Write an equation that represents the transformations formed by the following items: a) horizontally shifting the graph 4 units to the left of f(x) = √x and then vertically compression by a factor of 1/3

b) vertically stretching the graph by a factor of 4 of f(x) = √x and then vertically shifting the graph 3 units up

c) horizontally stretching the graph of f(x) = √x by a factor of 2 and then vertically shifting the graph 6 units down

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?

Evaluate the function , when d = {9, 15, 30}. r = {5, 7, 12} r = {6, 10, 15} r = {6, 10, 20} r = {5, 12, 20}

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. the function below shows the relationship between f(x) and x: f(x) = 10(1.3)xwhich of the following graphs best represents the function? graph of f of x equals 1.3 multiplied by 10 to the power of x graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity graph of f of x equals 10 multiplied by 1.3 to the power of x graph of f of x equals 1.3 to the power of x