Answer
$\frac{1}{2}$.
Work Step by Step
Step 1. As z varies inversely as w, we have $z=\frac{k}{w}$ where $k$ is a constant.
Step 2. As $z=10$ when $w=\frac{1}{2}$, we have $10=\frac{k}{1/2}$, thus $k=5$
Step 3. For $w=10$, we have $z=\frac{5}{10}=\frac{1}{2}$.
