Let cn be the number of binary strings of length n in which every block of consecutive os or 1s has odd length. for example, if n = 3 the allowed strings are 000, 111, 010, 101 and for n = 4 we have 0001, 1110, 0101, 1010, 0111, 1000. find (and prove) a formula for cn in terms of the fibonacci numbers fn. for the fibonacci numbers, use the indexing fi = 1, f2 = 1.

Miguel’s teacher asks him to color 4/8 of his grid. he must use 3 colors: red, blue, and green. there must be more green sections than red sections. how can miguel color all the sections of his grid to follow all the rules

In a survey of 1015 adults, a polling agency asked, "when you retire, do you think you will have enough money to live comfortably or not. of the 1015 surveyed, 534 stated that they were worried about having enough money to live comfortably in retirement. construct a 90% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.

Rick is driving to his uncles house in greenville, which is 120 miles from ricks town .after covering x miles rick she's a sign stating that greensville is 20 miles away. which equation when solved will give the value of x. a: x+120 = 20 b: x x120 =20 c: x +20 equals 120 d: x x20= 120