Use the left and right riemann sums with 100 rectangles to estimate the (signed) area under the curve of y=−4x+2y=−4x+2 on the interval [0,50][0,50]. write your answer using the sigma notation.

You and three friends will be going out to eat at your favorite restaurant! each of you will order three items of your choice. you will also need to leave a tip. if you split the bill evenly among all four of you, how much will each person need to contribute? locate a menu for your favorite restaurant and pick three items for yourself and each friend. list the restaurant name, items, and prices in a table like the one below. in the column labeled subtotal, determine the cost of each person’s order. the customary tip is 20% of the total bill. in the column labeled tip, calculate the amount of tip each person should leave. in the column labeled total bill, determine the total of each person’s order, including the tip. restaurant name: names item 1 price item 2 price item 3 price subtotal tip total bill your name friend #1 friend #2 friend #3 part 2: questions answer the following questions, showing all work: what is the total cost of the entire bill (all four meals), including tip? write an expression using fractions to show how to determine the amount that each person will pay. then calculate each person's contributions showing all steps in long division. if each person paid an equal amount, who would save the most money? explain your reasoning using at least two complete sentences.

Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory? 15, 20, 5, 10

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3