We describe a complete, flux-density-limited sample of galaxies at redshift $0.8 < z < 1.3$ selected at 16 micron. At the selection wavelength near 8 micron rest, the observed emission comes both from dust heated by intense star formation and from active galactic nuclei (AGNs). Fitting the spectral energy distributions (SEDs) of the sample galaxies to local-galaxy templates reveals that more than half the galaxies have SEDs dominated by star formation. About one sixth of the galaxy SEDs are dominated by an AGN, and nearly all the rest of the SEDs are composite. Comparison with X-ray and far-infrared observations shows that combinations of luminosities at rest-frame 4.5 and 8 micron give good measures of both AGN luminosity and star-formation rate. The sample galaxies mostly follow the established star-forming main sequence for $z=1$ galaxies, but of the galaxies more than 0.5 dex above that main sequence, more than half have AGN-type SEDs. Similarly, the most luminous AGNs tend to have higher star-formation rates than the main sequence value. Galaxies with stellar masses $>$10$^{11}$,Msun are unlikely to host an AGN. About 1% of the sample galaxies show an SED with dust emission typical of neither star formation nor an AGN.
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