To determine which product represents a [tex]$6 \frac{3}{4} \%$[/tex] tax on a price of [tex]$14.29, we'll convert the percent to a decimal and then compute the tax.
1. Convert $[/tex]6 \frac{3}{4} \%[tex]$ to a decimal:
- First, convert the mixed number to an improper fraction:
\[
6 \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}
\]
- To convert to a percentage, divide by 100:
\[
\frac{27}{4} \% = \frac{27}{4 \times 100} = \frac{27}{400} = 0.0675
\]
2. Calculate the tax:
- Multiply the price, $[/tex]14.29, by the decimal equivalent of the percentage:
[tex]\[
0.0675 \times 14.29
\][/tex]
3. Compare the products:
- Option a: [tex]\(0.00675 \times 14.29\)[/tex]
- Option b: [tex]\(0.0675 \times 14.29\)[/tex]
- Option c: [tex]\(0.675 \times 14.29\)[/tex]
- Option d: [tex]\(6.75 \times 14.29\)[/tex]
Since the tax is calculated as:
[tex]\[
0.0675 \times 14.29,
\][/tex]
the correct product is given by Option b.
Therefore, the best answer is:
B
