Find 3 ratios that are equivalent to the given ratio. 9:13 ​

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.

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

Select the correct answer. given: ∆abc with prove: statement reason 1. given 2. ∠cab ≅ ∠edb ∠acb ≅ ∠deb if two parallel lines are cut by a transversal, the corresponding angles are congruent. 3. ∆abc ~ ∆dbe aa criterion for similarity 4. corresponding sides of similar triangles are proportional. 5. ab = ad + db cb = ce + eb segment addition 6. substitution property of equality 7. division 8. subtraction property of equality what is the missing statement in the proof? scroll down to see the entire proof.