In which of the following sentences is the semicolon used correctly?

a. I haven't seen Jacob in over a month; I'm beginning to worry.
b. I haven't seen Jacob in over a month; and I'm beginning to worry.
c. Because I haven't seen Jacob in over a month; I'm beginning to worry.

The sentence in which the semicolon is used correctly is:

a. I haven't seen Jacob in over a month; I'm beginning to worry.

The correct usage of a semicolon is in option a: "I haven't seen Jacob in over a month; I'm beginning to worry." A semicolon is used to join two independent clauses that are closely related in meaning. In this sentence, the two independent clauses are "I haven't seen Jacob in over a month" and "I'm beginning to worry."