Joan buys a T-shirt and a hat. The price of the T-shirt is 8.99 and the price of the hat is 4.05 what is the total price of the two items?

The total price of the T-shirt and the hat is 8.99 + 4.05 = $<<8.99+4.05=13.04>>13.04. Answer: \boxed{13.04}.