The problem asks to select all ratios that are equivalent to the ratio $2:6$. The given ratios are $16:48$, $5:7$, and $3:9$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $2:6$. The given ratios are $16:48$, $5:7$, and $3:9$.

2. Solution Steps

First, simplify the given ratio $2:6$. Dividing both sides by 2, we get:

$\frac{2}{2} : \frac{6}{2} = 1:3$

Now, check each of the given ratios to see if they are equivalent to $1:3$.

Ratio 1: $16:48$

Divide both sides by 16:

$\frac{16}{16} : \frac{48}{16} = 1:3$

So, $16:48$ is equivalent to $1:3$ and $2:6$.

Ratio 2: $5:7$

This ratio is not equal to $1:3$, or $2:6$.

Ratio 3: $3:9$

Divide both sides by 3:

$\frac{3}{3} : \frac{9}{3} = 1:3$

So, $3:9$ is equivalent to $1:3$ and $2:6$.

3. Final Answer

$16:48$

$3:9$