To find the total cost of the t-shirt after the discount and sales tax have been applied, follow these steps:

1. Calculate the discount: $\text{Discount} = \text{Regular Price} \times \text{Discount Rate} = 34.50 \times 0.20 = 6.90$

2. Calculate the sale price: $\text{Sale Price} = \text{Regular Price} - \text{Discount} = 34.50 - 6.90 = 27.60$

3. Calculate the sales tax: $\text{Sales Tax} = \text{Sale Price} \times \text{Sales Tax Rate} = 27.60 \times 0.065 = 1.794$

4. Calculate the total cost: $\text{Total Cost} = \text{Sale Price} + \text{Sales Tax} = 27.60 + 1.794 = 29.394$

Rounding to two decimal places, the total cost after the discount and tax is $29.39.

Would you like more details or have any questions? Here are some related questions:

1. What would the total be if the discount was 30% instead of 20%?
2. How would the total change if the sales tax increased to 8%?
3. What is the final price if the item is bought without any sales tax?
4. If you bought two t-shirts, what would the total cost be?
5. How much do you save by waiting for a sale if you buy the shirt at regular price?

Tip: Always calculate the discount first before applying sales tax to find the best deal.