This sentence contains a dangling participle. The way the sentence is phrased, the introductory phrase "Gazing into the night sky" appears to describe "the stars" instead of "Galileo." The only answer choice that corrects this issue while creating a grammatically correct sentence is "Gazing into the night sky, Galileo was prompted by the stars."

The sentence is written in a manner that makes it appear that "the machine" was "working out the kinks," when the only logical noun to do this action is "the tinkerer." The sentence needs to be rearranged so as to indicate clearly who was doing the "working," a task best achieved by the answer choice "the tinkerer exhibited the machine in 1904."

The sentence as written features a dangling modifier, which makes the sentence read as though "the breeze" was "walking out of the house." The sentence needs to be rearranged to make it clear that the girl was the one doing the walking. The only answer choice that does this is "The breeze nearly knocked the girl down as she walked out of the house."

The sentence is written in a way that makes it appear that "the smog" was the thing "flying into the city." The sentence needs to be restructured to show that the plane, and the people on it, were "flying into the city." The answer choice that best clarifies the meaning of the sentence is "The smog was visible to everyone on the plane flying into the city."

The sentence as written contains what is known as a "dangling modifer," as the introductory clause does not describe action taken by the subject, "noises." This means the sentence needs to be fixed to make the subject fit with its modifying clause. The best choice among the answers is "Walking at night through the graveyard, people hear noises that seem."

The original text contains a misplaced modifier. When we have a modifying phrase at the beginning of a sentence, such as "Invented in China over three centuries ago," we know that the noun that appears right after that phrase must be the thing that the modifying phrase describes. In this case, this means the thing that was invented in China over three centuries ago. 

All of the answer choices except "Invented in China over three centuries ago, the compass has served as a navigational tool for explorers and trade merchants alike" make is sound as though explorers and trade merchants were invented in China over three centuries ago, which is not correct.

When a sentence begins with an introductory modifying clause, such as "A popular tourist destination," the noun right after that clause must be the entity that the clause describes—in this case, Central Park. Otherwise, an error known as a "dangling modifier" is created and the sentence becomes confusing and ambiguous.

Only the answer choice "Central Park was the subject of many of Edward Hooper's paintings" places the subject "Central Park" immediately after the modifying introductory clause and avoids confusion and ambiguity.

All of the other answer choices make it sound as though Edward Hooper is a popular tourist destination, which is somewhat silly and definitely incorrect.

With the sentence phrased the way it is, the thing that is "caring for a pet" appears to be "responsibility." This dangling modifier needs to be changed to make it clear that "children" are "caring for a pet." The correct answer choice is "Responsibility is something children can learn by caring for a pet."