
Calculate Tax/Sales:
Machinery: \( \frac{5,001}{67,005} \approx 0.0746 \)
Electricity: \( \frac{2,394}{82,308} \approx 0.029 \)
Diversified: \( \frac{2,394}{128,125} \approx 0.0187 \)
Food: \( \frac{7,467}{98,476} \approx 0.0758 \) Order: Diversified<Electricity<Machinery<Food So rank 3 goes to: Diversified





For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: