Explanation

For the first word, you want a word that agrees with “sophisticated,” but more importantly that explains why these mathematical tools are useful to those who aren’t even doing math, so you want a positive word that means “useful in many contexts.” Versatile is the best fit.

For the second word, you’d want something like the “model,” in the sense of “explain,” that you saw earlier in the sentence. Explicate is the best match.

Versatile, explicate.
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Why can't populist be the answer for the first blank? I was stuck between versatile and populist but went ahead with the latter.

Sorry if I ask sir

what was the reason you picked populist ?