we are multiplying the calculated value by 10
Because for the sensor to be most useful, we would like as large a signal change as possible when the sensor detects a tilt, and a resistor 10x your sensor resistance will give a 91% voltage swing (from a 12V supply, the output would change by 11V). If you chose to use the same value, without multiplying by 10, you'd just get 50% voltage swing (from a 12V supply, the output would change by 6V).
You can choose other values of course, but fungus's suggestion of 10x is a good start to see the sensor working.