Oh no! Thomas is lost in the GGBL building after an exam, and trying to get out. Thereare four identical hallways leading away from him. One of the hallways will take 12 minutesto walk and will lead him out. However the other three hallways will take 10 minutes, 10minutes, and 40 minutes respectively, to walk. At the end of those three hallways Thomasfalls through a trapdoor back to where he started. Assume the following:•Thomas can choose only one hallway at a time and cannot turn around•When Thomas falls through a trapdoor he cannot tell which hallway he chose last•The hallways are indistinguishable aside from their outcomeLetTbe a random variable for how long it will take Thomas to escape. What isE(T)?Hint:Consider three events, H1,H2,H3where Thomas chooses the escape hall, one of the10 minute halls, or the 40 minute hall, respectively. Note thatH1,H2, andH3cover allpossible cases for the first choice of hallway and do not overlap. The law of total expectationstates that:E(T) =E(T|H1)P(H1) +E(T|H2)P(H2) +E(T|H3)P(H3)

Check the explanation

Step-by-step explanation:

Since each and every one of the 4 hallways is equally likely then

Now, if he chooses H1 he escapes after 12 minutes then

If he chooses H2 then he wastes 10 minutes and then he is again in the same starting

position so he expects to escape in E(T) minutes, then

Analogously, if he chooses H3 then he wastes 40 minutes and then he is again in the same starting

position so he expects to escape in E(T) minutes, then

Therefore

So we have

Therefore he is expected to escape in 72 minutes

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

2

step-by-step explanation: