Final answer:
The final cost of the T.V. is $541.83.
Step-by-step explanation:
To find the final cost of the T.V., we first need to calculate the amount of discount David receives. The discount is 20% off the regular price of $649.99, which is $129.998. Therefore, the discounted price of the T.V. is $649.99 - $129.998 = $519.992.
Next, we need to calculate the sales tax on the discounted price. The sales tax rate is 4.2%, which is 0.042 as a decimal. So, the amount of sales tax is $519.992 * 0.042 = $21.839664.
Finally, we calculate the final cost by adding the discounted price and the sales tax: $519.992 + $21.839664 = $541.831664. Rounding this to the nearest cent gives us the final cost of $541.83.