To determine the scale factor between Horatio's and Kelli's circles, we start by noting the given radii:
- Horatio's radius: [tex]\( 6 \, \text{cm} \)[/tex]
- Kelli's radius: [tex]\( 18 \, \text{ym} \)[/tex]
For simplicity, we'll assume the units [tex]\( \text{ym} \)[/tex] and [tex]\( \text{cm} \)[/tex] are directly comparable. Therefore, we consider Kelli's radius as [tex]\( 18 \, \text{cm} \)[/tex] as well.
The scale factor between two circles is determined by the ratio of their radii. We will compute the scale factor by dividing Horatio's radius by Kelli's radius:
[tex]\[ \text{Scale factor} = \frac{\text{Horatio's radius}}{\text{Kelli's radius}} = \frac{6 \, \text{cm}}{18 \, \text{cm}} \][/tex]
Now simplify the fraction:
[tex]\[ \text{Scale factor} = \frac{6}{18} = \frac{1}{3} \][/tex]
Thus, the scale factor between the two circles is:
[tex]\[ \boxed{\frac{1}{3}} \][/tex]
