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Answer:
the reading on the scale is 158.5 mm.
Explanation:
Given;
upper fixed point of the temperature scale, x₁ = 260 mm
lower fixed point of the temperature scale, x₂ = 50 mm
upper temperature scale, T₁ = 212 °F
lower temperature scale, T₂ = 32 °F
thermometer reading, t = 125 °F, let the reading on the scale = x
Interpolate as follows to determine the value of "x"
[tex]\frac{X_1 - X}{X_1-X_2} = \frac{T_1-t}{T_1-T_2} \\\\\frac{260-X}{260-50} = \frac{212-125}{212-32} \\\\\frac{260 -X}{210} =\frac{87}{180} \\\\180(260-X) = 87(210)\\\\46800 -180 X = 18270 \\\\180X = 46800-18270\\\\180X = 28530\\\\X = \frac{28530}{180} \\\\X = 158.5 \ mm[/tex]
Therefore, the reading on the scale is 158.5 mm.