Use sigma notation to represent the following series for the first 12 terms.
+ (-8) + 32 + (-128) +
oloving seres og det er s9 + (+12)

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?

Two friends are reading books. jimmy reads a book with 21,356 words. his friend bob reads a book with one-and-a-half times as many words. which expression represents the number of words bob reads?

Find the unit rate for: 75% high-fiber chimp food to 25% high -protein chimp food.