Sarah has $8 and wants to buy a mixture of cupcakes and fudge to feed at least four siblings. each cupcake costs $2, and each piece of fudge costs $1. this system of inequalities models the scenario:
2x + y ≤ 8
x + y ≥ 4
part a: describe the graph of the system of inequalities, including shading and the types of lines graphed. provide a description of the solution set. (4 points)
part b: is the point (8, 10) included in the solution area for the system? justify your answer mathematically. (3 points)
part c: choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

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)