To determine the value of [tex]\( p \)[/tex] given that 21% of the organisms have short legs, we need to employ concepts from the Hardy-Weinberg principle.
### Step-by-Step Solution:
1. Identify Given Information:
- 21% of the fly population has short legs.
- The allele for short legs is recessive, represented by [tex]\( q \)[/tex].
- [tex]\( q^2 \)[/tex] represents the proportion of the population with short legs, as these flies must have the genotype [tex]\( qq \)[/tex].
2. Convert Percentage to Decimal:
- 21% can be written as 0.21.
- Thus, [tex]\( q^2 = 0.21 \)[/tex].
3. Find [tex]\( q \)[/tex]:
- To find [tex]\( q \)[/tex], we take the square root of [tex]\( q^2 \)[/tex]:
[tex]\[
q = \sqrt{0.21} \approx 0.458257569495584
\][/tex]
4. Find [tex]\( p \)[/tex]:
- The Hardy-Weinberg principle states that [tex]\( p + q = 1 \)[/tex].
- We already have [tex]\( q \)[/tex] and now we can find [tex]\( p \)[/tex] by subtracting [tex]\( q \)[/tex] from 1:
[tex]\[
p = 1 - q \approx 1 - 0.458257569495584 = 0.5417424305044161
\][/tex]
### Conclusion:
The value of [tex]\( p \)[/tex], which is the allele frequency of the dominant long legs trait, is approximately [tex]\( 0.54 \)[/tex].
Thus, the correct answer is:
C. 0.54
