Your car stereo can be programmed to hold six radio stations of your choice. there are nine stations you really like. how man different ways can you program your six buttons with different collections of your favorite stations? (a different ordering of the same six stations counts as different programming.) this is my guess 9! /(9-6)! = 9! /3! = 9 * 8 * 7 * 6 * 5 * 4 = 60,480.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: