Answer :
To find the mean of the numbers [tex]\(x+3, x-2, x+5, x+7,\)[/tex] and [tex]\(x+72\)[/tex], follow these steps:
1. Sum the Expressions:
Add up all the expressions:
[tex]\[
(x+3) + (x-2) + (x+5) + (x+7) + (x+72)
\][/tex]
2. Combine Like Terms:
Since each term includes an [tex]\(x\)[/tex], combine the [tex]\(x\)[/tex] terms first:
[tex]\[
x + x + x + x + x = 5x
\][/tex]
Next, combine the constant numbers:
[tex]\[
3 - 2 + 5 + 7 + 72 = 85
\][/tex]
So, the total sum is:
[tex]\[
5x + 85
\][/tex]
3. Calculate the Mean:
The mean is the sum of the expressions divided by the number of expressions. There are 5 expressions, so:
[tex]\[
\frac{5x + 85}{5}
\][/tex]
Simplify the division:
[tex]\[
\frac{5x}{5} + \frac{85}{5} = x + 17
\][/tex]
4. Find the Correct Option:
Compare the calculated mean, [tex]\(x + 17\)[/tex], to the given options:
- a) [tex]\(x + 5\)[/tex]
- b) [tex]\(x + 2\)[/tex]
- c) [tex]\(x + 3\)[/tex]
- d) [tex]\(x + 7\)[/tex]
None of these options match [tex]\(x + 17\)[/tex].
Therefore, according to the provided solution process and options, the correct answer to the question does not appear to be listed among the choices. Please double-check the options or ensure that no options were omitted.
1. Sum the Expressions:
Add up all the expressions:
[tex]\[
(x+3) + (x-2) + (x+5) + (x+7) + (x+72)
\][/tex]
2. Combine Like Terms:
Since each term includes an [tex]\(x\)[/tex], combine the [tex]\(x\)[/tex] terms first:
[tex]\[
x + x + x + x + x = 5x
\][/tex]
Next, combine the constant numbers:
[tex]\[
3 - 2 + 5 + 7 + 72 = 85
\][/tex]
So, the total sum is:
[tex]\[
5x + 85
\][/tex]
3. Calculate the Mean:
The mean is the sum of the expressions divided by the number of expressions. There are 5 expressions, so:
[tex]\[
\frac{5x + 85}{5}
\][/tex]
Simplify the division:
[tex]\[
\frac{5x}{5} + \frac{85}{5} = x + 17
\][/tex]
4. Find the Correct Option:
Compare the calculated mean, [tex]\(x + 17\)[/tex], to the given options:
- a) [tex]\(x + 5\)[/tex]
- b) [tex]\(x + 2\)[/tex]
- c) [tex]\(x + 3\)[/tex]
- d) [tex]\(x + 7\)[/tex]
None of these options match [tex]\(x + 17\)[/tex].
Therefore, according to the provided solution process and options, the correct answer to the question does not appear to be listed among the choices. Please double-check the options or ensure that no options were omitted.
