Suppose there are n people in a group, each aware of a scandal no one else in the group knows about. these people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. for example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals. the gossip problem asks for g(n), the minimum number of telephone calls that are needed for all n people to learn about all the scandals. use mathematical induction to prove that g(n)< =2n-4 forn> =4.[hint: in the inductive step, have a new person call a particularperson at the start and at the end.]

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?

If you are trying to move an attached term across the equal sign (=), what operation would you use to move it?

Boris needs to buy plastic spoons. brand a has a box 42 spoons for $2.37. brand b has a box of 72 spoons for $3.57. find the unit price for each brand. then state which brand is the better buy based on the unit price. round your answer to the nearest cent.