Consider the following lp: maximize z = 2x1 + 4x2 + 4x3  3x4 subject to x1 + x2 + x3 = 4 x1 + 4x2 + x4 = 8 x1, x2, x3, x4  0 using x3 and x4 as starting variables, the optimal tableau is given as basic x1 x2 x3 x4 solution z 2 0 0 3 16 x3 0.75 0 1 -0.25 2 x2 0.25 1 0 0.25 2 write the associated dual problem and determine its optimal solution

How can you find the conditional probability of a given b as the fraction of b’s outcomes that also belong to a, and interpret the answer in terms of the model? i just need a good explanation

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

What is the 12th term of b(n)=-4-2(n-1)