1. The problem asks to find the linear equation relating $x$ and $y$ from the table: | $x$ | 1 | 2 | 3 | |-----|---|---|---| | $y$ | 11 | 16 | 21 | 2. To find the linear relationship, calculate the slope $m$ using two points, for example $(1,11)$ and $(2,16)$: $$m = \frac{16 - 11}{2 - 1} = \frac{5}{1} = 5$$ 3. Use the point-slope form $y = mx + b$ and substitute one point to find $b$: $$11 = 5(1) + b \implies b = 11 - 5 = 6$$ 4. The linear equation is: $$y = 5x + 6$$ --- 5. Next, the problem asks for the value of $x$ in a system of equations with a solution $(x,y)$ where $x > 0$. However, the system is not provided, so this cannot be solved without more information. --- 6. For the ratio of coaches to athletes 1 to 26, if there are $x$ coaches, the number of athletes is: $$26x$$ --- 7. For the function $f(x) = (1.84)^{x/4}$, rewrite it as: $$f(x) = (1 + \frac{p}{100})^x$$ 8. Equate the bases: $$(1 + \frac{p}{100})^4 = 1.84$$ 9. Take the fourth root: $$1 + \frac{p}{100} = 1.84^{1/4}$$ 10. Calculate $1.84^{1/4}$: $$1.84^{1/4} \approx 1.16$$ 11. Solve for $p$: $$1 + \frac{p}{100} = 1.16 \implies \frac{p}{100} = 0.16 \implies p = 16$$ **Final answers:** - Linear equation: $y = 5x + 6$ - Number of athletes: $26x$ - Approximate value of $p$: 16