The decays of D⁰ and D⁰ mesons produced from e ⁺e^- annihilation at the ψ(3770) resonance reflect quantum correlations so that decay rates are sensitive to interference between indistinguishable final states. Using the 281 pb ^-1 of [special characters omitted] = 3.770 GeV e⁺e ^- data collected with the CLEO-c detector at the Cornell Electron Storage Ring, we measure the time-independent decay rates of D ⁰ decays to flavored states K^-π ⁺, K⁺π^-, and CP eigenstates K⁺K^-, π ⁺π^-, [special characters omitted], and [special characters omitted], as well as inclusive semileptonic modes, using both partially- and fully-reconstructed D⁰D ⁰ pairs. A χ² minimization fitter extracts from these decay rates the uncorrelated branching fractions of the modes used, the ratio of doubly-Cabibbo suppressed to Cabibbo favored amplitudes r_Kπ and the strong phase difference δ_Kπ (respectively, the magnitude and phase of [special characters omitted]), and the D mixing parameters y and x². By constraining the branching fractions and r_Kπ with independent measurements, we present a first measurement of cos δ = [special characters omitted], with a 95% C.L. that |δ| < 75°.