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Using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb(-1), recorded by the LHCb detector at center-of-mass energies of 7 and 8 TeV, the B-c(+) -> (DK+)-K-0 decay is observed with a statistical significance of 5.1 standard deviations. By normalizing to B-c(+) -> (D) over bar (0)pi(+) decays, a measurement of the branching fraction multiplied by the production rates for B-c(+) relative to B+ mesons in the LHCb acceptance is obtained, R-D0K = (f(c)/f(u)) x B(B-c(+) -> (DK+)-K-0) = (9.3(-2.5)(+2.8) +/- 0.6) x 10(-7), where the first uncertainty is statistical and the second is systematic. This decay is expected to proceed predominantly through weak annihilation and penguin amplitudes, and is the first B-c(+) decay of this nature to be observed.
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