To solve the problem, we will use the information provided in the table step-by-step.
First, let's summarize what we know from the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Grade Level vs. Movie Preference & Sci-Fi & Comedy & Total \\
\hline
Freshmen & 39 & 28 & ? \\
\hline
Sophomores & ? & 45 & 61 \\
\hline
Total & 55 & 73 & ? \\
\hline
\end{tabular}
\][/tex]
1. Calculate the total number of Freshmen:
From the table, we know that 39 Freshmen prefer Sci-Fi and 28 prefer Comedy.
[tex]\[
\text{Total Freshmen} = 39 + 28 = 67
\][/tex]
So, the total number of Freshmen is 67.
2. Calculate the number of Sophomores who prefer Sci-Fi:
The total number of Sophomores is given as 61, and 45 of them prefer Comedy.
[tex]\[
\text{Sophomores who prefer Sci-Fi} = 61 - 45 = 16
\][/tex]
So, the number of Sophomores who prefer Sci-Fi is 16.
3. Determine the grand total of students:
We are given the total number of students who prefer Sci-Fi (55) and the total number of students who prefer Comedy (73).
Adding these totals gives us:
[tex]\[
\text{Students who prefer Sci-Fi} + \text{Students who prefer Comedy} = 55 + 73 = 128
\][/tex]
However, when calculating the grand total, we must ensure we do not double-count any students. We must subtract the number of students who both are accounted in totals for preference and grade (the immediate sums from each preference and grade list):
[tex]\[
\text{Grand Total} = 55 + 73 - (\text{Total Freshmen + Total Sophomores - Students within genre preferences overlap})
\][/tex]
Here, 67 Freshmen and 61 Sophomores sum 128, but their preferences (39 Sci-Fi, 28 Comedy, and 45 Comedy + 16) not tallying differently impacts the subtractions are needed but directly:
[tex]\[
Directly combining leads \Rightarrow 128 - 73 (Consideringly the feasible-only freshmen's comedy inclusive) \Rightarrow 128-73 = 55 (Resolved Grand Total unlikely considering sum behavior actual)!
\][/tex]
Thus, the final number in the blank bottom right cell indicating the grand total of all students:
[tex]\[
\boxed{55}
\][/tex]
It reckoning finding the grand extension only a unique comprising tabular, thus we evaluate it's total student sections globally verifying non-redund mankind.
