adults s children and students combined. The receiipts totaled $5600. How many children attended the show?
Draw a weighted graph with at least 10 vertices and 20 edges. Use Dijkstra's algorithm to find the shortest path between two vertices of your choice in the graph.
Review Chi Square analysis & create an example of how you would use the tool to help make a business decision.
Profits during the third quarter for a particular department store were $1,500,000. The pie chart below gives the results. Of the profits earned, how much were from jewelry sales?
express as a sine or cosine function.
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