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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 32 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 solve the question, we need to understand what the function [tex]\( C(A) = \frac{5}{9}(F - 32) \)[/tex] is doing. This function is used to convert temperatures from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).

In the problem, we are asked specifically about [tex]\( C(76.1) \)[/tex]. This means that we're supposed to convert 76.1 degrees Fahrenheit to degrees Celsius using the given formula.

Let's break it down step by step:

1. Identify Fahrenheit Temperature: The temperature given in Fahrenheit is 76.1 degrees.

2. Apply the Conversion Formula:
- The formula to convert Fahrenheit to Celsius is [tex]\( C = \frac{5}{9}(F - 32) \)[/tex].
- Substitute [tex]\( F = 76.1 \)[/tex] into the formula:
[tex]\[
C = \frac{5}{9}(76.1 - 32)
\][/tex]

3. Calculate the Difference:
- First, calculate the difference inside the parentheses: [tex]\( 76.1 - 32 = 44.1 \)[/tex].

4. Multiply by [tex]\(\frac{5}{9}\)[/tex]:
- Next, multiply 44.1 by [tex]\(\frac{5}{9}\)[/tex]:

[tex]\[
C = \frac{5}{9} \times 44.1 \approx 24.5
\][/tex]

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

So, the correct answer is:
- the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

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