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][tex]$C(76.1)$[/tex][/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.

To determine what [tex]$ C(76.1) $[/tex] represents, let's look at the function [tex]$ C(F) = \frac{5}{9}(F - 32) $[/tex]. This function is used to convert a temperature from degrees Fahrenheit ([tex]$ F $[/tex]) to degrees Celsius ([tex]$ C $[/tex]).

In this problem, Kareem is trying to convert a temperature of 76.1 degrees Fahrenheit into degrees Celsius.

Here's a breakdown of the steps involved:

1. Identify the given Fahrenheit temperature: 76.1 degrees Fahrenheit.
2. Use the conversion formula for Fahrenheit to Celsius:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]
Substitute 76.1 for [tex]$ F $[/tex] in the formula:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]
3. Perform the arithmetic operation:
- Calculate [tex]$ 76.1 - 32 $[/tex]:
[tex]\[
76.1 - 32 = 44.1
\][/tex]
- Now, substitute 44.1 back into the formula:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]
- Calculate [tex]$ \frac{5}{9} \times 44.1 $[/tex]:
[tex]\[
\frac{5}{9} \times 44.1 \approx 24.5
\][/tex]

Thus, [tex]$ C(76.1) $[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to approximately 24.5 degrees Celsius. Therefore, the correct interpretation is:

The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.