Suppose nicole earns $20,000 per year, michelle earns $40,000 per year, and rosa earns $100,000 per year. under a regressive tax, who would pay a greater percentage of her income in taxes?

Nicole  
A regressive tax is a tax that effectively goes down percentage wise as the income goes up. A few examples would be a tax with an upper limit on the taxed amount. Or a tax on some commodity that a person will only use a fixed amount. For example: 
Assume a tax on cigarettes of $4.00 per pack. Also assume all three people smoke 1 pack per day. Since there's 365 days per year, that means that each person spends $4 * 365 = $1460 on tax on cigarettes. What percentage of their total income is that? 
Nicole = $1460 / $20000 = 0.073 = 7.3%
 Michelle = $1460 / $40000 = 0.0365 = 3.65%
 Rosa = $1460 / $100000 = 0.0146 = 1.46%  
As you can see, the higher the income, the lower the effective tax rate which is the definition of a regressive tax.

Answerpro-forma;