Certainly, let's work through each part of the question step-by-step.
### (a) How many seniors from the class went on the field trip?
We know that there are 30 seniors in the class and that [tex]\(\frac{7}{10}\)[/tex] of these seniors went on the field trip. To find the number of seniors who went on the trip, we multiply the total number of seniors by the given proportion:
[tex]\[ \text{Number of seniors who went} = 30 \times \frac{7}{10} \][/tex]
Calculating this, we get:
[tex]\[ \text{Number of seniors who went} = 30 \times 0.7 = 21 \][/tex]
So, 21 seniors went on the field trip.
### (b) How many juniors are in the class?
For this part, we don't have sufficient information. We know that 31 juniors went on the field trip, but we don't have any information about the total number of juniors in the class or the proportion of juniors who went on the trip. Hence, we cannot determine the total number of juniors in the class.
Therefore, the answer to this part is "Not enough information."
### (c) How many students from the class went on the field trip?
To find the total number of students who went on the field trip, we sum the number of seniors and juniors who went. From part (a), we know that 21 seniors went on the trip, and from the given information, we know that 31 juniors went on the trip.
[tex]\[ \text{Total students who went} = \text{Number of seniors who went} + \text{Number of juniors who went} \][/tex]
Thus,
[tex]\[ \text{Total students who went} = 21 + 31 = 52 \][/tex]
So, 52 students went on the field trip.
### Summary of Answers:
\begin{tabular}{|l|l|}
\hline (a) & 21 seniors went on the field trip. \\
\hline (b) & Not enough information. \\
\hline (c) & 52 students went on the field trip. \\
\hline
\end{tabular}
