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The greatest common divisor of (2x + 3)(7x + 2) and x is 18.

The probability is 7/120.

No here is how it looks

https://drive.google.com/file/d/1Hn33fC4FXymLRsWWbLKxQN89SIA8s20d/view?usp=drivesdk

i use an iPad. not a computer

Let $x = 0.\overline{6}$

Thus, $10x = 6.\overline{6}$

Subtract these equations to get: $9x = 6.$

Thus, $x = 0.\overline{6} = \frac{2}{3}.$

We have $3 \sqrt{\frac{2}{3}} = 3 \frac{\sqrt{2}}{\sqrt{3}} = \frac{3 \sqrt{2}}{\sqrt{3}}.$

Then, if we multiply both the numerator and denominator by $\sqrt{3}$ we have 

$\frac{3 \sqrt{2} \sqrt{3}}{\sqrt{3} \sqrt{3}} = \frac{3 \sqrt{6}}{3} = \sqrt{6}$.

Thus, the answer is $\sqrt{6}$

When you select browse , you need to click on the location on  the left for where to browse....

   here is my screenshot.....does yours not look the same?

Let  the  number of  marbles  that Kamal  had  in the  beginning=  K

Then  Jason had (128 - K)

Let the  number  of  marbles  that  Jason gave away =  G

Then the  number of marbles  that Kamal  gave away =  3G

And  the number that  Kamal had left = K  - 3G

And  we  know that, from Jason's point of view

What  he started with - what  he gave away =  what he had left

(128 - K)  -  G   = G - 4  simplify

(128 - K)   =  2G - 4

128  + 4  -  2G   = K   

132  -  2G     =    K       (1)

And  from  Kamal's   point of  view  we have  that

3 times  what  he  had left = what Jason had left

3(K - 3G)  =  G -  4       (2)

Sub  (1)  into (2)

3  (  132 - 2G - 3G)  =  G - 4

396 - 15G  = G  -  4

400  =  16G

G = 400/16  =   25

What Jason started with   =  2G  - 4   =  2*25 - 4   =  46

No prob  !!!

The locus of points equidistant from the two circles would be the third concentric circle with a radius of 8 inches.

The  scale factor =   (1.1)

If  we  let the  original surface  area = A

Then the new surface  area = A (scale factor)^2   =  A ( 1.1)^2 =  1.21A

So

The %  increase in the surface area   =

(1.21 A  -  A)                 A  ( 1.21  - 1)

__________  =           ___________  =      .21  =  21%

       A                                 A

Thank you

Since O  is  the  center......the measure of angle  COA  = (360  - 100 - 110) =  150

And  triangle COA  is  isosceles with OC = OA

So  angle OAC  =  (180 - 150) /2  =  15

And triangle  BOA is also  isosceles with OB = OA

So  angle OAB  = ( 180 - 110)  / 2   =   35

So angle BAC  = angle OAB + OAC  =  35  + 15   =  50°

Another (easier)  way to see this is to note  that central angle BOC  =100

And angle  BAC  is  an inscribed angle which subtends the same arc as BOC

So...its measure  = (1/2)  of BOC  = (100) / 2  =   50°

(1.13-1) x 100%=33 %

Don't look now, but your "o" key is stuck.  

If  the  total  profit  =  1000,  then  the total  sales  =  1000  + 5000  =  6000

If  the price of a football = 40, then the  price of a basketball  = 40 (1.20) = 48

And  the the number of  footballs  = F

So....the  number  of  basketballs =   F + 15

So

Number of footballs * cost each +  Number of basketballs  * cost each =  Total sales

F ( 40) +  (F + 15) (48)  =  6000   simplify

40F  + 48F  +  720  =  6000

88F  =  6000 -  720

88F  =  5280

F =  5280 / 88  =   60  (footballs)

???????

0.6666=2/3

3sqrt(2/3)=sqrt6

We  can  use the 3-D  Pythagorean analog

The distance,  D  =  sqrt ( 3^2 + 4^2  + 15^2)  = sqrt (250)  =   5sqrt (10)  units ≈  15.8  units

Aww, thank you. :))

I really need to work on rereading my answers and being more careful about questions too. 

=^._.^=

You  have 85  beads

85/4  =  21*4  + 1

21/4  =  5*4  + 1

5/4  =   1* 4  +  1

Total  volume = 

(4/3) pi  ( 2^3  + 3^3 + 6^3)  =

(pi )  * (4/3)   ( 251)  =

(1004 / 3)  pi   in^3

The  total possible arrangements  =  ( 6  + 4  + 3)!  =  13 ! 

From this....we  want to subtract  all the arrangents where  the cartoon pins are  together

Note  that  the could occupy  (13 - 4  + 1)  = 10 positions  (positions 1 thru  10)

And for  each of  these  the other pins could be arranged  is  ( 6 + 3)!  = 9 !  ways

So....the  number of possible arrangements where  they  are  not together   =

13!  - 10 (9 !)    =  

6,223,392,000  ways

Either I googled it or maybe I used duckduckgo    or similar......

This makes a right triangle ....the hypotenuse is the ladder ( 15 ft)

   on leg is the graden   5 ft

find the other leg using the Pythagorean theorem    ( w is the other leg = height of window)

15² = 5² + w²

w = sqrt 200 =   10 sqrt 2   ft

So you got it from google

Volume of a cylinder =   pi r^2 h

pi (r+6)^2 * 4  = pi r^2 (h+6)      eliminate pi

(r^2 + 12r + 36)   * 4   = 10 r^2

6r^2 - 48r - 144 = 0

r^2 - 8r -24 = 0          quadratic formula shows r = 4 + 2 sqrt 10   =   10 .32455532