Answer :
To understand what [tex]\( C(76.1) \)[/tex] represents, let's break down the function Kareem plans to use for converting temperatures from degrees Fahrenheit to degrees Celsius. The function given is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function takes a Fahrenheit temperature [tex]\( F \)[/tex] and converts it to Celsius. Kareem wants to find [tex]\( C(76.1) \)[/tex], meaning he wants to convert a Fahrenheit temperature of 76.1 degrees into Celsius.
### Step-by-step Conversion
1. Identify the Fahrenheit Temperature: We have [tex]\( F = 76.1 \)[/tex].
2. Subtract 32 from the Fahrenheit Temperature: This is the first step in the conversion formula to adjust for the Fahrenheit scale start.
[tex]\[
F - 32 = 76.1 - 32 = 44.1
\][/tex]
3. Multiply the Result by [tex]\(\frac{5}{9}\)[/tex]: This step scales the adjusted temperature from the Fahrenheit degree to the Celsius degree.
[tex]\[
C = \frac{5}{9} \times 44.1
\][/tex]
The result of this calculation is approximately 24.5 degrees Celsius. Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to Celsius. This matches with the first option:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
So, the correct answer is that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This function takes a Fahrenheit temperature [tex]\( F \)[/tex] and converts it to Celsius. Kareem wants to find [tex]\( C(76.1) \)[/tex], meaning he wants to convert a Fahrenheit temperature of 76.1 degrees into Celsius.
### Step-by-step Conversion
1. Identify the Fahrenheit Temperature: We have [tex]\( F = 76.1 \)[/tex].
2. Subtract 32 from the Fahrenheit Temperature: This is the first step in the conversion formula to adjust for the Fahrenheit scale start.
[tex]\[
F - 32 = 76.1 - 32 = 44.1
\][/tex]
3. Multiply the Result by [tex]\(\frac{5}{9}\)[/tex]: This step scales the adjusted temperature from the Fahrenheit degree to the Celsius degree.
[tex]\[
C = \frac{5}{9} \times 44.1
\][/tex]
The result of this calculation is approximately 24.5 degrees Celsius. Therefore, [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to Celsius. This matches with the first option:
- The temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.
So, the correct answer is that [tex]\( C(76.1) \)[/tex] represents the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius.