In a group of 47 pupils, 14 play the flute only. 8 play the piano only.
14 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?

The total number of students who play at least one instrument is 10 + 12 + 6 = 28. The means there are 32 - 28 = 4 students who play neither of the instruments. Therefore, the probability that a student plays neither instrument is 4/32 = 1/8 = 0.125 = 12.5%.

11/47

Step-by-step explanation:

Total number of pupils = 47

We are told that 14 play the flute only, 8 play the piano only and 14 play neither instrument.

So adding these together: 14 + 8 + 14 = 36

To find the number that played both instruments: 47 - 36 = 11

So 11 pupils play both instruments

The probability is the value divided by the total:  11/47

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!

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled