10. does the table show a proportional relationship? if so, what is the value of y when x is…

Explanation:

Step1: Check for proportionality

For a proportional relationship, $\frac{y}{x}$ should be constant. Calculate $\frac{y}{x}$ for each pair: For $(x = 4,y = 64)$, $\frac{y}{x}=\frac{64}{4}=16$. For $(x = 5,y = 125)$, $\frac{y}{x}=\frac{125}{5}=25$. Since the ratios are not the same, the relationship is not proportional. But we can observe that $y=x^{3}$ (because $4^{3}=64$, $5^{3}=125$, $6^{3}=216$, $10^{3}=1000$).

Step2: Find $y$ when $x = 11$

If $y=x^{3}$, then when $x = 11$, $y=11^{3}=1331$.

Answer:

1331