To determine the tax amount, let's break down the given problem step by step:
1. Convert the fractional percentage to a decimal:
- We are given a tax rate of [tex]\(6 \frac{3}{4}\%\)[/tex].
- Convert the mixed number into an improper fraction:
[tex]\(6 \frac{3}{4} = 6 + \frac{3}{4} = \frac{24}{4} + \frac{3}{4} = \frac{27}{4}\)[/tex].
- Convert this fraction into a decimal:
[tex]\(\frac{27}{4} = 6.75\)[/tex].
2. Express the percentage as a decimal for calculation:
- To use the percentage in calculations, convert [tex]\(6.75\%\)[/tex] to a decimal:
[tex]\(6.75\% = \frac{6.75}{100} = 0.0675\)[/tex].
3. Calculate the tax amount:
- The original amount is [tex]\(\$2305\)[/tex].
- The tax amount is calculated as:
[tex]\[
\text{Tax amount} = 0.0675 \times 2305
\][/tex]
4. Perform the multiplication:
- Multiplying [tex]\(0.0675\)[/tex] by [tex]\(2305\)[/tex] gives:
[tex]\[
0.0675 \times 2305 = 155.5875
\][/tex]
5. Match the calculated tax amount with the closest choice:
- The calculated tax amount is \[tex]$155.5875.
- The choices provided are:
\[
\text{a. } \$[/tex]15.56\quad \text{b. } \[tex]$145.22\quad \text{c. } \$[/tex]146.14\quad \text{d. } \[tex]$155.59
\]
- Out of these choices, the closest to \$[/tex]155.5875 is \[tex]$155.59.
Therefore, the best answer from the choices provided is:
\[
\boxed{d. \$[/tex]155.59}
\]
