Elle a beaucoup de responsabilités dans cette entreprise.
She has a lot of responsibilities in this company.
Il prendra la responsabilité de ce projet.
He will take responsibility for this project.
J'ai accepté la responsabilité de cette erreur.
I accepted responsibility for this mistake.
Note
The article is part of the word: la responsabilité. That way you learn the gender with it.
Remember la responsabilité for good. ripiti brings the word back just before you forget it, with these sentences. Free, no account needed, works offline.