Find the probability. There are six nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. Both times the coin is a nickel. a. 6/13b. 2/7c. 5/16d. 3/19

Step-by-step explanation:

We have been given that there are six nickels and seven dimes in your pocket. We are asked to find the probability of getting a nickel coin both times with replacement.

Let us find probability of getting a nickel in one pick.

There are 6 nickels and total coins are 6 nickels plus 7 dimes that 13 coins.

Since the coin is returned back in the pocket, so probability of choosing 2nd nickel will be .

Since both terms are independent, therefore, probability the required probability will be product of and .

Therefore, our required probability would be .    

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

answer is 12345678900987654321234567890987654321

step-by-step explanation: