If the length of is 4 units, the area of ∆adc is square units.

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.

Solve this 364x-64x=300x and 12(x2–x–1)+13(x2–x–1)=25(x2–x–1)

Solve these problems: 1.what is the perimeter of an equilateral triangle with sides measuring 6cm? 2. a regular pentagon has sides measuring 3.2 cm. what is its perimeter? 3. a regular decagon has sides of 3.5mm . what is it’s perimeter? 4. a regular octagon has a perimeter of 64cm. what is the length of one of the sides? 5. a regular hexagon has a perimeter of 72mm . what is the length of one of the sides? 6. what is the perimeter of a rhombus with sides measuring 11m?