CPhill

Total  Area  =   40 * 32  =  1280 ft^2

Area  occupied by each chair  = 4 * 5  =  20 ft^2

Number of chairs  =    1280  / 20   =     61   ≈   60 chairs

Surface  area  =   4 * 3 *  r^2

2700  =  12 * r^2        divide both sides by  12

225  = r^2         take the positive root

15  = r

So....the volume  is

(4/3) * 3 * r^3   =

4 * (15)^3   =    13500 cm^3

Good luck on the move.....!!!!!

We can break this up into 4 areas

If  we draw a horizontal lne at y  = 2, we have two triangles at the top.....each with a base of 4  and a height of 3

So...their total areas  =   4 * 3  =   12 units^2

Next.....if we draw another horizontal line at   y = -1....we will have a rectangle with a width of 8 and a height of 3......so its area  is   8 * 3   =   24 units^2

Finally...we have a triangle at the bottom with a width (base)  of 8   and a height of 2.....so its area is

(1/2) * 8 * 2   =    8 units^2

So....the total area is

[ 12 + 24  + 8  ] =    44 units^2

.1.

lim             (1 + h)^2  - 1^2

h →0        _____________

                         h

lim      ( 1 + 2h  + h^2  -  1)

h →0  ________________

                        h

lim       2h  +  h^2

h →0  ________

                  h

lim           h  ( 2  + h)

h →0  ____________

                  h

lim         2 +  h          =         2

h →0

lim           √x  -  2

h → 4      ________            we can factor the denominator  as

                 x   -   4   

lim                  √x - 2

h → 4        ___________

               (√ x - 2) (√x + 2)

lim                1                           1                            1                 1

h → 4      _______     =        _______       =      _______ =     ___  

                 √x + 2                   √4 + 2                     2  + 2             4

The unknown scale factor is  found by :

.938 / .878    ≈ 1.068

Considering each can to be unique, the number of diiferent  sets of cans  we can form on two successive draws  is C(40,2)  =  780

And since  10% of the cans are defective......this means that we have 4 defective cans......and we want to choose any 2 of them ....so   .....  C(4,2)  = 6   possible sets consisting of only defective cans

So....the probability that  any set we choose  will contain  2 defective cans  is :

Sets containing defective cans  / Total possible sets  =  

6 / 780   =   

1/ 130

 76, 55, 73, 93, 29, 74, 57, 34, 54, and 75 

Order the data from low to high

29  34  54  55  57  73  74  75  76  93  

The median  is :    [ 57 + 73] / 2   =  130/2   =  65

The mean is   [ 29 + 34 + 54 +  55 +  57 +  73  +  74 +  75 +  76 +  93]  / 10  = 62

The standard deviation  is ≈  20

We take the absolute value difference  of each score from the mean, square it  and add these squares together......then, for a sample,  we  divide this  by  the number of scores less one......the square root of the last calculation is the standard deviation

Let R  be the car's rate

Call the time for the car to travel  (in hours)  =  210/R

Call the total time for the bike to travel  (in hours)  =   210/R - 1/3

Now.....the distance bike travels   =  its rate * its time  =  120 *  [ (210/R) - 1/3 ] 

And the distance the  bike travels to meet the  car  = 120* [ (210/R - 1/3] / 2  =    60[ (210/R - 1/3 ] = the same distance the bike travels back to "A"

So.....the distance the bike travels back to "A" / ts rate  =  some time   (1)

And the distance the car travels after meeting the bike / its rate  =  the same time   (2)

So.......equating  (1)  and (2) in algebraic terms, we have

( 210 - 60 [ 210/R - 1/3] ) / R  =    60[ 210/R-  1/3 ] / 120

(210  - 60 [ 210/R - 1/3 ] ) / R  =   [ 210/ R - 1/3 ] / 2        cross-multiply

2(210 - 60[ 210/R - 1/3 ] =  R [ 210/R - 1/3 ]

420  - 120 [ 210/R - 1/3 ]  =  210  -  R /3 

420  - 25200/ R  +  40  =  210 - R/3

460 - 25200/R  = 210 - R/3 

R/3 + 250 - 25200/R  = 0        multiply though by R

(1/3)R^2 + 250R - 25200  = 0       multiply through by 3

R^2  + 750R  - 75600  = 0          factoring, we get

(R - 90) (R + 840)  = 0

Only the first factor set to 0  will provide a positive solution for R  =  90 kmh   =   the car's rate

For the events to be independent

P(A) * P(B)  =   P ( A and B)

( 1/4) * (2/3)  =  2 / 12  =  1/6

But  P ( A and B )  =   1/5

So....they are dependent events  and  "D"  is correct

Let  H  = the probability of eating a hot dog

Let S  = the probability of drinking a soda

So

P ( S  l  H )   =     P (S  and H)                .38    

                           ___________     =       ___    =   .62

                               P(H)                          .61