For 14a through 14d, tell which expressions require you to rename mixed numbers before you can subtract. find each difference. write each expression and the difference as an equation in the correct box answer

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?

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.

Consider the function y = f(x)=3^x the values of f(1/2) and f(1/4). rounded to the nearest hundredth, are__and__ respectively