Which sentences use a semicolon correctly?

The first and second sentences use a semicolon correctly.

A. By this time, the government had spent an estimated $22 million on the project; Hughes had personally spent $18 million of his own money.

B. Henry J. Kaiser, a steelmaker, and shipbuilder, originally conceived the idea for the new prototype; however, Howard Hughes and his staff are credited with the actual design and construction of the craft

Explanation:

Semicolons can be used to join two sentences or independent clauses that are closely related to each other but not linked with a conjunction like and, but, or, nor, for, yet, or so, such as in sentence A, where the semicolon marks a slight break between the first and second clause; and it can also be used before a transition word or phrase (like “however,” “of course” and “as a result”) to mark a slight pause (not as strong as a period) between two idea, just like it is being used in sentence B.