Hannah and Mason are playing a game where they roll 6-sided dice, and then they remove all the dice showing a 1. Then they roll the remaining dice and remove all the dice showing a 1 again, and so on.
Hannah and Mason started with 42 dice. According to the law of probability, find an explicit formula for the number of dice remaining after rounds of the game.
How many rounds does it take to remove roughly of the dice?
Two cars are bought at the same time. One of them costs and depreciates at each year. If the second car costs , at what rate does it depreciate if they have the same value after 5 years? Give your answer to one decimal place.
Two vehicles are bought in the same year. One car costs $27 000 and depreciates at a rate of per year. The second car is more expensive but depreciates faster, at per year. How much must this car cost if the two have exactly the same value after 4 years? Give your answer to the nearest dollar.