a$.(3$ points$)$ Use Thevenin's theorem to find $V_B$ in the following circuit.

b$.(3$ points$)$ Write the algebraic KVL expressions: BE and CE relating.

c$.(8$ points$)$ Calculate $I_B,I_C,I_E,$ and $V_{CE}$

d$.(3$ points$)$ Define if the transistor is in Cut$-$off, Saturation, or Active region.

Note: The current gain $()$ of the common emitter transistor circuit shown in the next figure is $150$ and $\frac{?}{\text{b}\text{a}\text{r}}(V_{BE})-=0\mathrm{.}7V$ when the transistor is working in saturation or active region.