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 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 use the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] to convert a temperature from degrees Fahrenheit to degrees Celsius.

Here's how you can understand this step-by-step:

1. Identify the Given Information:
- The temperature in Fahrenheit that Kareem recorded is [tex]\( 76.1^{\circ}F \)[/tex].

2. Use the Conversion Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] helps convert Fahrenheit to Celsius.
- Substitute [tex]\( F = 76.1 \)[/tex] into the function to find the corresponding Celsius temperature.

3. Substitute and Simplify:
- Start by substituting [tex]\( F = 76.1 \)[/tex] into the equation.
- You will calculate [tex]\( C(76.1) = \frac{5}{9}(76.1 - 32) \)[/tex].
- First, calculate [tex]\( 76.1 - 32 = 44.1 \)[/tex].
- Then, compute [tex]\( \frac{5}{9} \times 44.1 = 24.5 \)[/tex].

4. Interpret the Result:
- The value [tex]\( C(76.1) = 24.5 \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

Therefore, the correct interpretation is that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.