To determine the total number of miles walked by the person in two days, we first need to add the distances walked on Thursday and Friday.
1. Distance walked on Thursday: [tex]\(\frac{2}{3}\)[/tex] mile
2. Distance walked on Friday: [tex]\(\frac{5}{7}\)[/tex] mile
We start by converting each fraction into a decimal to facilitate addition:
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
[tex]\[
\frac{5}{7} \approx 0.7142857142857143
\][/tex]
Next, we add these decimal values to find the total distance:
[tex]\[
0.6666666666666666 + 0.7142857142857143 \approx 1.380952380952381
\][/tex]
To return to fraction form and simplify, we recognize that [tex]\(1.380952380952381\)[/tex] can be written as:
[tex]\[
1 \frac{380952380952381}{1000000000000000}
\][/tex]
Which is better simplified to the fraction [tex]\( \frac{29}{21} \)[/tex].
We should convert [tex]\( \frac{29}{21} \)[/tex] to a mixed number:
[tex]\[
\frac{29}{21} = 1 \frac{8}{21}
\][/tex]
Therefore, the total number of miles the person walked the dog is:
[tex]\[
\boxed{1 \frac{8}{21}}
\][/tex]
Hence, the correct answer is option D: [tex]\(1 \frac{8}{21}\)[/tex].
