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What is the "percent abundance" of the size 14d nails in this sample?

\begin{tabular}{|c|c|c|c|c|}
\hline
Nail Size & \begin{tabular}{c}
Number \\
of Nails
\end{tabular} & \begin{tabular}{c}
Abundance \\
[tex]$(\%)$[/tex]
\end{tabular} & \begin{tabular}{c}
Mass \\
[tex]$( g )$[/tex]
\end{tabular} & \begin{tabular}{c}
Weighted \\
Average [tex]$( g )$[/tex]
\end{tabular} \\
\hline
4d & 123 & & 3.65 & \multirow{2}{6}{6} \\
\hline
14d & 77 & [?] & 11.95 & \\
\hline
\end{tabular}


Sagot :

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].