Which of the following about the crusades is not true? (1 point)

1. the rise of the seljuk empire was the immediate cause of the crusades.
2. the concern of european christian leaders over the spread of the islamic faith was a long-term cause of the crusades.
3. the crusades were unsuccessful from the beginning, met with strong opposition from the united islamic world.
4. in the aftermath of the crusades, the nations of europe began to look inward.
10. if a frankish christian merchant traveled to the spanish city of córdoba in the 10th century, which would he or she not find? (1 point)

1. córdoba was the capital of al-andalus.
2. córdoba was a cultural center for the region.
3. córdoba's population was mainly arab.
4. córdoba was richer than any french city.

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.