High School

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be [tex]76.1^{\circ}[/tex]. He plans to use the function [tex]C(F)=\frac{5}{9}(F-32)[/tex] to convert this temperature from degrees Fahrenheit to degrees Celsius. What does [tex]C(76.1)[/tex] represent?

A. The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
B. The temperature of 76.1 degrees Celsius converted to degrees Fahrenheit
C. The amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius
D. The amount of time it takes a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit

Answer :

To solve the problem, we need to understand what the function [tex]$C(F)=\frac{5}{9}(F-32)$[/tex] is used for. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

Now, let's apply this function to convert [tex]$76.1^\circ$[/tex] Fahrenheit to degrees Celsius:

1. Identify the Fahrenheit temperature:
Kareem found the high temperature to be [tex]$76.1^\circ$[/tex] Fahrenheit.

2. Use the conversion formula:
The formula to convert Fahrenheit to Celsius is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

3. Substitute [tex]$F$[/tex] with [tex]$76.1$[/tex]:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

4. Calculate the result:
- First, subtract 32 from 76.1:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Next, multiply 44.1 by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1 \approx 24.5
\][/tex]

This result, [tex]\(24.5^\circ\)[/tex], represents the temperature of [tex]$76.1^\circ$[/tex] Fahrenheit converted to degrees Celsius. Thus, [tex]$C(76.1)$[/tex] indicates the Celsius equivalent of [tex]$76.1^\circ$[/tex] Fahrenheit.

Therefore, the correct interpretation is:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.