Suppose that ci has an associated frequency fi for all 1 ≤ i ≤ 4, and that for this specific character set, f1 ≥ f2 ≥ f3 ≥ f4. you find that the resulting encodings for each character is of length 2. find the maximum possible value of f1. prove your answer by showing that it is both feasible and maximal.

In trapezoid efgh, m∠hef=(4x2+16)∘ and m∠gfe=(5x2+12)∘. find the value of x so that efgh is isosceles.

The table shows the number of students who signed up for different after school activities. activity students cooking 9 chess 4 photography 8 robotics 11 select the true statements about the information in the table.

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.