worthy of or requiring responsibility or trust; or held accountable; “a responsible adult”; “responsible journalism”; “a responsible position”; “the captain is responsible for the ship’s safety”; “the cabinet is responsible to the parliament”

Responsibility

To be entrusted with or assigned a duty or charge. In many instances responsibility is assumed, appropriate with one’s duties. Responsibility is distinct from accountability. A supervisor can assign responsibility but cannot give away his or her accountability: the manager is ultimately responsible.

ex.

That boy is responsible / The responsible girl

or

He has a lot of responsibility.