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I believe it was 15, as every 3x3 magic square I have ever encountered in my life, having the digits 1-9, has had a sum of 15. If you include 0 and remove 9, things could change! :D

For the first team, the coach has \(9\) possible choices and picks \(3\) players. This is the same as \(\dbinom{9}{3}\) as order doesn't matter in a group. Thus, there are \(\dbinom{9}{3} = 84\) ways to pick the first team.

For the second team, the coach has \(6\) possible choices left and again picks \(3\) players. This is \(\dbinom{6}{3}\), due to the reasoning above. Thus, there are \(\dbinom{6}{3} = 20\) ways to pick the second team.

For the third team, the coach only has \(3\) choices for players, and there is only way to choose 3 people from 3 people. Thus, there is \(\dbinom{3}{3} = 1\) to pick the third and final team.

Multiplying it all together, we get \(84 \cdot 20 \cdot 1 = \fbox{1680}\) ways! :D

There are:999 - 100 + 1 =900 3-digit numbers between 100 and 999

There are 271 numbers between 1 and 999 that have a 3 in them.

There are 19 numbers between 1 and 99 that have at least one 3 in them.

So: 271 - 19 =252 numbers between 100 and 999 that have at least one 3 in them.

900 - 252 = 648 numbers between 100 and 999 that have NO 3 in them.

Let's see if we can find a pattern   

101^2  - 97^2  =  792

93^2  - 89^2  =  728

85^2  - 81^2  = 664

....

21^2 - 17^2  = 152

13^2 - 9^2  =  88

5^2 - 1^2  =  24

And note that

(792 + 24)  =  ( 728 + 88) =  ( 664 + 152)  =   816

5    13      21      29      37     45      53     61     69    77    85    93    101

1     9       17     25       33     41      49     57     65    73    81    89      97

So  we  will have 6 pairs  of  equal sums of 816   plus  the sum of  (53^2 - 49^2)  = 408

So....the sum is     6 (816) + 408  =  5304

5 * [2 + 3/5] =5 * 2.6 = 13

See https://web2.0calc.com/questions/reposted-because-the-answer-i-got-last-time-was-incorrect#r8

Heureka has also answered this previously I think.

e1:

E(steps) = 1*(1/2) + 3*(1/2²) + 5*(1/2³) + ... + (2n-1)*(1/2ⁿ) + ...

E(steps) = Sum_{n=1 to inf}( (2n-1)/2ⁿ ) = 2

e2:

E(steps) = 2*(1/2) + 4*(1/2²) + 6*(1/2³) + ... + 2n*(1/2ⁿ) + ...

E(steps) = Sum_{n=1 to inf}(2n/2ⁿ) = 4

(e1, e2) = (2, 4)

The area  =

(6)(6)sin (120°)  =  36 * sqrt (3) / 2   =   18 sqrt (3)  units^2

     D             C

A            B

Since it is a parallelogram....  BC  =  AD

So.....the  area  =     (DA)(AB) sin (45°)  =  (8)(6) sqrt (2) / 2  =  24 sqrt (2)  units^2

H=2; M=48; A=abs((30*H) - (5.5*M));print"A =", A,"Degrees")
A = 204 Degrees - This is the larger angle.
So: 360 - 204 =156 degrees - this is the smaller angle.

At 2:48 the hour hand is exactly at 14 minutes after 12. The minute hand at 48 minutes before 12 is =60 - 48 =12 minutes to 12.
So:12 minutes + 14 minutes =26 minutes
26 x 6 degrees each = 156 degrees.

Thanks! Yup the reason why I'm on this website is to help!.

Slope = rise over run    or   y /x         so   y = 4x

Pythag theor     x^2 + (4x)^2 = 1^2

                         17x^2 = 1

                               x^2 = 1/17

                                x = sqrt (1/17)      y = 4 sqrt (1/17)

Area = 1/2  b  h    =  1/2   x  y   =    1/2  sqrt 1/17   * 4 sqrt 1/17

                                                   = 2 (1/17) = 2/17    units²

We can use  similar triangles  to  find  the height of the cone

Let x  be the distance  from the cone's apex to  the  top of the smaller circle

We  have  that

[  x  + radius of smaller circle]           [ radius of larger circle + circum of small circle + x]

_________________________  =   ___________________________________________

     radius of smaller circle                      radius of large circle

[ 1 + x ]         [ 2 + 2 + x]

______   =    _________    cross- multiply

    1                      2

2 [ 1 + x ]  =   1 [ 2 + 2 + x ]

2 + 2x  =  4  + x

x  =  2

So....the  height of the  cone   =   4  + 2  + 2   =  8

Now...x + 1  = 3  is  the hypotenuse of a right triangle  with  one of the legs  =  the radius  of the smaller cone

Let A  be the apex of the cone....B  be  the center of the small circle  and   C  be the point where the radius of the small circle  intersects  the side of the cone

Then sin of angle ABC  =  BC/ AB  =   1 / 3

And the tangent  of  this angle  =  1/ sqrt (8)

And we can find the  radius  of the cone thusly :

tan ABC   =  r / height of cone

1/ sqrt (8)  =  r  /8

8/sqrt (8)  = r  =  sqrt (8)

tan 30°  =  r / 8

1/√ 3  =  r / 8

r  =  8 / √ 3

So....the  volume of the cone  is

(1/3)  pi ( radius)^2 (height)  =

(1/3) pi *(sqrt (8))^2(8)  =  (64/3) pi  units ^3   ≈  67.02  units ^3

why are you instantly getting so defensive and aggressive? he was just trying to help.

The answers there are wrong!

Thanks man 

Together we are the jam crew violin+rock

Good job, LD    !!!!!

A "Best Answer".....

The easiest way to  do this is to first  find the surface area  of both figures

Surface area  of  larger figure  =

2 ( 8*2  + 14*8  + 14*2]  =   2 [ 16 + 112  + 28]  =  2 [ 156]  =  312 cm^2

Surface area of smaller figure  =

2  [ 8*4  +  6*4  + 8*6]  =  2 [ 32 + 24 + 48]  =  2 [ 104]  =  208 cm^2

From this  we want to  subtract the area of two  8 x 4 rectangles  [the areas  where each of the two objects are touching each other =  2 x 32  =  64 cm^2

So.....the total surface area  = 

[ 312 + 208  -  64 ]  =   456 cm^2

Repost? - "https://web2.0calc.com/questions/help_84215"

Repost? - "https://web2.0calc.com/questions/anty-the-ant-is-on-the-real-number-line-and-anty"

:D

Its correct!

\(\begin{align*} \dbinom{14}{11} &= \dbinom{14}{3} \\ &= \dfrac{14!}{11!3!} \\ &= \dfrac{14\times 13\times 12}{3\times 2\times 1} \\ &= 14 \times 13 \times \dfrac{12}{3\times 2\times 1} \\ &= 14\times 13\times 2 \\ &= \boxed{364}. \end{align*}\)

By the way, I wrote this even though it may look similar to ones on different websites