Achemical supply company ships a certain solvent in 10-gallon drums. let x represent the number of drums ordered by a randomly chosen customer. assume x has the following probability mass function: x 1 2 3 4 5 p(x) 0.4 0.2 0.2 0.1 0.0 a. find the mean number of drums ordered. b. find the variance of the number of drums ordered. c. find the standard deviation of the number of drums ordered. d. let y be the number of gallons ordered. find the probability mass function of y. e. find the mean number of gallons ordered. f. find the variance of the number of gallons ordered. g. find the standard deviation of the number of gallons ordered.

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?

Suppose your school costs for this term were $4900 and financial aid covered 3/4 of that amount. how much did financial aid cover? and how much do you still have to pay?

Express the following as a function of a single angle. cos(60) cos(-20) - sin(60) sin(-20)