5of 5 [chapter 2] a system composed of two industries, coal and steel, has the following inputs: (a) to produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.60 of steel. (b) to produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. [10,000] find d, the input-output matrix for this system. then solve for the output matrix x in the equation x = dx + e where the external demand is e- (16,000 round all entries of the matrix to two decimal places, where applicable. o 10.30 0.10], [20,000] d=0.60 0.30]* * *40,000 50.30 0.607,540,000 d-030 0.10 - 20,000 50.60 0.30), 530,000] d-10.10 0.30142 10.60 0.307 y 27 d- 0.30 0.10 * 30,000 0

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)