Kate drew a 33×33 checkered square (lattice) on the asphalt with white chalk (i. e. there are 34 horizontal segments and 34 vertical segments drawn). By one move it is allowed to pick out an arbitrary square (of any size) and repaint its boundary using chalk of blue color. In different moves, it is allowed to repaint any segment more than once. What is the smallest number of such moves required to repaint all the initial lines in blue color?

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.