The velocity of the Hubble expansion has been added to General Relativity by Moshe Carmeli and this resulted in new equations of motion for the expanding universe. For the first time the observational magnitude-redshift data derived from the high-z supernova teams has been analysed in the framework of the Carmeli theory and the fit to that theory is achieved without the inclusion of any dark matter. Best fits to the data yield an averaged matter density for the universe at the present epoch Omega(m) approximate to 0.021, which falls well within the measured values of the baryonic matter density. And the best estimate of Omega(Lambda) + Omega(m) approximate to 1.021 at the present epoch. The analysis also clearly distinguishes that the Hubble expansion of the universe is speed-limited.