Consider the following game: Roll a fair 6-sided die. You win if the result is greater than 4; otherwise, you lose. To play, you must pay $4. If you win, you get $8; if you lose, the $4 fee is forfeited. What is the expected value for the amount gained/lost

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.