The beta-decay properties of the N=Z nuclei 96Cd, 98In, and 100Sn have been studied. These nuclei were produced at the National Superconducting Cyclotron Laboratory by fragmenting a 120 MeV/nucleon 112Sn primary beam on a Be target. The resulting radioactive beam was filtered in the A1900 and the newly commissioned Radio Frequency Fragment Separator to achieve a purity level suitable for decay studies. The observed production cross sections of these nuclei are lower than predicted by factors of 10-30. The half-life of 96Cd, which was the last experimentally unknown waiting point half-life of the astrophysical rp process, is 1.03_{-0.21};{+0.24} s. The implications of the experimental T_{1/2} value of 96Cd on the abundances predicted by rp process calculations and the origin of A=96 isobars such as 96Ru are explored.