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X-ray observations have been made of a sample of 20 classical Cepheids, including two new observations (Polaris and {\it l} Car) reported here. The occurrence of X-ray flux around the pulsation cycle is discussed. Three Cepheids are detected ($\delta$ Cep, $\beta$ Dor, and Polaris). X-rays have also been detected from the low--mass F, G, and K companions of 4 Cepheids (V473 Lyr, R Cru, V659 Cen, and W Sgr), and one hot companion (S Mus). Upper limits on the X-ray flux of the remaining Cepheids provide an estimate that 28\% have low mass companions. This fraction of low--mass companions in intermediate mass Cepheids is significantly lower than expected from random pairing with the field IMF. Combining the companion fraction from X-rays with that from ultraviolet observations results in a binary/multiple fraction of 57\% $\pm$12\% for Cepheids with the ratios q $>$ 0.1 and separations a $>$ 1 au. This is a lower limit since M stars are not included. X-ray observations detect less massive companions than other existing studies of intermediate mass stars. Our measured occurrence rate of unresolved, low-mass companions to Cepheids suggests that intermediate-period binaries derive from a combination of disk and core fragmentation and accretion. This yields a hybrid mass-ratio distribution that is skewed toward small values compared to a uniform distribution but is still top-heavy compared to random pairings drawn from the IMF., Comment: Accepted by ApJ