A superhero is rendered powerless when exposed to 60 or more grams of a certain element. A 650 year old rock that originally contained 600 grams of this element was recently stolen from a rock museum by the superhero's nemesis. The half-life of the element is known to be 200 years.
a) How many grams of the element are still contained in the stolen rock?
b) For how many years can this rock be used by the superhero's nemesis to render the superhero powerless?

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Part a what is the area of triangle i? show your calculation. part b triangles i and ii are congruent (of the same size and shape). what is the total area of triangles i and ii? show your calculation. part c what is the area of rectangle i? show your calculation. part d what is the area of rectangle ii? show your calculation. part e rectangles i and iii have the same size and shape. what is the total area of rectangles i and iii? show your calculation. part f what is the total area of all the rectangles? show your calculation. part g what areas do you need to know to find the surface area of the prism? part h what is the surface area of the prism? show your calculation. part i read this statement: “if you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” is this statement true or false? why? part j read this statement: “if you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” is this statement true or false? why?

The angle of depression from the top of the tree to the tip of the shadow is 25°. find the height of the tree to the nearest tenth. a. 16.8 feet b. 18.2 feet c. 23.4 feet d. 39.7 feet