Final answer:
1. The remaining length (L) of a rope is proportional to the amount cut off. 2. The total cost (T) after sales tax is proportional to the item's price (p). 3. The number of marbles each sister gets (x) when shared equally is proportional to the total number of marbles (m). 4. The volume (v) of a rectangular prism is proportional to the square of its side length (s).
Step-by-step explanation:
1. The remaining length (L) of 120-inch per rope after X inches have been cut off can be represented by the equation 120 - X = L. This equation is proportional because as more inches are cut off (increase in X), the remaining length of the rope (L) decreases.
2. The total cost (T) after 8% sales tax is added to an item's price (p) can be represented by the equation 1.08p = T. This equation is proportional because as the item's price (p) increases, the total cost (T) also increases.
3. The number of marbles each sister gets (x) when m marbles are shared equally among four sisters can be represented by the equation x = m/4. This equation is proportional because as the number of marbles (m) increases, each sister gets a larger share (x) of the marbles.
4. The volume (v) of a rectangular prism with a height of 12 cm and a base that is a square with side lengths (s) cm can be represented by the equation v = 12s^2. This equation is proportional because as the side length (s) increases, the volume (v) of the prism also increases.