Tisha and her academic team are working to go to state finals. they must have a certain number of points to advance. they have had three local matches and will attend a district match. district match points count for three times the number of points than local matches do. choose the equation that would tisha find how many points they need to earn in the district match, b, to advance.

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.

What are the measures of angles a, b, and c? show your work and explain your answers. 25 points

Atown has a population of 12000 and grows at 3.5% every year. what will be the population after 7 years, to the nearest whole number?