Among the many examples of $\mathrm{S}_{\mathrm{N}} 1$ reactions that occur with incomplete racemization, the optically pure tosylate of 2,2 -dimethyl-1-phenyl-1-propanol $\left([\alpha]_{D}=-30.3\right)$ gives the corresponding acetate $\left([\alpha]_{D}=+5.3\right)$ when heated in acetic acid. If complete inversion had occurred, the optically pure acetate would have had $[\alpha]_{\mathrm{D}}=+53.6 .$ What percentage racemization and what percentage inversion occurred in this reaction?