Sara has 3 choices to get to school: walk, ride a bike, or ride the bus. She has the same choices to get home after school. If Sara randomly
chooses how she is getting to school and home, what is the probability
that she will walk to school and then ride the bus home?

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?

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).

What is the circumference of the pie