To determine the "percent abundance" of the size 14d nails in the given sample, follow these steps:
1. Identify the total number of nails in the sample:
We have two sizes of nails:
- 4d nails: 123
- 14d nails: 77
2. Calculate the total number of nails:
[tex]\[
\text{Total number of nails} = 123 \, (\text{4d nails}) + 77 \, (\text{14d nails}) = 200 \, (\text{nails})
\][/tex]
3. Identify the number of 14d nails:
- Number of 14d nails: 77
4. Calculate the percent abundance of the 14d nails:
[tex]\[
\text{Percent abundance of 14d nails} = \left( \frac{\text{Number of 14d nails}}{\text{Total number of nails}} \right) \times 100
\][/tex]
Substitute the known values into the formula:
[tex]\[
\text{Percent abundance of 14d nails} = \left( \frac{77}{200} \right) \times 100
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{77}{200} = 0.385
\][/tex]
6. Multiply by 100 to convert to a percentage:
[tex]\[
0.385 \times 100 = 38.5\%
\][/tex]
Therefore, the percent abundance of the size 14d nails in the sample is [tex]\( 38.5\% \)[/tex].
