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So this is the question I suppose

Shaded area A - 48= shaded area B

Area of △GHI = 1/2 *10 * 24

                       = 120 cm² 

 

Total area of figure = Area△GHI + Shaded area B

                                     = 120 + Shaded area A - 48

                                     = Shaded area A + 72                                                    ...(1)

 

i.e. from figure, 

Total area of figure = Shaded area A + Area of rectangle EFGH                        ...(2)

 

From (1) and (2) we infer that 

Area of rectangle EFGH = 72 cm² 

 

⇒  72 = EH * HG 

⇒ 72 = EH * 24 

⇒ EH = 3 cm 

 

Perimeter of EFGH = 2( 3 + 24)

                                     = 2 x 27 

                                     = 54 cm 

Expanding, the coefficient of x is 6.

The smallest 4-digit n =1256

1256 mod 9 =5

1256 mod 7 =3

1256 mod 5 =1

If order counts     13P5

If order doesn't count  13C5 

Please include the address of the original.    AND   Ask people to post on the original.

310   /  91    =   3  +  37  / 91

K = 91

Let  A  = (0, 2)

Let  B =  (sqrt 3 ,  1)

Let C  =  (sqrt 3  - 1)

Let D =  ( 0 , - 2)

Let  E =  (-sqrt 3 ,  -1)

AB =  sqrt  [ 3 + 1] =  2

BE = sqrt  [  (2sqrt 3)^2  + 2^2] =  sqrt  [16] =  4

AE  = sqrt  [ 3  + 3^2]  = sqrt [12]

By the Law of  Cosines

AE^2  = AB^2  + BE^2  - 2 ( AB * BE)  cos ABE

12   =  4  +  16   -  2( 2 * 4)  cos ABE

-8 / ( -16)  = cos ABE  =1/2

arccos 1/2  =   60°  =  ABE

There are 14 choose 4 = 1001 times 13 choose 5 = 1287 = 1288287 possible ways for the committee to have 4 females and 5 males, and there are 27 choose 9 = 4686825 possible ways in total, so there are 1288287/4686825 ≈ $\boxed{0.27487}$

BP = PC

The ratio of BP to PC = 1:1

btw, the ratio of AO to OC = 2:1

the ratio of MO to OB = 1:2

we only have to find the constant of g for this problem:

-4$\cdot$c=3

c=-3/4

therefore, g(0) = 0x^2+0x-3/4=$\boxed{-\dfrac34}$

No prob  !!!

Using the degree angle formula, we have the number of degrees in one angle is:

( 6 - 2 ) $\cdot$ 180 / 6 =120

Angle ABE is a bisector of angle ABC, so 120 / 2 = $\boxed{60^\circ}$

8!  =  40320   ways  !!!!

Cos Y = adjecent side / hypotenuse = 7 / 25

If XY = 25, then YZ=7, and using Pythagorean theorum, we know that XZ = 24

tan X = opposite side / adjecent side = $\boxed{\dfrac7{24}}$

Thanks so much for your response! I understand the problem now :)

Note  that   we  will  have  the following  

As  EP  said   ....after  the  first pass  each subsequent pass  places  6  bags

So

[2021 - 7]  /  6  =   335 additional  passes   after  the  first pass  plus  4 additional bags 

Let   the  first pass =  pass 0 

And  notice  that  after  5 more passes we  end up  in  box 1

pass                0                  1                  2                   3                   4                   5                                                      

1 2 3 4 5 6 7  / 6 5 4 3 2 1  / 2 3 4 5 6 7 / 6 5 4 3 2 1  /  2 3 4 5 6 7  /  6 5 4 3 2 1 /  

We  have   335  additional passes  after  the  first  pass....so   there will  be  335/5  =   67  "red" cycles  with  30  boxes  in each cycle

And at the start of the  68th  cycle  we will  place   4  more  bags  in boxes  2 3  4  5

So...we end up in box  5.....just as EP  found    

Proof

7  +  30*67  + 4    =  2021   boxes filled

Sorry......you can re-post it though....

*** edited ***

distance traveled by tip of hour hand  =  1 * 10π cm  =  10π cm

distance traveled by tip of minute hand  =  12 * 20π cm  =  240π cm

     250 pi cm =~ 7.854 meters

First, we find how much it takes for the front wheel to make 100 revolutions, and one revolution is the length of the circumference. So we have:

$2.5\cdot12\cdot2\cdot\pi\cdot100=6000\pi$

Now, we find the circumference of the back wheel(the length of one revolution for the back wheel), and divide $6000\pi$ by that number to get our answer:

$3\cdot2\cdot\pi=6\pi$

$\dfrac{6000\pi}{6\pi}=\boxed{1000}$ revolutions.

But thats the thing I can't anymore, EP

8 P 8 = 40320 ways        8! = 40320 

Well ...your answer  has hour hand making 2 revs and minute hand making 24 revs....thought you might edit your answer.....

Okaaaaaaaaaaay, EP

eight have son only ......