Which describes the standard deviation?

a. a form of measurement of the average difference between sample values and the sample mean
b. the confidence level that a sample mean accurately represents a population mean
c. the value for which half of the sample elements are no bigger, and half are no smaller
d. the interval around the sample mean that you expect to contain the population mean

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?

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

Consider that lines b and c are parallel. what is the value of x? what is the measure of the smaller angle?