Aboy has 3 red , 6 yellow and 5 green marbles. in how many ways can the boy arrange the marbles in a line if: all marbles have different sizes?

8.72*10^10

Step-by-step explanation:

Total number of balls = 14

Now,

Make 14 lines.

_ _ _ _ _ _ _ _ _ _ _ _ _ _

In the first position, you can choose any ball from 14 balls. So,

14 _ _ _ _ _ _ _ _ _ _ _ _ _

In the second position, you can choose any ball from 13 balls. This is because you've already kept one ball in first position. So,

14 13 _ _ _ _ _ _ _ _ _ _ _ _

In the third position, you can choose any ball from 12 balls. So,

14 13 12 _ _ _ _ _ _ _ _ _ _ _

Do this until you fill all the place.

14 13 12 11 10 9 8 7 6 5 4 3 2 1

Multiply all of this.

14 *13 *12 *11 *10 *9 *8 *7 *6 *5 *4 *3 *2 *1

= 8.72*10^10

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:

the answer is b.

step-by-step explanation:

identity property is where 0+whatever number=whatever number. basically 0+ a number.