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Conversion to an arbitrary temperature scale.

The world seems to think that a new temperature scale is needed, the NurAn degree. On this scale it is decided that water will freeze at 17 degrees NurAn and boil at 167 degrees NurAn. On this scale, what is the body's average core temperature? How about absolute zero? One day a nurse's temperature is measured as 75 degrees NurAn. Is this nurse "hot"?

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Assuming this scale is linear we can calculate the linear equation relating "NurAn" to Celsius, in the form N=a*C+b where C is the temp in Celsius, N is the temp in ...