Final answer:
The provided sentence is a complex sentence, not a compound-complex sentence, because it has only one main clause and one dependent clause.
Step-by-step explanation:
The sentence "Because their car had a flat tire, Mimi and Joel arrived at the dance late" is not a compound-complex sentence.
It is a complex sentence, because it contains one main clause (“Mimi and Joel arrived at the dance late”) which can stand alone as a sentence, and one dependent clause (“Because their car had a flat tire”) which cannot stand alone. A compound-complex sentence is a sentence that contains at least two main clauses and at least one subordinate clause.