CPhill

{ 2,.....,14}   number of possible  subsets with these two members  = 2^(14 - 2 -1)  = 2^11

( 4,....,7}     number of possible subsets with these two members  = 2^(7 - 4 - 1)  =  2^2

Total  subsets =   2^11 + 2^2   =    2052

To see this, consider the second set  .....either the  integers  5 and 6 are in or out of each subset

So  2 states ^( number of integers)  =   = 2^2   = 4  subsets

And in the first subset   the integers  3,4,5,6,7,8,9,10,11,12,13    are  either in or out of each subset=

2states ^(number of integers) =  2^11

Slope =   ( 0 - 25)  / (160 - 0)  =  -25  /160  =   -5/32

y  changes by    -5  units  when x  changes by  32

The number of integer coordinates =  1 + (160/5)  =  1 + 32 =   33

  ABCD

+  BCD

+    CD

+       D

______

----  4D

Note that this is impossible

4D   must  be   an even  number for any positive digit D     so    it  cannot  end with a   "1"

4^1   = 4

4^2  =  16

4^3  =  64

4^4 = 256

4^(2n)   ends in 6

4^(2n -1)  ends in 4

4 ^(2 * 18   - 1)   =   4^35     ends in  4

See my answer under your original post

30 (A +.10)  + 35P  =  33.50    →   30A + 3 + 35P  =  33.50  →  30A + 35P  = 30.50    (1)  

24A + 24P  =  22.80     (2)

Multiply (1) by 24  and (2)  by  - 35

720A + 840P =  732

-840A - 840P  =  -798        add these

-120 A  =  -66

A =  66/120  =  .55 =  price of apple in store Y

See my answer under your original post

In vertex form we have

y = a ( x -  h)^2  + k             (h,k)  is the vertex  and (x,y)  is a point on the graph

So

-8  = a( 0 - 1)^2  + (-9)

1  =  a1^2

a =  1 

So we have

y = ( x - 1)^2 - 9 

y  =x^2 - 2x + 1   - 9

y  = x^2  - 2x  -  8

b = -2       c =  -8

a + 2b  - c   =

1 + (2)(-2)  - (-8)  = 

1   - 4  +  8   =

5

(5/15) (660) (6)  =  

(1/3) (660) (6)  =

2 * 660   =

1320  are sick

Let the number of cows = 30

Let the number of chickens = x

Let the number of horses =  50 - 30 - x =  20 - x

When he trades away  as many cows as horses he has   30 - (20- x)  =  10 + x cows left

So 

10 + x =  x + (20 - x)

10 + x =  20

x =10

So   he now has  10 +  x = 10 + 10 =  20 cows left

And the number of  chickens and horses =    x  + 20 - x  =   10 + 20 - 10  =   20 

And the number of  cows =  the number of  chickens and horses