Prove that the Goldbach conjecture that every even integer greater than 2 is the sum of two primes is equivalent to the statement that every integer greater than 5 is the sum of three primes.

Graph y ≥ -x^2 - 1. click on the graph until the correct graph appears.

What is the circumference of the pie

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?