A $109$ kg horizontal platform is a uniform disk of radius $1\mathrm{.}99$ m and can rotate about the vertical axis through its center. A $67\mathrm{.}1$ kg person stands on the platform at a distance of $1\mathrm{.}07$ m from the center, and a $26\mathrm{.}9$ kg dog sits on the platform near the person $1\mathrm{.}37$ m from the center.

Determine the moment of inertia I of the system the disk and its passengers with respect to the disk's rotation axis.

$I=$