Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the probability that the length $DG$ is less than or equal to $1.$

Part of the total score for each program is the sum of five program component scores. on the free program, the sum of these five program component scores is multiplied by a factor of 2.0. yuzuru hanyu, of japan, earned scores of 9.07, 8.96, 8.89, 9.21, and 9.36 for the program components portion of his free program. how many total points did he receive for this portion?

To find the extreme values of a function f(x. y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x, y)=xy

Mexico city, mexico, is the world's second largest metropolis and is also one of its fastest-growing cities with a projected growth rate of 3.2% per year. its population in 1991 was 20,899,000 people. use the formula p = 20.899e0.032t to predict its population p in millions with t equal to the number of years after 1991. what is the predicted population to the nearest thousand of mexico city for the year 2010?