To determine the average cat's temperature in Fahrenheit, we will use the given temperature in Celsius and convert it using the provided formula.
The given normal body temperature of an average cat is [tex]\( 38.6^{\circ} \)[/tex] Celsius.
We start with the formula that converts Celsius (C) to Fahrenheit (F):
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
Since we need to find the temperature in Fahrenheit, we can rearrange the formula to solve for [tex]\( F \)[/tex]:
[tex]\[
F = \left(\frac{9}{5}C\right) + 32
\][/tex]
Now, we substitute [tex]\( C = 38.6 \)[/tex] into the rearranged formula:
[tex]\[
F = \left(\frac{9}{5} \times 38.6\right) + 32
\][/tex]
Simplifying the calculation step-by-step:
1. First, multiply [tex]\( 38.6 \)[/tex] by [tex]\( \frac{9}{5} \)[/tex]:
[tex]\[
38.6 \times \frac{9}{5} = 38.6 \times 1.8 = 69.48
\][/tex]
2. Next, add 32 to the result:
[tex]\[
69.48 + 32 = 101.48
\][/tex]
Thus, the average cat's temperature in Fahrenheit is:
[tex]\[
101.48^{\circ} \text{ Fahrenheit}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{101.48^{\circ} \text{ Fahrenheit}}
\][/tex]
