4. Let x, y and z be integers between 0 and 9. How many ways can x, y, z be chosen such that xyz is odd?
5. What conditions on n, k need to hold so that n(n −1) ···(n −k + 1) =n!
(n−k)!is a true statement? Write this as a theorem and prove it.
6. Calculate ∫∞0xne−xdx for n = 0, 1, 2, 3, 4 (start with n = 0, and then
do integration by parts for n = 1 etc.) Give a formula for this integral
for n an arbitrary nonnegative integer. (You do NOT need to prove
this, just give a formula.)

75

step-by-step explanation:

stop cheating

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2