The billing cycle for a credit card goes from February 15 to March 16 during a non-leap year. The balance at the start of the billing cycle is \(\$ 292.82\). The list of transactions on the card is below. Find the average daily balance for the billing cycle.

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Date Activity Amount 15-Feb Billing Date Balance $292.82 21-Feb Food $64.57 22-Feb Gasoline $31.50 22-Feb Food $71.94 28-Feb Insurance $133.25 28-Feb Payment $100.00 3-Mar Gasoline $26.61 12-Mar School Trip $300.00