Tevatron Combination of Single-Top-Quark Cross Sections and Determination of the Magnitude of the Cabibbo-Kobayashi-Maskawa Matrix Element ${\mathbf{V}}_{\mathbf{t}\mathbf{b}}$

We present the final combination of CDF and D0 measurements of cross sections for single-top-quark production in proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. The data correspond to total integrated luminosities of up to 9.7 fb${}^{-1}$ per experiment. The $t$-channel cross section is measured to be ${\sigma }_t=2.25_{-0.31}^{+0.29}$ pb. We also present the combinations of the two-dimensional measurements of the $s$- vs. $t$-channel cross sections and of the $s+t$ channel cross section measurement resulting in ${\sigma }_{s+t}=3.30_{-0.40}^{+0.52}$ pb, without assuming the standard-model value for the ratio ${\sigma }_s\mathrm{/}{\sigma }_t$. The resulting value of the magnitude of the top-to-bottom quark coupling is $\mathrm{\mid }{V}_{tb}\mathrm{\mid }$ = $1.02_{-0.05}^{+0.06}$, corresponding to $\mathrm{\mid }{V}_{tb}\mathrm{\mid }>0.92$ at the 95% C.L.