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We study a composite medium consisting of insulating magnetodielectric spherical particles embedded in a background matrix. Using results from the literature going back as far as Lewin (1947), we show that the effective permeability and permittivity of the mixture can be simultaneously negative for wavelengths where the spherical inclusions are resonant and that the medium results in an effective "double negative (DNG) media". Materials of this type are also called negative-index materials, backward media (BW), and left-handed materials. This type of material belongs to a more general class of metamaterials. The theoretical results presented here show that composite media having much simpler structure than those reported in the literature can exhibit negative permeability and permittivity over significant bandwidths.