Sam, an active duty servicemember, is domiciled in Ohio. At the end of $2022,$ she moved to Missouri in compliance with a permanent change of duty station. She remained in Missouri for all of $2023.$ During the year, Sam earned $$39,000$ in military wages and $$8,000$ from a side job at a craft store. Assuming that Sam neither established a domicile in Missouri nor elected to treat it as her residence for tax purposes, how much of her wages are taxable by Missouri?

$$0$

$$8,000$

$$39,000$

$$47,000$