"Dormant" is an adjective that means "not doing anything at this time : not active but able to become active," or "having normal physical functions suspended or slowed down for a period of time; in or as if in a deep sleep." So, neither "awake" nor "energetic" can be the correct answer because each is an antonym of "dormant," not a synonym. "Inactive" is the closest synonym to "dormant" amongst the listed answer choices, so "inactive" is the correct answer.

To have a "hectic" schedule is to have an extremely busy one, so "busy" is the correct answer. As for the other answer choices, none are close in meaning to "hectic": "solitary" means alone; "radiant" means glowing; "surprised" means astounded or shocked; and "determined" means firmly decided on something.

To be "savage" means to be violent in a primitive way. To be "barbaric" means acting with unsophisticated aggression. Given how similar these two words are, they are synonyms.

"Domesticated" means tamed or made submissive to human beings. To be "tame" means no longer wild, and rather, under control of humans. Thus, "domesticated" and "tame" mean the same thing and are synonyms.

To be "sneaky" means to be trying to be undetected or unnoticed. To be "sly" means to be able to carry out activities without drawing attention to oneself. Given how similar these words are in meaning, they are synonyms. 

"Auspicious" is an adjective that can mean either "conducive to success; favorable," or "giving or being a sign of future success." So, we need to pick out an answer choice that is an adjective and means something like "favorable." So, "ominous" cannot be the correct answer because "ominous" means "giving the impression that something bad or unpleasant is going to happen; threatening; inauspicious," so "ominous" is an antonym of "auspicious." "Promising," however, is an adjective that means "showing signs of future success," and because it is the answer choice closest in meaning to "auspicious," "promising" is the correct answer.

"Precise" means marked by exactness, as in the sentence, "In order for the science experiment to work, we must make very precise measurements." "Exact" is most similar in meaning to "precise," so "exact" is the correct answer.

Incorrect answers:

"Perfect" is not the best answer because although you might describe precise measurements as being "perfect," the word "perfect" means as good as it is possible to be. For example, you might say "That was a perfect book report" or "I got a perfect score on my test." So, "exact" is close in meaning to "precise" than "perfect" is.

"Interesting" means holding or catching attention, as in the sentence, "The museum display of brightly colored butterflies was interesting to the students."

"Formal" means following accepted conventions or rules, as in the sentence, "My teacher's first name is Susan, but we address her formally as Mrs. Brown."

"Convoluted" is an adjective that means "extremely complex and difficult to follow" and is used of arguments, stories, or sentences. So, neither "simple" nor "straightforward" can be the correct answer because each of these words are antonyms of "convoluted," not synonyms. "Complex," however, is an adjective that means "consisting of many different and connected parts" or "not easy to analyze or understand; complicated or intricate." Because it is the answer choice closest in meaning to "convoluted," "complex" is the correct answer.

The adjective "intricate" refers to something that is complex or nuanced. It is sometimes used to describe physical complexity (like an intricate system of highways), but also applies to ideas that may be difficult to grasp. "Complicated" is the clear synonym here. Of the remaining choices, both "straightforward" and "simple" are antonyms of the given word, since they convey a lack of complexity. "Unified" is used to describe groups that have been united or brought together.

The adjective "precise" refers to an extremely accurate or specific measurement or assessment. "Exact," which also refers to an accurate or correct quantity, is our answer. "Careless" is clearly incorrect, since it describes something that is sloppy and unlikely to be perfectly measured. You might use the word "immature" to describe a person who acts unusually young and inexperienced; neither this term nor "incomplete" (unfinished) is related to the given word.