1. The problem asks us to identify which number in the set $\{-49, \frac{7}{22}, 3\pi, -2.5, 0.1\dot{2}\}$ is irrational. 2. Recall that an irrational number is a number that cannot be expressed as a fraction $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. 3. Let's analyze each number: - $-49$ is an integer, so it is rational. - $\frac{7}{22}$ is a fraction of integers, so it is rational. - $3\pi$ is $3$ times $\pi$. Since $\pi$ is irrational, multiplying by a rational number $3$ keeps it irrational. - $-2.5$ is $-\frac{5}{2}$, a rational number. - $0.1\dot{2}$ means $0.122222...$, which is a repeating decimal and can be expressed as a fraction, so it is rational. 4. Therefore, the only irrational number in the set is $3\pi$. Final answer: $3\pi$