High School

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be [tex]$76.1^{\circ}F$[/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 :

Sure! Let's solve the problem step-by-step.

### Given Information
- The temperature in degrees Fahrenheit: [tex]\( 76.1^\circ F \)[/tex]
- The formula to convert Fahrenheit to Celsius is:
[tex]\[ C(F) = \frac{5}{9} (F - 32) \][/tex]

### Steps to Solve
1. Identify the Function: The function [tex]\( C(F) = \frac{5}{9} (F - 32) \)[/tex] converts a temperature from degrees Fahrenheit (F) to degrees Celsius (C).

2. Substitute the Temperature: Substitute [tex]\( 76.1^\circ F \)[/tex] into the function [tex]\( C(F) \)[/tex].
[tex]\[ C(76.1) = \frac{5}{9} (76.1 - 32) \][/tex]

3. Perform the Subtraction: Subtract 32 from 76.1.
[tex]\[ 76.1 - 32 = 44.1 \][/tex]

4. Multiplication and Division: Now, multiply the result by [tex]\(\frac{5}{9}\)[/tex].
[tex]\[ C(76.1) = \frac{5}{9} \times 44.1 \][/tex]

5. Simplify: Perform the arithmetic operation.
[tex]\[ C(76.1) = \frac{5 \times 44.1}{9} = \frac{220.5}{9} = 24.5 \][/tex]

### Conclusion
The value of [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. The final temperature in degrees Celsius is approximately [tex]\( 24.5^\circ C \)[/tex].

So, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius. This matches the first choice provided.

Answer: The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.