ElectricPavlov

You are correct.....

they could be separated like this : 

 |     |     |     |     |     |     |     |     |     |   

T               T               T         T                   

                 or other ways.....   let me think about how to derive the answer for a little while......If I come up with a solution I will let ya know !

THANX !  ~ EP

Saw this presented the other day as

0 = 1 000 000  * .9^t

    This is just not possible to ever equal zero.....   . 9^t    will never equal 0

             in approx 131 days   (for  't' ) the value is  1      after that, as the value of 't increases the vlaue of f(t) is below one....but never ' 0 '

                  in 200 days the value is .000705              but it never reaches  ' 0 '   no matter how many days you put in for 't'

FOUR ways to keep the four  TRUES   separated in the line up of 10 questions

 |     |     |     |     |     |     |     |     |     |   

T         T          T         T                          This is one way.....then you can shift the line of trues to the right 3 more times    total   4 ways

From the picture below yo can see that the shaded area will be 12 semicircles of diameter 2    (radius 1)

    12 semi circles = 6 circles of radius 1

        6   * pi (r^2)   = 6 pi

144 degrees....here is a picture to explain:

There are 4 slots for math books    12 ways to place them   (4 P 2)

    for each of those 12 placements the other books can be arranged  4 * 3 * 2 * 1 = 24 ways

24 * 12 = 288 ways

14 / x    /   2/(5x)=

14 / x   *  5x / 2 =

70 /2 = 35

First  p (q(x) =

   (2x^3 +1)^2    = 4x^6 + 4x^3 + 1

       then add r(x)

                   4x^6      + 7x^4      + 4x^3 -5x^3      - 6x    -2  +1 =

                    4x^6     + 7x^4     - x^3   - 6x   -1

First digit   4 choices

Second digit 4 choices

Third digt   2 choices   (only  3 and 5 as we want odd numbers)

4 x 4 x 2   =  32 possibles

https://web2.0calc.com/questions/help-plz-thx_2#r1