CubeyThePenguin

k = probability of rolling a 1

k + 2k + 3k + 4k + 5k + 6k = 1

21k = 1

k = 1/21

probability of rolling an even number = 2/21 + 4/21 + 6/21 = 12/21 = 4/7

first prism: A_1 = Bh

second prism: A_2 = (4B)(h/2) = 2Bh

volume ratio = A_1/A_2 = 1/2

1/x + 1/y = 5

(x + y)/xy = 5

x + y = 5xy

3xy + x + y = 4

x + y = 4 - 3xy

5xy = 4 - 3xy

8xy = 4

xy = 1/2

\(x^2 y + xy^2 = (x+y)(xy) = 5(1/2)(1/2) = \boxed{5/4}\)

We can write everything in terms of x, the number of money Cathy has.

Cathy = x

Brenda = x/2

Andy = (x/2)/2 = x/4

x = x/4 + 78

3x/4 = 78

x = 104

So, Cathy has $104, Brenda has $52, and Andy has $26. In total, they have $182.

This question was asked before: https://web2.0calc.com/questions/help_12137

Let Joanne have x dollars, so Roy has x + 190 dollars.

x/3 = 25% * (x + 190) + 30

x/3 = (x + 190)/4 + 30

4x = 3(x + 190) + 360

4x = 3x + 570 + 360

x = 930

Roy has $930 + $190 = $1120.

x^2 + 8x + y^2 + 6y = -c

(x + 4)^2 + (y + 3)^2 = -c + 16 + 9 = -c + 25

The equation of a circle is (x - h)^2 + (y - k)^2 = r^2. So, we want:

-c + 25 = 3^2 = 9

c = 16.

x + 2 is a factor, so plugging in -2 into the function will get 0.

-8a + 4b - 8 = 0

when divided by x - 1, the remainder is 4, so plugging in 1 should get 4.

a + b - 5 = 4

We now have a system of equations:

-8a + 4b = 8

a + b = 9

Multiply the second equation by 8 to eliminate a.

-8a + 4b = 8

8a + 8b = 72

------------------------

12b = 80

b = 20/3

a = 9 - 20/3 = 7/3

x^2 - 8x + y^2 + 16y = -34

(x - 4)^2 + (y + 8)^2 = -34 + 16 + 64 = 66

center: (4, -8)

x + y = 4 - 8 = -4