We have that the total gross pay is $14,600.
The state tax rate is 3.5%.
First, we need to find the 3.5% of $14,600:
![14600\cdot(3.5)/(100)=(51100)/(100)=511](https://img.qammunity.org/2023/formulas/mathematics/college/os2vf2fpzgsu1jt7lislzkc28d4m6xjk29.png)
This is the total value of tax in a year. Then, to find how much she pays we need to divide this amount by 12 (number of months of the year). Then, we have:
![T=(511)/(12)\Rightarrow T=42.583333](https://img.qammunity.org/2023/formulas/mathematics/college/bd995j5ps33kxrw4nxqp9ykw7m1grspjr6.png)
Therefore, she needs to pay $42.58 a month in state taxes.