Five boys and five girls are seated around a table. How many ways can the seating be arranged to meet each condition? (Not meeting all conditions at once, one condition for one answer) a) Without restriction (literally anywhere they want)

b)If the boys and girls are in alternating order (boy, girl, boy, girl, etc.)

c)If there are 5 couples, all of whom sit together

d) If all the boys sit together and all the girls sit together.

e) If four couples sit together, but Walter and Maude do not.

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.

What is the 12th term of b(n)=-4-2(n-1)

Suppose you are going to graph the data in the table. minutes temperature (°c) 0 -2 1 1 2 3 3 4 4 5 5 -4 6 2 7 -3 what data should be represented on each axis, and what should the axis increments be? x-axis: minutes in increments of 1; y-axis: temperature in increments of 5 x-axis: temperature in increments of 5; y-axis: minutes in increments of 1 x-axis: minutes in increments of 1; y-axis: temperature in increments of 1 x-axis: temperature in increments of 1; y-axis: minutes in increments of 5