  We apply an equal-velocity quark combination model to systematically study
the transverse momentum (p_{T}) spectra of strange hadrons K_{S}^{0}, \phi,
\Lambda, \Xi^{-}, \Omega^{-}, \bar{\Lambda}, \bar{\Xi}^{+} and \bar{\Omega}^{+}
at mid-rapidity in Au+Au collisions at \sqrt{s_{NN}}= 7.7, 11.5, 19.6, 27, 39,
54.4 GeV. Relative deviation between the model calculation and experimental
data of these eight hadrons is generally about 2-3% at \sqrt{s_{NN}}= 27, 39,
54.4 GeV and in central collisions at 7.7, 11.5, 19.6 GeV. The deviation
slightly increases up to about 4% in the semi-central and peripheral collision
at \sqrt{s_{NN}}= 7.7, 11.5, 19.6 GeV. We systematically explain the dependence
of two baryon-to-meson ratios \bar{\Lambda}/K_{S}^{0} and \Omega/\phi on p_{T},
collision centrality and collision energy by the property of quark p_{T}
spectra at hadronization. We derive the analytic relations between R_{CP} of
hadrons and those of quarks, and we use them to naturally explain the species
and p_{T} dependence of R_{CP} of those strange hadrons.
