Answer:
To find n if the mean of 30n, 12, 40, and 10 is n, we can use the formula for the mean of a set of numbers:
mean
=
sumofnumbers
numberofnumbers
mean=
numberofnumbers
sumofnumbers
In this case, we have four numbers: 30n, 12, 40, and 10. The mean is n. So we can write:
�
=
30
�
+
12
+
40
+
10
4
n=
4
30n+12+40+10
Simplifying the right-hand side:
�
=
30
�
+
62
4
n=
4
30n+62
Multiplying both sides by 4:
4
�
=
30
�
+
62
4n=30n+62
Subtracting 30n from both sides:
−
26
�
=
62
−26n=62
Dividing both sides by -26:
�
=
−
31
13
n=−
13
31
Therefore, if the mean of 30n, 12, 40, and 10 is n, then n is approximately -2.381.