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And, make sure they are even

First one:

https://web2.0calc.com/questions/pl-hhelp-quick#r1

If you need help for getting the outside, all you have to do is list all the numbers from 20 to 50 that does not include numbers from A and B.

Height of a triangle is   √3 / 2

Diagonal of a large square is  1 + √3

Area = ( 1 + √3 )² / 2

1 - 15^2 =9^2 + 12^2
2 - 17^2 =8^2 + 15^2
3 - 25^2 =20^2 + 15^2
4 - 39^2 =36^2 + 15^2
5 - 113^2 =112^2 + 15^2

Q  1019    answer is  B

Q 17370    Area is:   NOT (a U b)      Not sure of the notation used .....is that  ( A  U  B)'   ???

tan 30 =  1/sqrt3 =  a/AD

              AD = sqrt 3  *a

tan45 = 1 = a/DB

            DB = a

AD + DB  = AB   = sqrt3 * a  + a  = (1+ sqrt 3) a

figured it out! :)

nvm figured it out!

The following are number of ways you can choose 2 numbers out of 10:
{1, 2} | {1, 3} | {1, 4} | {1, 5} | {1, 6} | {1, 7} | {1, 8} | {1, 9} | {1, 10} | {2, 3} | {2, 4} | {2, 5} | {2, 6} | {2, 7} | {2, 8} | {2, 9} | {2, 10} | {3, 4} | {3, 5} | {3, 6} | {3, 7} | {3, 8} | {3, 9} | {3, 10} | {4, 5} | {4, 6} | {4, 7} | {4, 8} | {4, 9} | {4, 10} | {5, 6} | {5, 7} | {5, 8} | {5, 9} | {5, 10} | {6, 7} | {6, 8} | {6, 9} | {6, 10} | {7, 8} | {7, 9} | {7, 10} | {8, 9} | {8, 10} | {9, 10} (total: 45)

Their sums =(3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 19)>Total = 45

There are 39 out of 45 which are 8 and >. Therefore, the probability is: 39 / 45

(1) sqrt2  + 1/2 sqrt2      +  (1) sqrt3  + 1/3 sqrt3 =

3/2 * sqrt2      + 4/3 * sqrt 3 =

9 sqrt2  + 8 sqrt 3

             6

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Bob rate   1 table /4hr  = 1/4

Sue rate   = 1/6

Jim rate  = 1/12

Build 1 table          1  /  (1/4 + 1/6 +1/12 )   hr   = 2 hours 

First, let's decide what the denomintor will be. In this case, it is 10 times 9, which is 90. Since there can be repeats of the same group, we devide by 2!, which is 2, and that will give us 90

From here, let's see what combos will end up being greater than or equal to 8 by using a table:

Now, we have to add all the totals up. This is 4+5+6(2)+7+8+4(9) = 72. Dividing by 2, we get 36. Therefore, the probability is 36/45, which is 4/5.

Line equation    y = mx + b     m = slope  =   (y1-y2) / (x1-x2)

    then you will have    y = m x + b 

                                            plug in one of the given points to calculate 'b' and complete your equation

From an online listing:

9  12  15

15  20 25

15  36  39

8 15 17            That is all I saw....

....and the one the guest listed below...that I missed...     15  112   113

Area of triangle = 1/2 b h  =   1/2  2r * 2r  = 2r^2  

           2r^2 = 20

            r^2 = 10

Area of rectangle   3r x 2r = 6 r^2      = 60

Area of semicircle  1/2   pi r^2 =         = 5pi

Add the REDs for the total area  

The first candle burns at rate   1 candle / 4 hrs

    multiply rate * time   to get amount burned    1/4 t

       the amount REMAINING  is    1 candle - 1/4 t    = 1- 1/4t

 Similarly for the SECOND candle, the amount remaining is   1 - 1/3 t

We want the time for the length of first to be 2 times length of second:

1-1/4t   =  2   *   (1 - 1/3t)     solve for   t = ........ hrs

Thank you so much!!!! I was able to solve it myself using the first few lines that you gave me! There are a bunch of trolls on this website that just post completely wrong answers. Thank you!

To start: 

2^{a + 3} + 3^{b + 1}  =  33   --->   8·2^a + 3·3^b =  33   --->   3·3^b  =  33 - 8·2^a 

               --->    3^b  =  ( 33 - 8·2^a ) / 3

2^{2a - 1} + 3^{b + 2}  =  11   --->   ½·2^2a + 9·3^b  =  11   --->   9·3^b  =  11 - ½·2^2a 

              --->   3^b  =  ( 11 - ½·2^2a ) / 9

Setting these equal to each other:  ( 33 - 8·2^a ) / 3  =  ( 11 - ½·2^2a ) / 9

Multiply by 9:                                     3·( 33 - 8·2^a )  =  ( 11 - ½·2^2a )

                                                                99 - 24·2^a  =  11 - ½·2^2a 

Multiply by 2:                                         198 - 48·2^a  =  22 - 2^2a

                                                      2^2a - 48·2^a - 176  =  0

Factor:                                             (2^a - 4)(2^a - 44)  =  0

So, either:  2^a  =  4   --->   a  =  2

            or:  2^a  =  44   --->   a  =  log(44) / log(2)

etc ....

Two numbers    x     and   x-21    sum to 63

x     +      x-21     = 63

2x = 84       x = 42      x-21 = 21  

9 (x^2 + 8/3 )       complete the square

9 ( x+ 8/6)^2        now put '9' back into the parentheses  expand to find 'a'

   (3x+4)²                expand to see what 'a' is

9x^2 +24x + (16)            a = 16

See https://web2.0calc.com/questions/help_35095#2