In which type of triangle is the orthocenter on the perimeter of the triangle?

a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle

If there is 20 dogs in the shelter and 5 dogs get homes, and then 43 more dogs come. how many dogs are there in the shelter?

Complete each sentence with the correct form of the verb ser or estar to say where the following people are from or where they are right now claudia y maria en méxico

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.