In a group of 25 students at lunch, 10 prefer ketchup on their hamburger, 12 prefer mustard on their hamburger, and 5 like both ketchup and
mustard on their hamburger. The rest of the students in the group prefer
neither. CREATE A VENN DIAGRAM to find the probability that a student
selected from this group will prefer ketchup or mustard on their
hamburger.

Emma will roll two number cubes labeled 1 through 6. she will record the sum of the two numbers after each roll. she will roll the two cubes 540 times. how many times should emma expect the sum to equal 5?

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.

Which inequality comparing two of the expressions is true when 0.7 < x < 0.9