Final answer:
Nation Mobile is the only company that maintains a constant rate, hence has a proportional relationship between the number of minutes and the monthly cost.
Step-by-step explanation:
To determine which company or companies have a proportional relationship between the number of minutes and the monthly cost, we must look at the rates provided by each company for different amounts of minutes. A proportional relationship exists when the rate or ratio between two quantities is constant. We can calculate this by dividing the cost by the number of minutes for each plan.
- Mobile Plus: $20/100, $30/200, $40/500, $50/1200.
- Cellular Prime: $10/100, $20/200, $50/500, $60/1200.
- Nation Mobile: $5/100, $10/200, $25/500, $60/1200.
By examining these calculations, we can determine if the ratios remain consistent for each company:
- Mobile Plus: $0.20, $0.15, $0.08, $0.04167.
- Cellular Prime: $0.10, $0.10, $0.10, $0.05.
- Nation Mobile: $0.05, $0.05, $0.05, $0.05.
Based on the computed rates, only Nation Mobile maintains a constant rate throughout all the minute brackets, indicating a proportional relationship between the number of minutes and the cost.
Therefore, the answer to the question is: B. Nation Mobile only.