Transistors have a range of current gain so they also have a range of base current in a circuit.
The 2N3904 has a current gain from 100 to 300. I selected the divider's current to be 10 times the base current if the gain is 200.
Transistors have a range of base to emitter voltage. I selected the emitter resistor value to be 1/10th the collector resistor value so that the emitter voltage (and also the base voltage) are high enough that the actual base to emitter voltage doesn't matter.
At idle, the base voltage is 1.1V and the emitter voltage is at about 0.45V. Then the collector voltage is at about 5.5V. The signal at the collector can swing up to 10V if there is plenty of negative feedback and can swing down to 1V.