1. **State the problem:** We need to find which value of $x$ satisfies the inequality $$\frac{1}{9} < x < 19\%.$$ 2. **Convert all values to decimals for easy comparison:** - $\frac{1}{9} \approx 0.1111$ - $19\% = 0.19$ 3. **Check each option to see if it lies between 0.1111 and 0.19:** - $0.08$ is less than $0.1111$, so it does not satisfy the inequality. - $\sqrt{0.03} \approx 0.1732$ (since $\sqrt{0.03} = 0.1732$), which is between $0.1111$ and $0.19$. - $1.9$ is greater than $0.19$, so it does not satisfy the inequality. - $\frac{1}{4} = 0.25$ is greater than $0.19$, so it does not satisfy the inequality. 4. **Conclusion:** The only value that satisfies $$\frac{1}{9} < x < 19\%$$ is $$x = \sqrt{0.03}.$$