We report the realization of a quantum degenerate mixture of bosonic Rb-87 and fermionic Yb-171 atoms in a hybrid optical dipole trap with a tunable, species-dependent trapping potential. Rb-87 is shown to be a viable refrigerant for the noninteracting Yb-171 atoms, cooling up to 2.4 x 10(5) Yb atoms to a temperature of T/T-F = 0.16(2) while simultaneously forming a Rb-87 Bose-Einstein condensate of 3.5 x 10(5) atoms. Furthermore we demonstrate our ability to independently tailor the potentials for each species, which paves the way for studying impurities immersed in a Bose gas.