I NEED HELP PLEASE! ITS DUE TOMORROW!! THANKS! James and Katie play a board game online which uses two dice to move around the board. Katie doesn’t have two dice, so uses a 12-sided spinner instead. The rules say that each player moves along the board the number of spaces shown on the two dice together. For example, throwing a 3 and a 6 means the player can move 9 spaces. An extra go is awarded each time the player rolls a double-six – James and Katie agree that Katie earns her extra ‘roll’ if she spins a ‘12’.After playing several games, James claims that Katie must be cheating because she gets many more extra ‘rolls’ than him on every game.
• Try to decide whether James is right. Must Katie be cheating, or is there some other explanation for her luck?
• Use probability to explain why this problem has arisen
• Try to devise a fairer way to play the game.

Katie is not cheating. From the question, it sounds like Katie's spinner is 1-12. James has two dice so he has two sets of each number 1-6. This means that Katie can roll two numbers greater than six but James can only roll up to six. Using probability, I think there is a 50% chance that Katie's number will be bigger than James every time she spins. A fairer way would be for them both to play with the same dice or spinner.

Step-by-step explanation:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

tangent

step-by-step explanation: