This is an incorrect use of a semi-colon. If you use a semi-colon, you should not follow it with a conjunction. In this case, it sounds best to keep the conjunction “so” and switch the semi-colon to a comma: "Joe was feeling particularly happy on Tuesday, so he decided to treat himself to a cup of coffee and a slice of pie."

Semicolons should be used to separate two independent clauses that are not connected by a conjunction. "So" is a conjunction here, so a semicolon is not appropriate. Use a comma instead: "The sidewalk is covered in black ice, so you should be careful when you walk outside."

The semicolon is used to combine two related sentences without a conjunction. This one should be replaced with a comma because the second part of the sentence would not be a complete sentence on its own. So, the correct answer is "relaxed ;" because this part of the sentence contains an error.

This sentence's error lies in the incorrect way in which it uses a semicolon to introduce a list. "Knit stitches and purl stitches" are the "two stitches" that the sentence introduces earlier, so a colon is the most appropriate punctuation mark to use in this instance. The corrected sentence reads, "Knitting may appear complex, but even its most complicated patterns can be created from a combination of just two stitches: knit stitches and purl stitches."

This sentence misuses a semicolon, which is generally used to separate two independent clauses. In this adverbial phrase, no punctuation is needed. The corrected sentence reads, "Frances took a moment to collect herself before pressing the button and sealing the pneumatic door forever."

This sentence misuses a semi-colon. These should be used to separate two independent clauses, so either side should be able to stand on its own as a sentence. Here, the latter half of the sentence is not an independent clause and cannot stand on its own, so you should use a comma instead: "The community members voiced various complaints, such as their distrust of the new energy company buying up local property."

A comma should be used instead of a semicolon to separate the introductory phrase "without their best player" from the rest of the second independent clause "the team didn't have a chance of winning."

A semicolon is meant to connect two thoughts that are both independent clauses. However, the second clause here is dependent and is connected by the word "so." In this situation, a comma would be appropriate to link that subordinate clause to the first independent clause. So, the corrected sentence would read, "That book over there belongs to Eileen, so we should help return it to her before she needs to study for the massive English test next week."

The option with an error is “hiking; and she.” Semicolons can be used to separate two phrases that could each stand as their own sentence but are related to each other in topic. The problem with “hiking; and she” is that the semicolon is being used to separate two ideas that are related, but the material that follows the semicolon is a fragment and cannot stand as a sentence on its own. This problem could easily be corrected by removing the “and” so the entire passage reads, “Abigail’s favorite pastime was hiking; she often hiked with friends in the mountains near her house.” 

Two independent clauses that can each stand alone must be separated by either a period or a semicolon, or connected by a comma followed by a conjunction. Because this sentence doesn't include a conjunction like "and" after its comma, it is incorrect. (This error, where two independent clauses are incorrectly connected by a comma, is known as a "comma splice.")