Answer:
The value of w is lie from 95 to 120.
Step-by-step explanation:
The temperature humidity index is given by the equation
[tex]T=\frac{2}{5}(w+80)+15[/tex]
where w represents the wet-bulb thermometer reading.
We have to find the values of w for which T range from 85 to 95.
[tex]85\leq T\leq 95[/tex]
[tex]85\leq \frac{2}{5}(w+80)+15\leq 95[/tex]
Subtract 15 from all the sides.
[tex]85-15\leq \frac{2}{5}(w+80)+15-15\leq 95-15[/tex]
[tex]70\leq \frac{2}{5}(w+80)\leq 80[/tex]
Multiply all sides by 5.
[tex]70\times 5\leq 2(w+80)\leq 80\times 5[/tex]
[tex]350\leq 2w+160\leq 400[/tex]
Subtract 160 from all the sides.
[tex]190\leq 2w\leq 240[/tex]
Divide all sides by 2.
[tex]95\leq w\leq 120[/tex]
Therefore the value of w is lie from 95 to 120.
