$1)$ Kate earned $$100,000$ from her job at a local business in $2023.$ She also had $$75,000$ in self$-$employed consulting income. What is the amount of her self$-$employment tax rounded to the nearest dollar?

A$)$ $$0.$

B$)$ $$9,473.$

C$)$ $$10,597.$

D$)$ $$11,475.$