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Thanks geno .....here's another way

If    f (g)  = x      and g (f)  = x   then they are inverses

f (g)  =     2 [ [ (x - 5) / 2 ] ^1/3 ]^3    +  5    =      2  ( x  -5) / 2  + 5  =   x - 5 + 5  = x

g (f)  =  (  [ 2x^3 + 5 - 5 ] / 2 )^(1/3)  =   [2x^3/ 2] ^(1/3)   [ x^3]^(1/3)  = x

So....inverses

2   3

∫    ∫     3x^2  + 3xy  + 2 dx  dy  =

1    0

Integrating first with respect to x

                                         3

 [ (x^3 + (3/2)x^2y  + 2x ]    =      27 + (27/2)y  + 6 =    33 + (27/2)y

                                         0

Then integrate with respect to y

2

∫     33   +  (27/2)y    dy     =

1

                             2

[ 33y + (27 /4)y^2  ]  =    [  66 +27  ]  -  [ 33 + 27/4]   =  213  / 4

                             1

25 are red

So

green  + blue = 75

And there  are 4 times as many  green balls as blue

So

4B +  B =   75

5B  = 75

B =  75 /5  =  15  = blue ones

And the number of green ones  =  60 

               A

                         E

 B            D                C

If AB = AC  then the triangle is isosceles

If BC is 15   then AD  =   2 * 200 / 15    =     80/3

And because ABC is isosceles, then  DC = BD  = 15 /2

And since DE is parallel to AB  and AC is a transversal cutting both, then triangles   ABC  and EDC are similar because angle ACD = angle ECD   and angle BAC  = angle   DEC

And  since  BC = 2 DC.. then  2 is  the  scale factor between triagles ABC and EDC.....then the area of triangle  ABC  =  area of triangle EDC * scale factor ^2

So

200 =  area of EDC * 2^2

200 = area of EDC * 4

200  / 4  =  area of EDC  = 50

So  [ ABDE ]  =    area of ABC - area of EDC  =  200 -  50     =  150

The cone's radius =    1/2 the side lengt of  the  cube  = 5

And its height  = the side length  =10

So

Volume   = pi * r^2 * h  / 3   =    pi * 5^2 * 10   / 3  =  (250 pi) / 3   units^3

5041 is the square of 71 because \(71 \times 71 = 5041\). 

Likewise, 16 is the square of 4 because \(4 \times 4 = 16\)

You can think of 5041 as the area of a square with side lengths of 71

Thus, the cube of 71 is the volume of a cube with a side length of 71, which is \(71 \times 71 \times 71 = \) 357,911

Do you mean 25% of the balls are red?

Probabilty oooo

First, the chance of getting 1 black ball.

\(\frac{6}{9}\) aka \(\frac{2}{3}\)

Then, the chance of getting another one.

\(\frac{5}{8}\)because you already removed one, so total is 8, and 5 black balls left.

You times \(\frac{2}{3}\)by \(\frac{5}{8}\) and you get \(\frac{10}{24}\)or \(\frac{5}{12}\)

By Law of Cosines, ||b|| = 2*sqrt(13).

Mean: ( 0+0+1+2+16+23+15+2+1 )/ 9

60/9

6 2/3

Median: 0, 0, 1, 1, 2, 2, 15, 16, 23

The middle number is 2 because when we cross out from the outside the last number we are left with, ( the middle ) is 2.

Mode(s): Out of the data set of 0, 0, 1, 1, 2, 2, 15, 16, 23, we see that the most frequently appearing numbers are 0, 1, and 2. 

6 2/3 + 2 + 0 + 1 + 2 = 11 2/3

You are right, I did .   Thanks Builderboi! 

Hi Hipie, 

Welcome to Web2.0calc forum :)

Here is a video that explains it well.

You forgot 6 and 9, making the probability \({21 \over 36} = \color{brown}\boxed{7 \over 12}\)

3f ( n - 2) - f(n - 1)

So

f(1) =

3f (-1)  - f(0)  =  -1

f(2)  =

3 f(0)  - f (1) =   3

f(3) =

3f(1) - f (2)  =  3 (-1) - 3   =    -6

f (4) = 

3 f(2)   - f(3) = 3(3)  -  (-6)  =  15

f(5)  =

3f(3) - f (4)  =  3(-6) - 15  =  -  33

Thanks hipie, that question was similar.  (I did give you a point but someone else deducted one, you can give yourself a point though.) 

I just want to play with it myself

14,15,16,17,18,19,

25,26,27,28,29

36,37,38,39,

47,48,49

58,59

These are the acceptable pairs there are  6+5+4+3+2 = 20 of them

9C2=36 possible pairs

P(success)=20/36  = 5/9

The diagonal across the base =   sqrt ( base area) * sqrt 2  =   sqrt (288) * sqrt 2 =    12 sqrt 2* sqrt 2  = 24

1/ 2 of  this =   12

18 is the slant  height

The true height , h  =   sqrt  [18^2  -12^2 ]   = sqrt [ 324 - 144 ]  =  sqrt 180  =  6sqrt 5

The volume is

base area * height /  3  = 

288 * 6 sqrt 5  / 3  =   

288 * 3sqrt 5  cm^3  ≈   1932 cm^3

Sum of 1st n odds  =  n^2  ......we  have   [ 199 + 1 ]  / 2   =  100  odds

Sum of first evens =    [ first even + last even ] * n  / 2 

We have  202 / 2 = 101 evens

So  [ 204] * [101] / 2  =   even sum =  101 * 101

So

sum of odds  /sum of evens   =

100^2   / [ 102 * 101 ]  =

5000 /5151

 log(ln(log(∫ln(dx(log(f(x+(log(al($3$))))))))))

looks like a nonesense question to me.

French=   .11 * 5000  =   $  550

History  = .21 * 5000 =     $1050

Reference   =  .15 * 5000 =  $750

Science = .15 * 5000 =  $750

Bio =  .11 * 5000 = $550

Geo  = .09 * 5000 = $450

Fic =  .18 * 5000 =

Add the numbers in  the right hand  column as  a  check

550 + 1050 + 750 + 750 + 550 + 450 + 900 =    $5000

(529, 667, 713, 841, 851, 899, 943, 961, 989) >>Total =  9 such numbers.

To find the inverse of  f(x)  =  2x³ + 5  follow these steps:

1)  Replace  'f(x)'  with  'y':  y  =  2x³ + 5 

2)  Interchance  'x'  and  'y':  x  =  2y³ + 5

3)  Solve this equation for y:  x  =  2y³ + 5

                                          x - 5  =  2y³  

                                  (x - 5) / 2  =  y³

                          [ (x - 5) / 2 ]^1/3  =  y

4)  Replace  'y'  with  'f^-1(x)'  indicating that this equation is the inverse:  f^-1(x)  =   [ (x - 5) / 2 ]^1/3 

This shows that  g(x)  is the inverse of  f(x). 

If you want to, you can follow these steps to find the inverse of  g(x), showing that  f(x)  is the inverse of  g(x).

https://web2.0calc.com/questions/help-please_55057 here's a similar problem

ln e    =  x

This   means  we  want  to  find the  value of    e^x  = e

It's obvious that  x =   1