otto has some whipping cream that is 30% butterfat and some milk that is 2% butterfat. he wants to make 500 mL mixture of them that is 12% butterfat heres a graph that shows a system of equations for this senario where x is the volume of whipping cream he uses and y is the volume of milk he uses what does point k represent

Ron has 8 caps and 4 of his caps are blue. thes rest of his cap are red. how many of ron's caps are red

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.

If the line in the graph is shifted up two units which is the equation of the new line