Ted has a credit card that uses the average daily balance method. for the first 9 days of one of his billing cycles, his balance was $2030, and for the last 21 days of the billing cycle, his balance was $1450. if his credit card's apr is 23%, which of these expressions could be used to calculate the amount ted was charged in interest for the billing cycle?

Your question doesn't say what are the options, but we can make some reasoning.

The average daily balance method is based, obviously, on the average daily balance, which is the average balance for every day of the billing cycle. Therefore, in order to calculate the average daily balance, you need to sum the balance of every day and then divide it by the days of the billing cycle.
In your case:
ADB = (9×2030 + 21×1450) / 30 = 1624 $

Now, in order to calculate the interest, you should first calculate the daily rate, since APR is usually defined yearly, and therefore:
rate = 0.23 ÷ 365 = 0.00063 

Finally, the expression to calculate the interest could be:
interest = ADB × rate × days in the billing cycle
or else:
interest = ADB × APR ÷ 365 × days in the billing cycle

In your case:
interest = 1624 × 0.23 ÷ 365 × 30
             = 30.70 $

The first option would be correct if it were one half and not one