To determine where Genevieve should cut the ribbon, we'll follow the given formula and the described situation step by step.
### Step-by-Step Solution
1. Understand the Problem:
Genevieve needs to cut a 60-inch piece of ribbon into segments with a ratio of [tex]\( 2:3 \)[/tex]. There is 2 inches of frayed ribbon which she won't use, starting to measure from the 2-inch mark.
2. Given Values:
- Total length of the ribbon: 60 inches
- Ratio values: [tex]\( m = 2 \)[/tex], [tex]\( n = 3 \)[/tex]
- Starting point: [tex]\( x_1 = 2 \)[/tex] inches from one end (the part of the ribbon that is frayed)
3. Calculate the Total Ratio Parts:
The total ratio parts [tex]\( m + n = 2 + 3 = 5 \)[/tex].
4. Calculate the Effective Ribbon Length:
Since the first 2 inches are frayed and can't be used, we work with the remaining:
[tex]\[
x_2 - x_1 = 60 - 2 = 58 \text{ inches}
\][/tex]
5. Calculate the Fraction of the Ribbon for Segment [tex]\( m \)[/tex]:
The fraction of the ribbon for segment [tex]\( m \)[/tex] is:
[tex]\[
\frac{m}{m+n} = \frac{2}{5} = 0.4
\][/tex]
6. Find the Location of the Cut:
Use the formula [tex]\( x = \left(\frac{m}{m+n}\right) \left(x_2 - x_1\right) + x_1 \)[/tex]:
\begin{align}
x &= \left(0.4 \right) \left( 58 \right) + 2 \\
&= 23.2 + 2 \\
&= 25.2
\end{align}
So, the location of the cut is at [tex]\( 25.2 \)[/tex] inches.
### Final Answer:
Genevieve should make the cut at 25.2 inches, rounded to the nearest tenth.
Therefore, the correct option is:
[tex]\[ \boxed{25.2 \text{ in}} \][/tex]
