Operations are placed in each $\bigcirc$ so that $3 \bigcirc 5 \bigcirc 7 \bigcirc 9=78$. Listed from left to right, the operations are
(A),$+ \times,+$
(B),,$++ \times$
(C) $\times, \times,-$
(D) $\times, \times,+$
(E) $\times,+, \times$
We try each of the five options:

$$
\begin{aligned}
& (\mathrm{A}): 3+5 \times 7+9=3+35+9=47 \\
& (\mathrm{~B}): 3+5+7 \times 9=3+5+63=71 \\
& (\mathrm{C}): 3 \times 5 \times 7-9=15 \times 7-9=105-9=96 \\
& (\mathrm{D}): 3 \times 5 \times 7+9=15 \times 7+9=105+9=114 \\
& (\mathrm{E}): 3 \times 5+7 \times 9=15+63=78
\end{aligned}
$$

Therefore, the correct operations are, in order, $x,+, x$.

ANSWER: (E)