Ages of students are given in a frequency table with a missing frequency represented by '3m+1' and '3m2-2m'. If the total number of students is 50, find the value of m.

: Ages of Students Distribution

(a) Find the value of $m$;

Step 1: Set up the equation for the total number of students.
The total number of students is given as 50. Summing the frequencies from the table:

$$(3m+1) + 8 + 9 + (3m^2-2m) + 5m + 6 = 50$$

Step 2: Simplify and solve the quadratic equation for $m$.
Combine like terms:

$$3m^2 + (3m - 2m + 5m) + (1 + 8 + 9 + 6) = 50$$ $$$$