Which sentence does not use a gerund? a) shopping is my favorite thing to do on the weekend. b) nancy enjoys walking around her neighborhood each evening. c) peter is exercising because he wants to be on the lacrosse team. d) libraries are a great place for studying because they are usually quiet.

The sentence that does not use the gerund is option C. Peter is excercising because he wants to be on the lacrosse team.  The verb phrase is in the present continuous or present progressive that is formed by the verb Be + the main verb +ing.  This tense is used to talk about actions happening at the time of speaking, for temporary actions or descriptions

c) peter is exercising because he wants to be on the lacrosse team

teenagers are certainly stereotyped as moody.

most people view teenagers as naturally moody and grumpy, even when this is wrong. many teens are suffering from depression but it is brushed off as "just a phase" or "that's just cause they're a teenager"

true. the definition explains it: a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. this is a dictionary definition that i have looked up in a dictionary.