Given:
- Average height of Billy's first-grade class $\(=110 \mathrm{~cm}\)$
- Average height of Andrea's fifth-grade class $\(=140 \mathrm{~cm}\)$
- Number of students in Andrea's class $=30$
- Combined average height of both classes $\(\geq 130 \mathrm{~cm}\)$

Let the number of students in Billy's class be $x$.

Step 1: Write the expression for combined average height

$$
\(\frac{110 x+140 \times 30}{x+30} \geq 130\)
$$


Simplify:

$$
\(\frac{110 x+4200}{x+30} \geq 130\)
$$


Step 2: Multiply both sides by $\((x+30)\)$ (positive since number of students $\(>0\)$ )

$$
\(\begin{aligned}
& 110 x+4200 \geq 130(x+30) \\
& 110 x+4200 \geq 130 x+3900
\end{aligned}\)
$$


Step 3: Rearrange terms

$$
\(\begin{gathered}
4200-3900 \geq 130 x-110 x \\
300 \geq 20 x \\
x \leq \frac{300}{20}=15
\end{gathered}\)
$$

Step 4: Since $x$ (number of students) must be an integer and less than or equal to 15 , possible values from the options are:

$$
\(5,10,12,15\)
$$


Final answer:
The possible total number of students in Billy's class are: $\(\mathbf{5 , 1 0 , 1 2 , 1 5}\)$ (options A, B, C, D).For the combined average to be at least 130 cm , the number of students in Billy's class must be less than or equal to 15 . Among the options given, the possible values are $\(5,10,12\)$, and 15 .