Sure, let's solve the problem step-by-step.
1. Determine the length of an average man:
- Given that the length of an average blue whale is 100 feet.
- The average man is [tex]\(\frac{1}{17}\)[/tex] the length of a blue whale.
[tex]\[
\text{Length of an average man} = 100 \text{ feet} \times \frac{1}{17} = \frac{100}{17} \text{ feet} \approx 5.88235294117647 \text{ feet}
\][/tex]
2. Determine the length of an average human baby:
- The length of a human baby is [tex]\(\frac{1}{4}\)[/tex] of the length of an average man.
[tex]\[
\text{Length of an average human baby} = \left(\frac{100}{17}\right) \times \frac{1}{4} = \frac{100}{68} = \frac{50}{34} = \frac{25}{17} \text{ feet} \approx 1.4705882352941175 \text{ feet}
\][/tex]
3. Compare this result with the given options:
- The given options are:
1. [tex]\(1 \frac{8}{17}\)[/tex] feet
2. [tex]\(2 \frac{3}{5}\)[/tex] feet
3. [tex]\(2 \frac{5}{17}\)[/tex] feet
4. [tex]\(2 \frac{5}{21}\)[/tex] feet
Let's convert the mixed numbers into improper fractions for comparison, if necessary:
- [tex]\(1 \frac{8}{17} = \frac{17 + 8}{17} = \frac{25}{17}\)[/tex]
- [tex]\(2 \frac{3}{5} = 2 + \frac{3}{5} = \frac{10}{5} + \frac{3}{5} = \frac{13}{5}\)[/tex]
- [tex]\(2 \frac{5}{17} = 2 + \frac{5}{17} = \frac{34}{17} + \frac{5}{17} = \frac{39}{17}\)[/tex]
- [tex]\(2 \frac{5}{21} = 2 + \frac{5}{21} = \frac{42}{21} + \frac{5}{21} = \frac{47}{21}\)[/tex]
Since the length of an average human baby is [tex]\(\frac{25}{17}\)[/tex] feet, the correct option is [tex]\(1 \frac{8}{17}\)[/tex] feet.
Thus, the answer is:
[tex]\[ 1 \frac{8}{17} \text{ feet} \][/tex]
