Mrs. gustafsson's english class is taking an exam that is made up of short-response questions and essay questions. there are 22 questions that are worth 100 points in total. each short-response question is worth 4 points, and each essay question is worth 10 points. how many short-response question are on the exam?

Abox contains 1 plain pencil and 4 pens. a second box contains 5 color pencils and 5 crayons. one item from each box is chosen at random. what is the probability that a plain pencil from the first box and a color pencil from the second box are selected? write your answer as a fraction in simplest form.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Look at arnold's attempt to solve the equation for b: 3b = 12 b = 3 · 12 b = 36 describe the mistake that arnold made.