Final answer:
In this X-linked cross, the recombinant class in the F1 progeny would be the white-eyed females with genotype Xy+w+Xyw.
Step-by-step explanation:
In an X-linked cross, the genotypes of the F1 and F2 offspring depend on whether the recessive trait was expressed by the male or the female in the P generation. In this case, a gray-bodied, red-eyed female with genotype Xy+w+Xyw is mated to a gray-bodied, red-eyed male with genotype Xy+w+Y. The female is heterozygous with genotype Xy+w+Xyw, and the male is hemizygous with genotype Xy+w+Y. To determine the phenotypic class counted as a recombinant in the F1 progeny, we look at the possible genotypes of the offspring. The possible genotypes for the F1 progeny are Xy+w+Xyw (red-eyed females), Xy+w+Y (red-eyed males), Xy+w+Xyw (white-eyed females), and Xy+w+Y (white-eyed males). The recombinant class would be the one that has different combinations of traits compared to the parental genotypes. In this cross, the recombinant class would be the white-eyed females with genotype Xy+w+Xyw.