Let bin(n) denote the binary representation of n > 0, leading zeros omitted. For example, bin(0) = 0, bin(5) = 101, and bin(12) = 1100. (a) Show that the language {bin(n)#bin(n+1)} is not a context-free language
(b) Suppose we reverse the first numeral; that is, consider the language {bin(n)"#bin(n+1)}
Show that this language is context-free.

You eat $0.85 for every cup of hot chocolate you sell. how many cups do you need to sell to earn $55.25

Which has the greater energy, light of wavelength 519 nm or light with a frequency of 5.42 x 10^8 sec^-1?

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.