Which two sentences uses the colon correctly?

a) henry slept through his alarm so: he didn’t make it to his first day of work, no matter how many times it went off.
b) erica's morning routine consisted of waking up, brushing her teeth, meditating for ten minutes: eating breakfast, and finally bathing.
c) jessica's supplies for the trip included these items: a hairbrush, moisturizer, a toothbrush, and four bottles of mineral water.
d) annette left her hometown with just one goal in mind: to see the world and experience different cultures.
e) joel was unable to attend the game because he had forgotten to complete his homework: he had wanted to attend the game with friends.

Colon is one of the punctuation which is used to:

1. Lay emphasis

Example: He loved just one: Bruno, his dog

2. To present dialogue ( we write the name of the speaker and then insert colon followed by his/her dialogue.)

Example: Rita: How are you?

Mary: Fine, and you?

3. Clarify composition titles ( to explain parallel ideas colon is used in compositions like lectures or book titles), and

Example: Rousseau’s Dog: Two Great Thinkers at War in the Age of Enlightenment

4. To introduce text or lists.

Example: Three types of Subordinate or Dependent Clauses are: Adjective clause, Adverb clause and Noun clause

Hence, two sentences which uses the colon correctly is :

C) Jessica's supplies for the trip included these items: a hairbrush, moisturizer, a toothbrush, and four bottles of mineral water.  

D) Annette left her hometown with just one goal in mind: to see the world and experience different cultures.  

Both the sentences introduces the list of items and things in the text. Hence, it uses the colon appropriately.