We investigate the effect of a hybrid electron population, consisting of both thermal and non-thermal particles, on the synchrotron spectrum, image size, and image shape of a hot accretion flow onto a supermassive black hole. We find two universal features in the emitted synchrotron spectrum: (i) a prominent shoulder at low (<=sssim 1011 \rmHz) frequencies that is weakly dependent on the shape of the electron energy distribution, and (ii) an extended tail of emission at high (> 1013 \rmHz) frequencies whose spectral slope depends on the slope of the power-law energy distribution of the electrons. In the low-frequency shoulder, the luminosity can be up to two orders of magnitude greater than with a purely thermal plasma even if only a small fraction (< 1%) of the steady-state electron energy is in the non-thermal electrons. We apply the hybrid model to the Galactic center source, Sgr A^*. The observed radio and IR spectra imply that at most 1% of the steady-state electron energy is present in a power-law tail in this source. This corresponds to no more than 10% of the electron energy injected into the non-thermal electrons and hence 90 % into the thermal electrons. We show that such a hybrid distribution can be sustained in the flow because thermalization via Coulomb collisions and synchrotron self-absorption are both inefficient. The presence of non-thermal electrons enlarges the size of the radio image at low frequencies and alters the frequency dependence of the brightness temperature. A purely thermal electron distributions produces a sharp-edged image while a hybrid distribution causes strong limb brightening. These effects can be seen up to frequencies 1011 Hz and are accessible to radio interferometers.