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 solution of this system of equation -7x+y=-20 9x-3y=36

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round your answers to four decimal places.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error %

Which situation is an example of an observational study?