What term describes the developmental state of insects that hatch from eggs?

The term that describes the developmental state of insects that hatch from eggs is "nymph." Insects that undergo incomplete metamorphosis, such as grasshoppers and cockroaches, transition from the egg to the nymph stage. Nymphs are small versions of the adult insect and typically resemble adult forms but lack fully developed wings and reproductive structures.

In contrast, larva refers to a different developmental stage of insects that have complete metamorphosis, like butterflies and beetles. These insects hatch into larvae, which are distinct from their adult forms. Similarly, caterpillars are the larval stage of butterflies and moths, while a pupa is the transitional stage between larva and adult in species undergoing complete metamorphosis. Therefore, the correct term that specifically relates to the developmental state after hatching from an egg for insects that experience incomplete metamorphosis is nymph.