answer:Stacy assigns x problems for homework. There are twice as many multiple choice problems as free response, so the number of multiple choice problems is 2 times the number of free response problems. There are 7 more free response problems than true/false, so the number of free response problems is 7 more than the number of true/false problems. The total number of problems is the sum of the number of true/false, free response, and multiple choice problems: true/false + free response + multiple choice = x. We are given that the number of true/false questions is 6, so we can write: 6 + (6 + 7) + 2(6 + 7) = x. Simplifying the right side, we get: 6 + 13 + 2(13) = x. Simplifying further, we get: 6 + 13 + 26 = x. Adding the numbers, we get: 45 = x. The value of x is 45. 45 The answer is: 45

answer:Let the common ratio of the geometric sequence be r. Then the second term is 3r, the third term is 3r^2, and the fourth term is 3r^3. We are given that the fourth term is 192, so 3r^3 = 192. Simplifying, we have r^3 = 64. Taking the cube root of both sides, we find that r = 4. Therefore, the third term of the sequence is 3r^2 = 3(4^2) = 3(16) = boxed{48}. The answer is: 48

answer:We begin by factoring out an x from the left-hand side of the equation, so 5x(x+2y)=x^2(x+2y). We can then divide both sides of the equation by x(x+2y) (since x and x+2y are both positive, we know that x(x+2y) is not zero), giving 5=x.The answer is: 5

answer:Carter goes through 5 sets of drum sticks per show and he performs for 30 nights straight, so he goes through 5 * 30 = <<5*30=150>>150 sets of drum sticks. After each show, he tosses 6 new drum stick sets to audience members, so he gives away an additional 6 * 30 = <<6*30=180>>180 sets of drum sticks. Therefore, he goes through a total of 150 + 180 = <<150+180=330>>330 sets of drum sticks. 330 The answer is: 330