Agoat is tethered by a 6 metre rope to the outside corner of a shed measuring 4 metres by 5 metres in a grassy field. what area of grass can the goat graze?

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12

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 its non of them tell me..valerie took a day-trip. she drove from her house for a while and took a coffee break. after her coffee break, she continued driving. after  2  hours of driving after her coffee break, her distance from her house was  210  miles. her average speed during the whole trip was  60  miles per hour. valerie created the equation  y−210=60(x−2)  to represent this situation, where  xx  represents the time in hours from her coffee break and  yy  represents the distance in miles from her house. which graph correctly represents valerie's distance from her house after her coffee break?