$3.$ Carla is a single mother with one child who is $9$ years old. She earns $$45,000$ in wages and lives alone with her daughter in a $2-$bedroom apartment. Her daughter lives with her full$-$time and Carla provides more than half of the child$$s financial support. She receives no child support or other assistance.

a$.$ Determine Carla$$s filing status and explain why she uses this status.

b$.$ Calculate the standard deduction amount based on the filing status identified in part $($a$).$