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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 solve the problem step by step.

We need to convert the temperature from degrees Fahrenheit to degrees Celsius using the given function: \
[tex]\[ C(F) = \frac{5}{9} \times (F - 32) \][/tex]

Here, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit, and [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.

### Step-by-Step Solution:

1. Identify the given temperature in Fahrenheit:
Kareem found the high temperature to be [tex]\( 76.1^\circ \)[/tex] Fahrenheit.

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

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

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

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

6. Divide to get the final result:
[tex]\[ C(76.1) \approx 24.5 \][/tex]

So [tex]\( C(76.1) \)[/tex] represents the temperature of [tex]\( 76.1^\circ \)[/tex] Fahrenheit converted to degrees Celsius.

Given the choices:
- the temperature of [tex]\( 76.1 \)[/tex] degrees Fahrenheit converted to degrees Celsius
- the temperature of [tex]\( 76.1 \)[/tex] degrees Celsius converted to degrees Fahrenheit
- the amount of time it takes a temperature of [tex]\( 76.1 \)[/tex] degrees Fahrenheit to be converted to [tex]\( 32 \)[/tex] degrees Celsius
- the amount of time it takes a temperature of [tex]\( 76.1 \)[/tex] degrees Celsius to be converted to [tex]\( 32 \)[/tex] degrees Fahrenheit

The correct answer is:
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.

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