CPhill

[(-2)^2]^3  =

[4]^3  =

64

Let x  be the amount he started with

So....he first spends  1/5 of this  = (1/5)x

So....what's left  =   (4/5)x

And he spends (1/5)  of this  = (1/5)(4/5)x =  (4/25)x

So  he spends   (1/5)x + (4/25)x   and this = $36.......so we have

(1/5)x + (4/25)x  = 36

(5/25)x + (4/25)x   = 36

(9/25)x   = 36      multiply both sides by  25/9

x =36 (25/9)

x = (36/9) * 25

x = 4 * 25   =   $100       and this is what he started with

Proof......he spends  1/5 of  $100  = $ 20

Then....he spends 1/5 of  what's left = (1/5)($80)  = $16

And $20 + $16   = $36

( 1 / 20)  /  (3 / 4)       invert the second fraction and multiply

(1 / 20)  * (4 / 3)         swap denominators

( 1 / 3 ) * ( 4 / 20)

(1 / 3 ) * ( 1 / 5)  =

1 / 15

The probability is given by :

[ The number of was to choose 2 Dems. out of  6 ] * [ The number of ways to choose 2 Reps. out of 8] / [ The number of ways of choosing 4 people out of 14]

So we have  :

C(6, 2) * C(8,2)  / C(14, 4)   = 

[15 *28 ] / 1001 =

60 / 143    about  41.9%

No prob....

Landry.....these look to be Venn Diagrams

As an example for the second one :

The yellow part could be interpreted as all the citizens of Chicago

The blue part could be interpreted as all the citizens of Illinois

And the green part could be interpreted as all the citizens of the US

Thus....the yellow is a subset of the blue.....and both of these are subsets of the green

[ x^(1/3)  - a^(1/3)]  / [ x - a ]  ........factor the denominator as a difference of cubes......assuming that x and a are both positive

[ x^1/3  - a^1/3] / [ (x^(1/3) - a^(1/3))(x^(2/3) + (ax)^1/3 + a^(2/3)) ]  =

1 / [ x^(2/3) + (ax)^1/3 + a^(2/3) ]

Whether or not this is more "simple" is debatablle.......

Here's the answer to your second question : http://web2.0calc.com/questions/helppp-i-wanna-know-if-i-did-it-right-i-got-21-i-multiplied-70-and-30-0-70-x-0-30

B is correct....the  probability of drawing a second blue marble - without replacement - out of the same jar is affected by [ depends upon] what color you drew on the first draw

This Venn Diagram might help

Notice that 70% have blue eyes....and of these, 30% also have dark hair

So,   30/70  of the people who have blue eyes also have dark hair

And  30/70  = 3/7  =  about   43%

So.....C is the correct answer