College

On his first day of school, Kareem found the high temperature to be [tex]76.1^{\circ}[/tex] Fahrenheit. 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 2 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 understand what [tex]\( C(76.1) \)[/tex] represents, we need to look at the function [tex]\( C(R) = \frac{5}{9}(F - 32) \)[/tex], which is used to convert a temperature from degrees Fahrenheit to degrees Celsius.

### Step-by-Step Solution:

1. Identify the Meaning of [tex]\( C(R) \)[/tex]:
- The function [tex]\( C(R) \)[/tex] takes a Fahrenheit temperature, subtracts 32, multiplies the result by [tex]\(\frac{5}{9}\)[/tex], and gives us the equivalent temperature in Celsius.

2. Apply the Function to the Given Temperature:
- You're given a temperature [tex]\( F = 76.1 \)[/tex] degrees Fahrenheit, which you want to convert to Celsius.
- Replace [tex]\( F \)[/tex] in the function with 76.1:

[tex]\[
C(76.1) = \frac{5}{9}(76.1 - 32)
\][/tex]

3. Perform the Calculation:
- Subtract 32 from 76.1:

[tex]\[
76.1 - 32 = 44.1
\][/tex]

- Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:

[tex]\[
C(76.1) = \frac{5}{9} \times 44.1
\][/tex]

- The calculation results in approximately 24.5 degrees Celsius.

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

So, the correct interpretation is: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.