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0.09523809523809524

Melody's  method  :

Triangle AOB  is  similar to triangle OCM

This means that

CM / AB  = OC / OA

CM  = (1/2)AB   .....

(1/2) AB          OC

_______  =     ___

     AB              OA

1                 OC

__  =         ____

2                 OA

Let A  = (0,4)    B  = ( 4,4)    C   =(4,0)   D   =  (0, 0)

The  line segment AC  lies on a line with an equation  of  

y = -x + 4

AC  = 4sqrt (2)

The  segment MB   has a slope  of  [4 -0 ]  /[ 4 - 2]  =  4/2  = 2

So....this segment lies on a line with an equation of

y= 2 ( x  - 2)   

y = 2x  - 4

The  x  coordinate of the  intersection of these  two lines is

-x + 4 =  2x  - 4

8 = 3x

x  = 8/3

And y  = -(8/3)  + 4 =   4/3

So  OC   =    sqrt  [  (4 - 8/3)^2  + (4/3)^2 ] = sqrt  [ ( 4/3)^2  + (4/3)^2  ] =  (4/3)sqrt (2)

And OA  =  AC  - OC  =  (4  - 4/3)sqrt (2) =   (8/3)sqrt (2)

So

OC             (4/3) sqrt (2)                  4               1

___  =       ____________  =         ___   =     _____

OA             (8/3) sqrt (2)                  8                2

 865546476465546746465*4354646/98908908+565670

[Multiply the  first two  intergers ] [ divide  by the  thrird ]  [ add the last one to  the  result ]

[ This is  obviously  messy  !!!!!   ]  

269224892968203087650629625

_____________________________      [ exact result  ] 

               7064922 

d is  correct.......rotating,  reflecting  and translating a  figure  will have  no  effect  on the  figure's shape....the figures will be exactly the  same  [  the  definition of  congruence ] 

T = third evening

S = second evening = 4 T

F = first evening = T-10             Summed = 122

T + 4T  + T-10 = 122     Solve for T, third evening.....then S = 4T   and F = T-10

A)  x  +  y  =   (2⁰  - 3^-1) +  (5⁰ - 2^-1)  =  (1  - 1/3)  + (1 - 1/2) =  2/3  + 1/2 =  [ 2*2  + 1*3 ]  / [ 2 * 3 ] =  7/6

B) x  - y   =   (2⁰  - 3^{-1) -}  (5⁰ - 2^-1)   = (1 - 1/3)  - (1 - 1/2)  =  2/3  -  1/2  =  [ 2*2  - 1*3  ]/ [ 2 * 3 ] =  1/6

C)  x * y   =   (2/3)(1/2)  = 1/3

D)  y  / x  =   (1/2) / (2/3)  =  (1/2) * (3/2)  =  3/4

you rom

Note   P(2)  =   1  - .41  - .38  - .08  - .02  =  .11

a. P( x =2)    = .11

b. P ( x < 2)   =  P(x  =1)   or P(x = 0)  =  .38  +  .41  = .79

c. P (x ≤ 2)  =    P(x = 2)  + P(x  =1)  +  P (x  = 0)   =   .11 + .38  + .41 =  .90

d.  P(x ≤ 1 )  =   P(x  = 1)   or P(x  = 0 ) =   .38  + .41  =   .79

e. P ( x  > 2)    =  P(x  = 3)  or  P ( x  =4)   =  .08 + .02   =  0.1

f.  P ( x = 3 or  x  =4)  =  .08  + .02  =  0.1

  CORRECTED   .  thanks to alan for  pointing out  my  earlier error  !!!!

We can use the tangent to  solve this

tan (80°) =    20  / D                    where D is the distance  we  need

Rearrange  as

D  = 20  / tan (80“)   ≈   3.5 ft     [ this is reasonable because the ladder  is at a  steep angle with the ground ]

3 (a)   Not sure about this one  

3(b)  Expansion is

(3x^5)^4    -  4(3x^5)^3 * [(1/9)y]^3    +  6(3x^5)^2 * [ ( 1/9)y^3]^2   -  4 (3x^5)* [(1/9)y]^3   + [ (1/9)y^3]^4   =

81x^20   -  12x^15y^3   +  (2/3)x^10 y^6  - (4/243)x^5 y^9     +   (1/6561)y^12

2 . 

(a)   Ratio Test  =    a  (n + 1)  / a (n)  =   

[2(n + 1 )! ] / [ 2^(2n + 1)  ]                   2 (n + 1)!     2^(2n)                     n

_____________________      =          ________ * _________  =     _____    =      r

         2n!  / 2^(2n)                                    2n!          2^(2n + 1)                 2 

(b)  This series will diverge  as  n  grows  larger and  larger

First one

120  - 80  +160/3  -320 / 9 +.....

r  =   (-80 / 120)    =  -2/3

The sum is

First  term          120                  120

_________  =   _______    =  ______   =    120  (3/5)   =  72

 1 - r                   1 - (-2/3)          (5/3)

12/32 x 100% = 37.5 percentile rank

9000 - 2000 salary = 7000 in commission

7000/50000 x 100% = 14% commission

You need to repaint the floor and inside wall of your circular swimming pool. It has a diameter of 16 feet and a depth of 5 feet. What is the surface area that needs to be repainted? 

1) The surface area is 20 + 600/4 = 170.

2) The length of the diagonal is 2*sqrt(17).

3) The height of the pyramid works out to 4*sqrt(3), so the volume is 1/3*4*sqrt(3)*12^2 = 192*sqrt(3).

1    put in  -2   where you see 'X'  and calculate the answer

I looked at a couple of the others.....they are pretty basic....have you TRIED to answer any of them?   This forum is not here to do your homework!

With out  nuts =  w

with nuts = 6w

total candies =   w + 6w = 7w

prob =   w   out of 7w  =    w/7w =   1/7

Not positive

but I think the biggest would be

(1 4 5 8 9 ) ( 2 3 6 7 10) = 756

smallest would be

(1 2 3 4 5 ) ( 6 7 8 9 10)   = 600

Future pop   =   12 000 (1 + .05)¹²     then round to the nearest whole number.....

The hand travels 25 min /60 min of a full circle (360 degrees)

25/60 x 360 = 150 degrees

pi * d    is the circumference of this circle   and d = 2r = 2 x 8 inches = 16 inches

      and the hand travels 150 out of 360

pi * 16  *  150/360   inches      You can take it from here ! 

300 m = .3 km

when the first car passes and slows to 40 km/hr    the last car is still travelling 60 kmhr

   to get to the point wher it slows down will take   .3 km / 60 km/hr = .005 hr

      the FIRST car travels  40 km/hr   * .005 hr   during this time = .2 km

          so now there is .2 km from the fron car to the back car  ...or the line of cars compresses to 200 m length

1/2 w / 1/3m =   3/2  w/m