Suppose you have two disks each with 128 pie-shaped sectors. one disk has 32 red sectors and 96 white sectors. the other disk has 64 white sectors and 64 red sectors. the two patterns can be completely arbitrary. can we place one over the other such that at least 64 sectors on each disk have the same color? justify your answer using probabilistic methods and be sure to provide a sample space to support your reasoning.

Paula makes stained-glass windows and sells them to boutique stores. if her costs total $12,000 per year plus $4 per window for the frame. how many windows must she produce to earn a profit of at least $48,000 in one year if she sells the windows for $28 each? 1. define a variable for the situation. 2. write an inequality that represents her profit. note: revenue is money coming in. cost is money going out. profit is the difference between the revenue and the cost. in other words: revenue - costs profit 3.using words, describe how many windows she must sell to have a profit of at least $48,000.