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We have used the Australia Telescope Compact Array (ATCA) at 95 GHz to carry out continuum observations of 130 extragalactic radio sources selected from the Australia Telescope 20 GHz (AT20G) survey. We use a triple‐correlation method to measure simultaneous 20‐ and 95‐GHz flux densities for these objects, and over 90 per cent of our target sources are detected at 95 GHz. We demonstrate that the ATCA can robustly measure 95‐GHz flux densities with an accuracy of ∼10 per cent in a few minutes for sources stronger than about 50 mJy.  We measure the distribution of radio spectral indices in a flux‐limited sample of extragalactic sources, and show that the median 20–95 GHz spectral index does not vary significantly with flux density for   S  20  &gt; 150 mJy . This finding allows us to estimate the extragalactic radio source counts at 95 GHz by combining our observed 20–95 GHz spectral‐index distribution with the accurate 20‐GHz source counts measured in the AT20G survey.  Our derived 95‐GHz source counts at flux densities above 80 mJy are significantly lower than those found by several previous studies. The main reason is that most radio sources with flat or rising spectra in the frequency range 5–20 GHz show a spectral turnover between 20 and 95 GHz. As a result, there are fewer 95‐GHz sources (by almost a factor of 2 at 0.1 Jy) than would be predicted on the basis of extrapolation from the source populations seen in lower‐frequency surveys. We also derive the predicted confusion noise in cosmic microwave background surveys at 95 GHz and find a value 20–30 per cent lower than previous estimates.  The 95‐GHz source population at the flux levels probed by this study is dominated by quasi‐stellar objects with a median redshift   z ∼ 1 . We find a correlation between optical magnitude and 95‐GHz flux density which suggests that many of the brightest 95‐GHz sources may be relativistically beamed, with both the optical and millimetre continuum significantly brightened by Doppler boosting.

The extragalactic radio‐source population at 95 GHz