Solve the geometric probability scenario that you created in the previous question. Include all appropriate geometric formulas, and when applicable, leave your answer in terms of and include all necessary calculations.

List the elements of the set in roster notation. (enter empty or ∅ for the empty set.) {x | x is a letter in the word hippopotamus}

Polygon mnopq is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image m′n′o′p′q′. the coordinates of point m are (2, 4), and the coordinates of point n are (3, 5). the slope of is .

Aplane is taking off from bangladesh headed to new york city. at the same time, a plane from new york city is headed to bangladesh is also taking off. the plane bound to new york city is traveling at 600 mph, while the plane traveling to bangladesh is traveling at 400 mph. how far from new york city will the two planes meet if the distance between new york city and bangladesh is 8,000 miles?