1. **State the problem:** We are given a ratio of coaches to athletes as 1 to 26. If there are $x$ coaches, we need to find an expression for the number of athletes. 2. **Understand the ratio:** The ratio $1:26$ means for every 1 coach, there are 26 athletes. 3. **Set up the expression:** If there are $x$ coaches, then the number of athletes is $26$ times $x$ because the ratio is constant. 4. **Write the expression:** Number of athletes $= 26x$ 5. **Answer:** The correct choice is B) $26x$. --- 1. **State the problem:** Find the value of $\tan\left(\frac{92\pi}{3}\right)$. 2. **Recall the periodicity of tangent:** The tangent function has period $\pi$, so $$\tan\left(\theta\right) = \tan\left(\theta + k\pi\right)$$ for any integer $k$. 3. **Reduce the angle modulo $\pi$:** Calculate $$\frac{92\pi}{3} \mod \pi = \frac{92\pi}{3} - 30\pi = \frac{92\pi - 90\pi}{3} = \frac{2\pi}{3}$$ 4. **Evaluate $\tan\left(\frac{2\pi}{3}\right)$:** Recall that $\tan\left(\frac{2\pi}{3}\right) = \tan\left(\pi - \frac{\pi}{3}\right) = -\tan\left(\frac{\pi}{3}\right)$. 5. **Calculate $\tan\left(\frac{\pi}{3}\right)$:** $$\tan\left(\frac{\pi}{3}\right) = \sqrt{3}$$ 6. **Therefore:** $$\tan\left(\frac{2\pi}{3}\right) = -\sqrt{3}$$ 7. **Answer:** The correct choice is A) $-\sqrt{3}$.