7. Let's do some taxes. The following table are the 2020 tax brackets for single tax filers. Tax rate 10% 12% 22% 24% 32% 35% 37% Amount $0 to $9,700 $9,701 to $39,475 $39,476 to $84.200 $84,201 to $160,725 $160,726 to $204,100 $204,101 to $510,300 $510,301 or more a) For example, if you make $54,000 in 2020, the first $9,700 is taxed at 10%, the next amount from $9,701 to $39,475 is taxed at 12%, and finally, the amount from $39,476 to $54,000 is taxed at 22% (there are also deductions and credits, but let's ignore those for now). What is the total amount of tax you would need to pay? b) Write the tax rates as a 7-dimensional vector (0.1,0.12, 0.22, 0.24, 0.32, 0.35,0.37). Represent the amount of tax you need to pay as a dot product . . What is the value of the vector that corresponds to the calculation you made in part a)? c) Our current system is a "progressive tax system, since tax rates increase as income increases. Flat tax proposals have also been proposed. Under the flat tax system, suppose all income is taxed at 17%, regardless of your income. How much would you have to make in 2020 in order to pay the same amount of tax under both systems? 2 d) If you make less than your answer in part c), which system do you pay more tax under