Question: All Year 9. An inequality is shown. $$\frac{11}{100} < x < \frac{\pi}{23}$$ The table lists possible values of $x$. Which values of $x$ would make the inequality true? Select the correct answer in each row. Value True False 15.7% $\frac{3}{25}$ 0.1333 $\frac{\sqrt{3}}{10}$ $\frac{1}{8}$

1. **State the problem:** We need to determine which values of $x$ satisfy the inequality $$\frac{11}{100} < x < \frac{\pi}{23}$$. 2. **Convert the bounds to decimal approximations:** - Lower bound: $$\frac{11}{100} = 0.11$$ - Upper bound: $$\frac{\pi}{23} \approx \frac{3.1416}{23} \approx 0.1366$$ So the inequality is $$0.11 < x < 0.1366$$. 3. **Evaluate each value and check if it lies between $0.11$ and $0.1366$:** - $15.7\% = 0.157$ which is greater than $0.1366$, so **False**. - $\frac{3}{25} = 0.12$ which is between $0.11$ and $0.1366$, so **True**. - $0.1333$ is between $0.11$ and $0.1366$, so **True**. - $\frac{\sqrt{3}}{10} \approx \frac{1.732}{10} = 0.1732$ which is greater than $0.1366$, so **False**. - $\frac{1}{8} = 0.125$ which is between $0.11$ and $0.1366$, so **True**. 4. **Summary:** - $15.7\%$: False - $\frac{3}{25}$: True - $0.1333$: True - $\frac{\sqrt{3}}{10}$: False - $\frac{1}{8}$: True This completes the solution.