Answer:
The sentence in this passage that correctly uses the semicolon is the following one: She had made up her mind; she was going to travel the world one way or another.
Explanation:
A semicolon is used to join in a single sentence two independent clauses that are closely related in thought. When a semicolon is used to join two ideas, these ideas are given equal position. In the sentence above, the second clause specifies the first one. The first one states that she had made up her mind and the second one specifies what this means: she made up her mind, she had decided to travel the world.
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