Apolice department wants to find out if a correlation exists between x = the number of muggings per night during warmer nights in a particular park not far from downtown and y = degrees fahrenheit. this is to decide how police duties should be allocated on these nights. some data points for some nights from the spring and summer of the past year are listed below. x: {5,7,8,4,11,12,8,7} y: {79,82,83,81,86,89,91,84,} compute the coefficient of correlation r. compute the coefficient of determination r^2. what percentage of the variation in y can be explained by the corresponding variation in x using the least-squares line? what percentage of the variation is unexplained?

Simplify (1/2)4th power a. (1/16) b.(1/8) c.(1/4)

Acampus club held a bake sale as a fund raiser, selling coffee, muffins, and bacon and eggs sandwiches. the club members charged $1 for a cup of coffee, 3$ for a muffin , and $4 for a back. and egg sandwich. they sold a total of 55 items , easing $119. of the club members sold 5 more muffins than cups of coffee, how many bacon and egg sandwiches he’s did they sell

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.