College

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 for a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius

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

Answer :

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

In this specific situation, Kareem has the temperature [tex]\( 76.1^\circ \)[/tex] Fahrenheit, and he wants to convert it to degrees Celsius. Here's the step-by-step breakdown:

1. Identify the function: We're using the conversion function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

2. Substitute the Fahrenheit temperature: We need to plug in [tex]\( F = 76.1 \)[/tex] into the function. So, we calculate [tex]\( C(76.1) \)[/tex].

3. Execute the conversion:
[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

4. Simplify the expression:
[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]

5. Perform the multiplication:
[tex]\[
C(76.1) \approx 24.5
\][/tex]

Thus, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to approximately 24.5 degrees Celsius.

The first option is correct: "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius."