Please check my work.

Correctly identifying the part of speech of each of the word in the sentence.

The new mail carrier finally arrived.

The (definite article) new (adjective) mail (noun) carrier (noun) finally (adverb) arrived (past tense verb).

I'd call "mail carrier" a noun -- it's a compound noun.

http://grammar.ccc.commnet.edu/grammar/compounds.htm

The word "mail" is a noun or an adjective in the sentence?

http://www.jiskha.com/display.cgi?id=1311122906

Your analysis is mostly correct, but there is a small error. Let me explain each part of speech in the sentence:

- "The" is indeed a definite article.
- "New" is an adjective because it describes the noun "mail."
- "Mail" is a noun because it is the object being referred to.
- "Carrier" is also a noun because it is the noun form of the verb "carry."
- "Finally" is an adverb that describes when the action happened.
- "Arrived" is a past tense verb because it shows the action of the subject.

So, your analysis is correct for all the words except for "arrived." It should be labeled as a past tense verb, not a noun. Keep up the good work!