The correct answer is but. It is the best conjunction to complete the sentence out of the four options because it is used to introduce a phrase that contrasts with the previous part of the sentence.
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In this excerpt, Paine uses hyperbole to
A) inspire his readers to persevere.
B)warn readers of the difficulties ahead.
C)teach readers how to survive cold weather.
D)describe the sacrifices readers must make.
Answer: A) inspire his readers to persevere.
Explanation: A hyperbole is a type of figurative language that consists in exaggerating an event or a statement. In the given excerpt from "The Crisis Number I" we can see a clear example of hyperbole in the phrases "in the depth of winter, when nothing but hope and virtue could survive" and "the city and the country, alarmed at one common danger, came forth to meet and to repulse it" this hyperbole is used to inspire the readers to persevere.