Option A correctly uses a comma to separate the introductory dependent clause "Before the main event began" from the main clause. Option B is incorrect because it omits the necessary comma after the introductory dependent clause. Option C incorrectly places a comma between the subject ("audience") and its verb ("enjoyed"). Option D uses unnecessary commas that incorrectly set off "enjoyed a lively musical performance" as if it were a non-essential phrase.

Option B correctly uses a comma before the coordinating conjunction "yet" to separate two independent clauses. Option A is incorrect because it omits the necessary comma before "and" when joining two independent clauses. Option C is incorrect because "and" connects a compound predicate, not two independent clauses, so a comma is not required. Option D is a comma splice, as two independent clauses are incorrectly joined by only a comma without a coordinating conjunction.

Option A correctly uses two commas to enclose the nonessential clause "which stood on a hill overlooking the town." Option B is incorrect because it is missing the first comma before "which" to begin the nonessential clause. Option C is incorrect as it omits both commas, making the nonessential clause appear essential to the sentence's core meaning. Option D is incorrect because it misplaces a comma after "hill," incorrectly splitting the nonessential clause and failing to properly close it.

A is correct because the introductory dependent clause ("Because the weather improved") is properly followed by a comma before the main clause. B is incorrect because it omits the necessary comma after the introductory dependent clause ("Although she had studied diligently"). C is incorrect because it uses a semicolon instead of a comma to separate the introductory dependent clause from the main clause. D is incorrect because the dependent clause ("since the movie started too late") is not introductory; it follows the main clause.

Option A is correctly punctuated; it uses a comma after the introductory phrase "After a long day of hiking" and uses a pair of commas to set off the non-essential appositive phrase "eager for rest." Option B incorrectly omits the comma after the introductory phrase and the commas around the appositive. Option C incorrectly omits the closing comma for the non-essential appositive phrase. Option D incorrectly omits the opening comma for the appositive and includes an unnecessary comma before "and" where it joins a compound verb, not two independent clauses.