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Jane rate    1 job / 15 days      John rate =  1 job/10 days

together     1 job / ( 1/15 + 1/10)   = 1/ ( 2/30 + 3/30)   = 1/ ( 5/30) = 30 / 5 = 6 days

thanks that will help. 

This just seems needlessly tedious........

Go! , asinus, GO!   LOL ......

x  and  8x  if  x is a perfect square then

sqrt (x) = integer       then sqrt (8x) = integer * sqrt 8         you are stuck with sqrt 8 as a factor.....not an integer

Setting a, b, and c is really smart. 

a = 3x

b = 5y

c = -6z

3x + 5y - 6z = 2

a + b + c = 2

5xy - 10yz - 6xz = -41

ab + bc + ac = -123

xyz = 6

abc = -540

x^3 - 2x^2 - 123x + 540

(x - 5)(x - 9)(x + 12)  # I don't know how to factor cubic equations, I just plugged it into a calculator. 

x = 5, 9, -12

a = 3x

b = 5y

c = -6z

a = 5, b = 9

5/3 + 9/5 = 52/15

a = 5, b = -12

5/3 - 12/5 = -11/15

a = 9, b = 5

9/3 + 5/5 = 4

a = 9, b = -12

9/3 - 12/5 = 3/5

a = -12, b = 5

-12/3 + 5/5 = -3

a = -12, b = 9

-12/3 + 9/5 = -11/5

Everything looks right to me, I'm not sure why it's wrong. :((

Looking at Asinus's answer from the link guest sent, he had the same aproach too. 

=^._.^=

I couldn't  get  it  to  add  up either, EP   !!!!!

Volume of  the  hemisphere   =  

(1/2) (4/3)  pi ( 3)^3    =   18 pi   cm^3

To  find  the  radius  of  the  original bubble

18 pi   = ( 4/3) pi  ( r)^3

18 ( 3/4)  =  r^3

(27/2)  =  r^3

cube root   ( 27 / 2)  =  r     =     3  / cube root 2    cm  ≈   2.38 cm

10 * 10 * 10  * 1/3 = 500 cubic inches of water

    then add    10  cubic inches of ice     =     510 in³   total

yeah i got it

Are you sure you posted the numbers correctly?    In particular the   20   number.....but it could be oneof the others....is there only 30 students?

The numbers don't add up....here is a Venn Diagram    (bottom nember is 13)

Note  that  every hour.....the  faster  car  makes  up     60  -  45   =  15 miles on the slower car

So.....to close  a  30 mile gap   it will take    30   /  15   =    2  hours

this is a repost btw it wasnt answered earlier

thank you :))

6^2*pi*10/2. 

It's the volume of a cylinder/2. 

=^._.^=

Re - write as

x^2 + 12x + 9 = 0        in the QUadratic formula   a =1    b = 12   c = 9

\(x = {-12 \pm \sqrt{12^2-4(1)(9)} \over 2(1)a}\)     You can finish I'm sure !     (Ignore the 'a' on the bottom....I forgot to delete it) 

You're welcome. :))

=^._.^=

Let's start with the 5 by 3 graph. 

You need to go 3 Up and 5 Right in some combination. 

8!/3!/5! = 56. 

Now the 2 by 2 graph. 

You need to go 2 Up and 2 Right in some combination. 

4!/2!/2! = 6. 

56*6 = 336

=^._.^=

Thanks!

LCM(4, 6) = 12

100/12 = 8.333333

So our answer is 8. 

=^._.^=

thank you :)

floor((100185-100000)÷9 + 1)=21