Can you use the mana from Dark Ritual to pay for a spell with a hybrid mana cost?

Dark Ritual produces three black mana ({B}{B}{B}). Hybrid mana symbols — written as {B/R}, {G/W}, etc. — can each be paid with either of the two colors shown, or in some cases with two generic mana (for Phyrexian or twobrid symbols). Because black mana satisfies the black half of any hybrid symbol containing black, Dark Ritual's mana can pay for it directly.

According to CR 202.2c, a hybrid mana symbol contributes both colors to a spell's color identity, but when it comes time to actually pay the cost, you choose one of the two options. CR 107.4c states that a hybrid mana symbol is paid by paying either of the two mana types it represents.

Even if a hybrid symbol pairs black with a color Dark Ritual doesn't produce — say {B/R} — you can still use the black mana from Dark Ritual to pay the black option of that symbol. You simply choose the {B} mode when paying.

Concrete example: You cast Rakdos Cackler, which costs {B/R}. You tap a land for {R} but want to use Dark Ritual's mana too. You cast Dark Ritual first, getting {B}{B}{B}. You then cast Rakdos Cackler, choosing to pay the {B} option of its {B/R} hybrid symbol using one of those black mana. This is perfectly legal.

Note that if a hybrid symbol pairs black with a color and you want to pay the other color's option (e.g., pay {R} for {B/R}), Dark Ritual's black mana cannot fill that role — but that's a player choice, not a restriction on Dark Ritual itself.