Since the 3-Dimensional Matching Problem is NP- complete, it is natural to expect that the corresponding 4-Dimensional Matching Problem is at least as hard. Let us define 4-Dimensional Matching as follows. Given sets W , X , Y , and Z , each of size n, and a collection C of ordered 4-tuples of the form (wi, xj, yk, zl), do there exist n 4-tuples from C so that no two have an element in common? Prove that 4-Dimensional Matching is NP-Complete.

Find the roots of the polynomial function f(x) = x^3 + 2x^2 + x

Formulate the indicated conclusion in nontechnical terms. be sure to address the original claim. the foundation chair for a hospital claims that the mean number of filled overnight beds is over 523, and she is therefore justified starting a funding campaign to add a wing to the hospital. assuming that a hypothesis test has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

The price of a dozen eggs was $1.63. suppose the price increases m dollars per dozen and then the price decreases $0.12 per dozen. which expression represents the current price of eggs after the two price changes?