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Here's my best attempt

Easiest way to do this is  with a  table....we will have to round a little  so that we get whole numbers....

                Canine  Preference          Feline Preference

Male                 ???                              .538 *.251 * 101

Female       .427 * ( 1-.251) * 101             ???

                _______________________________________   

                  (1-.251) * 101                       .251 * 101

Filling in what we  know and  solving  for  what we don't.... we have

                  Canine Preference             Feline Preference             Total

Male                ≈  44                                      ≈  14                          ≈ 58                                             

Female            ≈  32                                       ≈ 11                          ≈ 43                          

                 _________________________________________________                                

                       ≈  76                                        ≈ 25                           101

P ( canine preference  or female gender )  =

P ( canine)  + P (female)  - P ( canine and female)  =

 76/101  + 43/101  - 32/101  = 

≈ 87 / 101

*** edit ***

canine OR female =    (320 +116   + 429 )/1000 = .865

Again with the Venn diagram:

canine OR female =    (320 +116   + 135 )/1000 = .571

  I have no idea if the above answer is correct.....hope it is

     here is my take on it

          there are   8! seating arrangements = 40320

             there are 14 ways those two knuckleheads could be seated next to each other ( you can reverse their order to get 14)

                 those 14 ways leave 6! for the rest of the folks to be seated

40320 - 14 * 6! = 30240 ways  

    I do not know if this is correct.....it MIGHT be...it might NOT be !  

Let's pick  a few values and  see what happens

x= 1....ceiling  [ 5 (1)  - 5 floor (1) ] / 5 =   ceiling [ 5 - 5 ] / 5  =  ceiling 0   = 0

x  =1.2.....ceiling  [ 5(1.2)  - 5 floor (1.2) ]  /5 =  ceiling [ 6 - 5 ] / 5 =    1/5

x = 1.4  .....ceiling  [ 5 (1.4)  -5 floor (1.4) ] / 5 =  ceiling [ 7 - 5(1) ]/ 5 = 2/5

x = 1.6  .....ceiling [ 5 (1.6 )  - 5floor (1.6) ] / 5 = ceiling  [ 8 - 5 ] /5  =  3/5

x  =1.8.....ceiling  [ 5 (1.8) - 5 floor (1.8) ] /5  = ceiling [ 9 - 5] /5 = 4/5

x = 1.9.....ceiling  [ 5 (1.9)  - 5 floor (1.9] / 5  = ceiling [  9.5 - 5 ] / 5  = ceiling (4.5) /5 = 5/5  =1

And look at the  graph here : https://www.desmos.com/calculator/ixgipsfctk

It appears that  this patern is  repeated infinitely between integers

So....there are 6 numbers in the range of  this function

0, 1/5 , 2/5 , 3/5 , 4/5  and 1

ABCD is a square with a side length of 1.  A circle passes through B, C, and is tangent to the midpoint of AD (at E).  What is the radius of the circle?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AB = EF = 1      BF = 1/2         ∠BEF = tan^-1(1/2) = 26.56505118º

EB = sqrt(EF² + BF²) = √1.25

Radius      EO = 1/2 (EB / cos ∠BEF) = 0.625     or   5/8

Well I'm really tired but here we go, let us use complementary counting, so that is 

$total$ $outcomes$ - unfavorable$ $outcomes$, total outcomes is all ways that can be seated without restrictions so that is

8!= $40320$, then the unfavorable outcomes is if John and Paul sit next to each other, we can pretend that the pair is one person and that is how many ways to arrange 7 people, which is 7!, that results in $5040$

Subtracting, we get:

$40320-5040$ = $35280$
 

Please check, as I possibly have missed somethings but that's the idea.

y = x^2 - 8  ⇒  y^2 = ( x^4  - 16x^2 + 64)      (1)         

y^2 = -6x  + 40     (2)

Sub (1)  into (2)   and we  have that

x^4 -16x^2  +  64 =  -6x  + 40      simplify

x^4  - 10x^2  + 24   = 0       factor as

(x^2  - 6)  ( x^2 - 4)   = 0

(x^2 - sqrt (6) ) ( x + sqrt (6)) ( x - 2) ( x + 2)   = 0

Setting each of these to 0 and solving for  x produces

x = sqrt (6)   x = -sqrt (6)    x = 2 and x = -2

And the associated   y  values will  be

y = [ ±sqrt (6) ]^2 - 8    =   6 - 8 =  -2   (twice)        and  y=  (±2)^2  - 8  =  4 - 8  =  -4  (twice)

So....the sum of these  =   -2 + -2 + -4 + -4  =  -12

Hi guest!

you did the mulitplication  problem that i had already answered, the addition problem that you need to do is 48+12=?

Please tell me if you still need any help!

3x-7 <= 6x+9        subtract 3x from both sides and subtract 9 to both sides

-16 0<= 3x

   x >= -16/3

[-16/3 , +inf)

A circle is centered at O  and has an area of 48pi. Let  Q and R  be points on the circle, and let P be the circumcenter of triangle QRO. If P is contained in triangle QRO  and triangle PQR  is equilateral, then find the area of triangle PQR.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

OQ = OR = r = 4√3

∠QOR = 30º         ∠QOP = 15º           ∠QPR = 60º

QR = 2 (OQ * sin∠QOP) ==>         QR = 3.586301889

Height of ΔPQR      h = sqrt[PQ² - (QR/2)²] = 3.105828541

[PQR] = h * QR / 2 = 5.569219382 u²

.068 (201)  / (.068(201) + .248(201) ) = 21.5  %           sorry....dropped the leading zero there,,,,,   D'Oh!

Then it would be   .068 / (.068 + .248) =  21.5%

If you want actual numbers of the 201 people randomly surveyed people then:

.68 (201)  / (.068(201) + .248(201) ) = 21.5  %      Do you see now?

This Probability is based on percentages

    example   people with no pu truck is given as .784    

       the diagram shows

                 (248+536) / (148 + 68 + 248 + 536) = .784

        you just have to scale the numbers    

            if it makes you feel better, you can just divide all of the numbers in the Venn diagram by 1000

                 .148       .068      .248      .536  

That is surely incorrect, as you have stated that the number of people surveyed with attached earlobes is greater than the number of people actually surveyed, which is not possible.

there are 12 squares so 12x2=48     ??????

See the Venn below:

Total people with attached ealobes = 68 + 248 = 316

      68 of these have a p/u      68 / 316 = 21.5%

We would have the best luck of using our information of the total number of people and getting a venn diagram. So let's do that.

Favorable/possible = 0.784, so f/201 = 0.784. Thus, there are 201-157.584 = 43.416 people who have pickup trucks.

Favorable / possible = 0.684, so f/201 = 0.684. Thus, there are 201-137.484=63.516 people who have attached earlobes (ik right?)

favorable / possible = f/#of attached earlobes = f/63.516, and 43.416 + 63.516 = 106.932, so there are 0 people that have both attached earlobes and a pick up truck? I'm probably wrong, just this question is an incorrect question because it doesn't have integer number of people for each case.

each square =2 triangles

there are 12 squares so 12x2=48

there are 12 regular triangles

48+12+?

You can solve the addition  problem to get your answer Guest!

40.cos(50) = 25.71150438748

I used the caculator on  this site....