Question

the formula for converting fahrenheit temperature, f, to celsius temperature, c, is $c = \frac{5}{9}(f - 32)$. if the celsius temperature ranges from $10^\circ$ to $40^\circ$, inclusive, what is the range for the fahrenheit temperature? use interval notation to express the range for the fahrenheit temperature. select the correct choice below and fill in the answer boxes to complete your choice. (type integers or decimals.) \\(\bigcirc\\) a. $\square ^\circ\text{f}, \square ^\circ\text{f})$ \\(\bigcirc\\) b. $(\square ^\circ\text{f}, \square ^\circ\text{f})$ \\(\bigcirc\\) c. $\square ^\circ\text{f}, \square ^\circ\text{f}$ \\(\bigcirc\\) d. $(\square ^\circ\text{f}, \square ^\circ\text{f}$

Explanation:

Step1: Rearrange formula for F

Start with $C = \frac{5}{9}(F - 32)$. Multiply both sides by $\frac{9}{5}$:
$\frac{9}{5}C = F - 32$
Add 32 to both sides:
$F = \frac{9}{5}C + 32$

Step2: Calculate lower F bound

Substitute $C=10$ into the formula:
$F = \frac{9}{5}(10) + 32 = 18 + 32 = 50$

Step3: Calculate upper F bound

Substitute $C=40$ into the formula:
$F = \frac{9}{5}(40) + 32 = 72 + 32 = 104$

Step4: Determine interval notation

Original range is inclusive (10° to 40° C), so F range is inclusive. Use square brackets.

Answer:

C. $[50^\circ\text{F}, 104^\circ\text{F}]$