Given 12 consecutive integers, how many ways can three of these integers be selected to give a sum which divides by 4. Disclaimer: A lot of points to be given, Full explanation required. Not only answer. Remember the sum of the number must be divisible by 4. I think modular arithmetic is the way to solve it, but who knows???

Which region represents the solution to the given system of inequalities? |-0.5x+y23 | 1.5x+ys-1 5 4 -3 -2 -1 1 2 3 4

The price of a dozen eggs was $1.63. suppose the price increases m dollars per dozen and then the price decreases $0.12 per dozen. which expression represents the current price of eggs after the two price changes?

(05.03 mc) part a: explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) part b: make tables to find the solution to 4x = 2x−2. take the integer values of x between −3 and 3. (4 points) part c: how can you solve the equation 4x = 2x−2 graphically? (2 points)