Are these sentences using the adjective and adverb correctly? Do they make sense?

1) The girl is a "bad" softball player.(Adjective)

2) The girl played softball "badly." (Adverb)

1) I am "cautious" when I run at night. (Adjective)

2) I "cautiously" run at night. (Adverb)

1) I am "hopeful" that we will receive our bonus. (Adjective)

2) "Hopefully," we will receive our bonus. (Adverb)

Great!

Some grammar purists argue that your use of "hopefully" is not correct. Check this site for the details.

http://www.merriam-webster.com/dictionary/hopefully

yes, correct. I would have used "poor" and "Poorly" instead of bad, due to recent connotations of the word "bad."

In the vernacular, "bad" can have some weird implications.

Thank you!

Yes, all of the sentences use the adjective and adverb correctly, and they also make sense. Here's how to determine whether the sentences use the correct adjective or adverb:

1) The girl is a "bad" softball player. (Adjective)
To determine if the adjective is used correctly, ask yourself if "bad" describes the softball player. In this sentence, "bad" describes the player's skill in softball, so it is used correctly.

2) The girl played softball "badly." (Adverb)
To determine if the adverb is used correctly, ask yourself if "badly" describes the action of playing softball. In this sentence, "badly" describes how the girl played softball, so it is used correctly.

1) I am "cautious" when I run at night. (Adjective)
To determine if the adjective is used correctly, ask yourself if "cautious" describes the subject ("I") in the sentence. In this case, it describes how the speaker (subject) feels, so it is used correctly.

2) I "cautiously" run at night. (Adverb)
To determine if the adverb is used correctly, ask yourself if "cautiously" describes the action of running. In this sentence, "cautiously" describes how the action of running is done, so it is used correctly.

1) I am "hopeful" that we will receive our bonus. (Adjective)
To determine if the adjective is used correctly, ask yourself if "hopeful" describes the subject ("I") in the sentence. In this case, it describes how the speaker (subject) feels, so it is used correctly.

2) "Hopefully," we will receive our bonus. (Adverb)
To determine if the adverb is used correctly, ask yourself if "hopefully" describes the verb ("will receive") in the sentence. In this sentence, "hopefully" describes the speaker's expectation about the outcome of receiving the bonus, so it is used correctly.

Overall, all the sentences use the adjective and adverb correctly and make sense.