High School

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 [tex]6.1^\circ[/tex] Fahrenheit.
B. The temperature of [tex]76.1^\circ[/tex] Fahrenheit converted to degrees Celsius.

Answer :

To determine what [tex]\( C(76.1) \)[/tex] represents, we need to use the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] to convert a given temperature from Fahrenheit to Celsius.

In this case, [tex]\( F = 76.1 \)[/tex] degrees Fahrenheit is the temperature that Kareem found. By plugging [tex]\( 76.1 \)[/tex] into the function, we can find the equivalent temperature in degrees Celsius.

### Step-by-Step Calculation:

1. Start with the given function:
[tex]\[
C(F) = \frac{5}{9}(F - 32)
\][/tex]

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

3. Calculate inside the parentheses first:
[tex]\[
76.1 - 32 = 44.1
\][/tex]

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

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

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