# What is the arithmetic mean of the numbers f(a), f(b) ?a=3, b=30 f(x)=x/3+10

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f(x) = x/3 + 10

a= 3 b = 30

We know that the mean for f(a) + f(b) is:

m =[ f(a) + f(b)]/2

Let us determine f(a) and f(b):

f(a) = a/3 + 10

= 3/3 + 10 = 11

==? f(a) = 11

f(b) = b/3 + 10 = 30/3 + 10= 20

==> f(b) = 20

Now let us calculate the Arthemetical mean:

M = [f(a) + f(b)]/2

= (11+20)/2 = 31/2

= 15.5

**Then the arthemetical mean = 15.5**

We'll determine the arithmetic mean of the numbers f(a) and f(b):

A.M. = [f(a) + f(b)]/2

To compute the value of A.M., we'll have to compute the values of f(a) and f(b).

For this reason, we'll substitute a and b in the expression of f(x).

For a = 3, we'll get:

f(3) = 3/3 + 10

f(3) = 1 + 10

**f(3) = 11**

For b = 30, we'll get:

f(30) = 30/3 + 10

f(30) = 10 + 10

**f(30) = 20**

Now, we'l substitute f(a) and f(b) by the values of f(3) and f(30) in the expression of A.M.

A.M. = [f(3) + f(30)]/2

A.M. = (11+20)/2

**A.M. = 31/2**

To find the arithmetic mean of f(a) and f(b)

a=3, b=30

f(x)=x/3+10

The arith metic mean of f(a) and f(b) = {f(a) +f(b)}/2.

Now we calculate f(a) substituting x = a = 3 in f(x) = x/3.

f(a) = f(3)= 3/3+10 = 11

Now we calate f(b) by putting x= b= 30 in f(x) = x/3+10.

f(b) = f(30) = 30/3+10 = 10+10 = 20.

Therefore the mean of f(a)+f(b) = {f(a)+f(b)}/2 = {11+20}/2 = 31/2 = 15.5.

Therefore the mean of f(a) and f(b) = 15.5.