answer:First, we need to find g(5). Plugging x=5 into g(x)=2x-1, we get g(5)=2(5)-1=9. Next, we need to find f(g(5)). Plugging x=9 into f(x)=x^2+1, we get f(g(5))=(9)^2+1=boxed{82}. The answer is: 82

answer:First, we find the critical points by setting the numerator and denominator equal to zero: [x = 0 quad text{and} quad x + 3 = 0 Rightarrow x = -3.] Next, we test the intervals created by these critical points. When x < -3, both the numerator and denominator are negative, so the fraction is positive. When -3 < x < 0, the numerator is negative and the denominator is positive, so the fraction is negative. When x > 0, both the numerator and denominator are positive, so the fraction is positive. Therefore, the solution to the inequality is x in boxed{(-infty, -3) cup [0, infty)}. The answer is: (-infty,-3)cup[0,infty)

answer:We can rewrite each fraction as frac{1}{n(n+1)}. So the sum becomes frac{1}{1times2} + frac{1}{2times3} + frac{1}{3times4} + frac{1}{4times5} + frac{1}{5times6} = frac{1}{1times2} + frac{1}{2times3} + frac{1}{3times4} + frac{1}{4times5} + frac{1}{5times6} = frac{1}{1} - frac{1}{2} + frac{1}{2} - frac{1}{3} + frac{1}{3} - frac{1}{4} + frac{1}{4} - frac{1}{5} + frac{1}{5} - frac{1}{6} = 1 - frac{1}{6} = boxed{frac{5}{6}}. The answer is: frac{5}{6}

answer:Ellen takes 5 minutes to paint one lily, so to paint 17 lilies she will need 5 * 17 = 85 minutes. She takes 7 minutes to paint one rose, so to paint 10 roses she will need 7 * 10 = 70 minutes. She takes 3 minutes to paint one orchid, so to paint 6 orchids she will need 3 * 6 = 18 minutes. She takes 2 minutes to paint one vine, so to paint 20 vines she will need 2 * 20 = 40 minutes. In total, Ellen will need 85 + 70 + 18 + 40 = 213 minutes to paint all the flowers. 213 The answer is: 213