Question

Read each sentence and select the word after which a colon should be placed.

Answer 1

One thought kept crossing Jen's mind as Friday approached "Please let this week be over."

In this sentence, the colon should be placed after "approached", as you are separating Jen's thought from the main statement.

One thought kept crossing Jen's mind as Friday approached: "Please let this week be over."

Thomas Jefferson famously stated that people's unalienable rights included the following life, liberty, and the pursuit of happiness.

In that sentence, I would add "ones" after "following" for the sentence to be completly correct as "following" modifies the element it precedes.  However, the colon should be placed after "following" because the next information presented is a list.

Thomas Jefferson famously stated that people's unalienable rights included the following: life, liberty and the pursuit of happiness.

Ander's family comes from two different cultures his mother's side of the familiy is Swedish, while his father's side is Brazilian.

The colon should be placed after "cultures", as you are specifying the two different cultures mentioned.

Ander's family comes from two different cultures: his mother's side of the familiy is Swedish, while his father's side is Brazilian.

Answer 2

I believe the colons should be placed as follows:

1. One thought kept crossing Jen's mind as Friday approached: 
2. included the following: life, liberty, and the pursuit of happiness
3. cultures: 

on the first sentence you are separating her thought from the statement
on the second, you are separating a list from the statement
on the third, you are separating the two different types of cultures from the statement. 

I really hope these are correct for you :) good luck!