Acumen—keen insight; shrewness.

Founder—to sink; to fail utterly.

"Spate" is the correct answer, as it meansa group of events occurring one after another in a short amount of time. The construction site is implied to have had enough accidents to justify increased caution.

For this blank, we're looking for a noun that refers to pieces of broken pottery. "Shards," which meanspiecesof broken pottery, is the best answer.

"Requisite" means that something is necessary and most accurately completes the sentence. The sentence indicates that self confidence is not merely helpful or sufficient for achieving success, but is essential. For that reason, "requisite" is a better answer than "condition" or "quality," the only other answers that could potentially complete the sentence.

None of the answers to this question are ideal; however, the sense of the second sentence indicates that it is a question of "learning." Perhaps the most tempting words are "stupor" or "indolence." The first, however, deals with a state of being dazed, not necessarily lack of intellectual acumen. The latter indicates laziness. The closest word on the list would be "stultification," which can mean the process of making of one become stupid.

The key word in the second sentence is "both." It is particularly tempting to choose "premises," "conclusions," or "implications;" However, these do not deal two cases—a "both" fulfilling the "whence" and "whither." The only word that really fits that is "termini" —as strange as it might seem in this context.

The fact that the professor was ostracized means his calculations were at the very least controversial and against the prevailing thought of the scientific community.Breakthroughandachievementdo not have the kind of disagreement indicated in the sentence, while恢复andreformationdo not convey the appropriate level of hatred for the professor's ideas.

The fact the producers of the film did not know where the actor went indicate he had gone somewhere.Hiatus, meaning a pause or leave of absence, fits best in the context of the sentence.

The two words that give the best context for the sentence are "intelligence" and "underestimated." Both words indicate the kindergartner showed smarts and ability beyond her teachers assumptions. Onlyacuity, meaning "mental sharpness," fits the appropriate meaning.