We present a combined measurement of R-b = Gamma(Z --> b (b) over bar)/Gamm
a(Z --> hadrons) and the semileptonic branching ratio of b quarks in Z deca
ys, Br(b --> l nu X), using double-tag methods. Two analyses are performed
on one million hadronic Z decays collected in 1994 and 1995. The first anal
ysis exploits the capabilities of the silicon microvertex detector. The tag
ging of b-events is based on the large impact parameter of tracks from weak
ly decaying b-hadrons with respect to the e(+)e(-) collision point. In the
second analysis, a high-p(t) lepton tag is used to enhance the b-component
in the sample and its momentum spectrum is used to constrain the model depe
ndent uncertainties in the semileptonic b-decay. The analyses are combined
in order to provide precise determinations of R-b and Br(b --> l nu X):
R-b = 0.2174 +/- 0.0015 (stat.) +/- 0.0028 (sys.);
Br(b --> l nu X) = (10.16 +/- 0.13 (stat.) +/- 0.30 (sys.))%.