We have studied the relationship among nuclear radio and X-ray power, Bondi rate and the kinetic luminosity of sub-Eddington active galactic nucleus (AGN) jets, as estimated from the pdV work done to inflate the cavities and bubbles observed in the hot X-ray-emitting atmospheres of their host galaxies and clusters. Besides the recently discovered correlation between jet kinetic and Bondi power, we show that a clear correlation exists also between Eddington-scaled kinetic power and bolometric luminosity, given by log(Lkin/LEdd) = (0.49 ± 0.07) log(Lbol/LEdd) − (0.78 ± 0.36). The measured slope suggests that these objects are in a radiatively inefficient accretion mode, and have been used to put stringent constraints on the properties of the accretion flow. Interestingly, we found no statistically significant correlations between Bondi power and bolometric AGN luminosity, apart from that induced by their common dependence on Lkin, thus confirming the idea that most of the accretion power emerges from these systems in kinetic form. We have then analysed the relation between kinetic power and radio core luminosity. Combining the measures of jet power with estimators of the unbeamed radio flux of the jet cores as, for example, the so-called Fundamental Plane of active black holes, we are able to determine, in a statistical sense, both the probability distribution of the mean jet Lorentz factor, which peaks at Γm∼ 7, and the intrinsic relationship between kinetic and radio core luminosity (and thus the jet radiative efficiency), which we estimate as log Lkin= (0.81 ± 0.11) log LR+ 11.9+4.1−4.4, in good agreement with theoretical predictions of synchrotron jet models. With the aid of these findings, quantitative assessments of kinetic feedback from supermassive black holes in the radio mode (i.e. at low dimensionless accretion rates) will be possible based on accurate determinations of the central engine properties alone, such as mass, radio core and/or X-ray luminosity. As an example, we suggest that Sgr A* may follow the same correlations of radio-mode AGN, based on its observed radiative output as well as on estimates of the accretion rate both at the Bondi radius and in the inner flow. If this is the case, the supermassive black hole in the Galactic Centre is the source of ∼5 × 1038 erg s−1 of mechanical power, equivalent to about 1.5 supernovae every 105 yr.