Check if this point lies within the circular region:
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- Set $\sin(2\theta) = 1 \Rightarrow 2\theta = \frac{\pi}{2} + 2k\pi \Rightarrow \theta = \frac{\pi}{4} + k\pi$.
- Try $\theta = \frac{\pi}{4}$:
- Then $r^2 = \frac{100}{1} = 100 \Rightarrow r = 10$.
- The circle has radius 10, so $r = 10$ is on the boundary — valid.
- Thus, the **maximum possible value of $r$** is:
- \boxed{10}
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Therefore, the probability that **at least one** has a GPS collar is:
- \frac{1}{6} = \frac{5}{6}
\boxed{\frac{5}{6}}
$$Question: Find all real numbers $ x $ such that
\frac{x^2 - 4x + 3}{x^2 - 5x + 6} \geq 0.
We begin by factoring both the numerator and the denominator:
\frac{(x - 1)(x - 3)}{(x - 2)(x -
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