CPhill

OK...we have....

V   =     L         *        W         *       H        =

         (2x^2)    *    (2x^3)    *         5x          =

                      4x^5           *           5x         =

                                 20 x^6

Imagine, for convenience sake, that there are 100 children at  the school

So  8 have both

We have this

Number Total =  Total Number Umbrellas +Total  Number Raincoats - Number Both

Let x be the number with raincoats.....so 2x = number with umbrellas

So we have

100  =   2x   + x     -   8     rearrange as

108  = 3x           divide both sides by 3

36 = x

And the number with umbrellas  = 2(36) = 72

But 8 of these have both....

So....the number with only umbrellas is   72 - 8  =  64  =   64/ 100  =  64%

Here's a Venn Diagram

BX = 2sqrt(13) =   sqrt (52) = CX

And since AX is a median,  OX = (1/3)12 =  4

And since triangle OBX is right

OB = sqrt (BX^2 - OX^2) =  sqrt (52 - 16) = sqrt (36) = 6

sin OXB = sin OXC =  OB/BX =  6 / [ 2sqrt (13)] =   3 /sqrt (13)

Note that  angle OXC is obtuse....so its cosine is negative

And cos OXC =   - sqrt [ 1 - sin^2 OXC ]  = -sqrt [ 1 - 9/13] = -sqrt (4 /13] =  -2/sqrt (13)

Using the Law of Cosines

OC^2  = OX^2  + CX^2 - 2( OX * CX) cos OXC

OC^2 =  4^2 + 52 - 2  [4 * 2sqrt(13) ] (-2/sqrt (13)   

OC^2  =   16 + 52 - 2 [ 4*2 ] (-2)  

OC^2 =  16 + 52 + 32 

OC^2 = 100

OC = 10

And this is 2/3 of  CZ ....so....

(2/3)CZ = 10

CZ =  15

Remember that  if we divide by x + a, we are dividing by "-a" in the synthetic division process

So.....  in  x + 3....."a" = 3....so  we are dividing by  " - 3"

So we have

-3   [   7      15       -12

                 -21        18

        ______________

         7      - 6          6

The remainder is 6

We are testing to see if "5" is a root

We multiply 5 *2 = 10

We add this to the "-1"  and get "9"

Thus....

The answer on the top right is the correct one 

No prob....

Remember that  the  "range" refers to the y values covered by the graph

The  range  here is  just   from  - 3 to 6, inclusive

So....every answer is good except for  - 4   and 7

All the others are in the range....

Click on the "Image" icon   

This will bring up the "Image Properties" screen

Hit the "or Upload" tab on this page

You will see "Image Upload"

Choose the file from your hard drive to upload  and hit "Upload Tab"

Make sure to verify that you are not a robot   {LOL!!]

You should see the image in the next window

Hit "OK"

NSS....See if you can do this one based on my answer to your other question

Remember.....we are dealing with the theoretical probability, here....!!!!!

The  experimental probaility of a "1" on the next roll  is

245 / 1230   =

.1992  ⇒ B

Note something, NSS.....this isn't the theoretical probability....past outcomes have no effect on the next roll in the theoretical pobability because these are independent events.....thus the  theoretical probability of rolling a "1" on the next roll is still 1/6  = .1667   !!!!