Tanya is making goodie bags for her party. each bag has 6 toys, 4 pieces of candy, and 12 stickers. there are stickers for every 1 toy. tanya decides to change the bags to have 6 pieces of candy. to keep the proportions the same, she will need toys and stickers in each bag.

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?

What will be the end result for the taxpayer who filed his federal income tax return using the 1040ez form shown belowa he'll owe $173b he'll receive a refund of $173c he'll owe $3921d he'll receive a refund of $3921

Find the derivative of the function