how to write |x| after it has been shifted 3 units to the left, stretched vertically by a factor of two , reflected over the x axis and translated up four units

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?

How many square inches are in 60 square feet?

Find the area of the surface obtained by rotating the curve z=4e^2y from y = 0 to y =1 about the y-axis. the area is square units