We are asked to select all ratios that are equivalent to the ratio $7:10$. The given ratios are $9:15$, $20:14$, $70:100$, and $1:2$.

1. Problem Description

We are asked to select all ratios that are equivalent to the ratio $7:10$. The given ratios are $9:15$, $20:14$, $70:100$, and $1:2$.

2. Solution Steps

We need to check each ratio to see if it is equivalent to $7:10$.

A ratio $a:b$ is equivalent to $7:10$ if $\frac{a}{b} = \frac{7}{10}$.

First, consider $9:15$. $\frac{9}{15} = \frac{3 \times 3}{3 \times 5} = \frac{3}{5}$. Since $\frac{3}{5} \neq \frac{7}{10}$, the ratio $9:15$ is not equivalent to $7:10$.

Next, consider $20:14$. $\frac{20}{14} = \frac{2 \times 10}{2 \times 7} = \frac{10}{7}$. Since $\frac{10}{7} \neq \frac{7}{10}$, the ratio $20:14$ is not equivalent to $7:10$.

Next, consider $70:100$. $\frac{70}{100} = \frac{10 \times 7}{10 \times 10} = \frac{7}{10}$. Since $\frac{7}{10} = \frac{7}{10}$, the ratio $70:100$ is equivalent to $7:10$.

Finally, consider $1:2$. $\frac{1}{2}$. Since $\frac{1}{2} \neq \frac{7}{10}$, the ratio $1:2$ is not equivalent to $7:10$.

Therefore, only $70:100$ is equivalent to $7:10$.

3. Final Answer

70:100