The total cost of producing a type of tractor is given by C(x)=11000−20x+0.02x2, where x is the number of tractors produced. How many tractors should be produced to incur minimum cost?

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?

Drag each tile to the correct box. not all tiles will be used. consider the recursively defined function below. create the first five terms of the sequence defined by the given function