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$19.(15$ pts $)$ A Marshall pat compacted at a binder content of $6\mathrm{.}7\%$ has a bulk specific gravity of $2\mathrm{.}262.$ The maximum relative density of the asphalt mix is $2\mathrm{.}376$ and the bulk relative density of the aggregate blend is $2\mathrm{.}518.$ Calculate the VTM$,$ VMA, and VFA of the pat.