Javier wants to go to the movies. He has some money saved but does not want to use all his savings on a movie ticket. Javier’s mother offers to pay some of the cost of the ticket for every pound of potatoes he peels for her. The graph shows the cost to Javier for the purchase of the movie ticket after peeling x pounds of potatoes for his mother.

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?

Which of the following is the result of expanding

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0