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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 :

Sure! Let's break down the solution step by step.

The problem provides the temperature in degrees Fahrenheit and a function to convert this temperature to degrees Celsius. The function used for this conversion is:

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

where:
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius,
- [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.

We are given that the temperature in degrees Fahrenheit is [tex]\( 76.1^\circ F \)[/tex]. We need to determine what [tex]\( C(76.1) \)[/tex] represents.

Step-by-Step Solution:

1. Identify the given temperature in Fahrenheit:
[tex]\[ F = 76.1^\circ F \][/tex]

2. Plug the given temperature into the conversion formula:
[tex]\[ C(76.1) = \frac{5}{9}(76.1 - 32) \][/tex]

3. Perform the subtraction inside the parenthesis first:
[tex]\[ 76.1 - 32 = 44.1 \][/tex]

4. Calculate the value of the fraction:
[tex]\[ \frac{5}{9} \][/tex]

5. Multiply the result from step 3 by the fraction from step 4:
[tex]\[ \frac{5}{9} \times 44.1 \approx 24.5 \][/tex]

So, [tex]\( C(76.1) \approx 24.5^\circ C \)[/tex].

As a result, [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ F \)[/tex] converted to degrees Celsius, which is approximately [tex]\( 24.5^\circ C \)[/tex].

Therefore, the correct answer is:

the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

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