"If we make a list of any four consecutive Fibonacci numbers, twice the third one minus the fourth one is always equal to the first one." Write a formal proof by strong induction. [Note: There are easier ways to prove this fact. However you must use strong induction, or you will receive zero credit]

Someone answer asap for ! the following statements are true about the coins calvin and sasha have collected. * calvin and sasha has the same amount of money. * calvin has only quarters. * sasha has dimes, nickels, and pennies * calvin has the same number of quarters as sasha has dimes. * sasha has $1.95 in coins that are not dimes. exactly how many quarters does calvin have?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

If wxyz is a square, which statements must be true?