#### Answer

$z=\dfrac{5}{8}=0.625$

#### Work Step by Step

Recall:
If $y$ varies inversely as $x$, then the inverse variation's equation is $y=\frac{k}{x}$ where $k$ is the constant of variation.
Since $z$ varies inversely as $w$, then the equation of the direct variation, with $k$ as the constant of variation, is:
$$z=\frac{k}{w}$$
When $w=0.5$, $z=10$. Substitute these into the equation above to obtain:
\begin{align*}
z&=\frac{k}{w}\\\\
10&=\frac{k}{0.5}\\\\
10(0.5)&=k\\\\
5&=k\\\\
\end{align*}
Thus, the equation for the inverse variation is:
$$z=\frac{5}{0.5}$$
To find the value of $z$ when $w=8$, substitute $8$ to $w$ in the equation above to obtain:
\begin{align*}
z&=\frac{5}{8}=0.625\\\\
\end{align*}