CPhill

A 25 foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down 4 feet, how many feet will the bottom slide out?

In the first instance, the ladder's height up the wall =

√ [25^2 −  7^2]  = √ [625 −  49]  = √ 576   =  24 ft

If it slips down 4 ft....the bottom  will be

√ [25^2 −  20^2]  = √ [625 −  400]  = √ 225   =  15 ft     from the wall

So....he bottom slides out  15 −  7   = 8 ft

Very nice, Melody.....!!!!

Well....three "great minds"  couldn't possibly be wrong.......LOL!!!!!

"Quadruple"   = "fourth"  ....so......

⁴√ 242    ≈   3.94415      .....[ assuming the principle root   ]

I don't see much room for debate here, EP...........LOL!!!!!

Here's my take:

Total identifiable "words"  generated by the arrangements of the letters in"SEVEN"   =

5!  / 2!  =   120  / 2   =   60

Possible identifiable "words"  formed by having "E's"  next to each other  = the "E's"  can occupy any of 4 positions....and for each of these......the oher letters can be arranged in 3!  = 6 ways  =  4 * 6    = 24

So.....the probability =   24/ 60    =    2 / 5

I agree with NinjaAnswer  !!!!

Use the inverse cosine  :

arccos ( 0.7977 )  = x  ≈  37.09°

Another way to see this  =  total arrangements possible  less the arrangements where the math books are together

Total arrangements  =  6!   = 720

Total arrangemens where the  math books are together = they can occupy any of 5 positions....and for each of these positions, they can be arranged in two ways......and for each of these, the other books can be arranged in 4! ways  ......so we have     5 * 2! * 4!  =  10 * 24   = 240

So........720 −  240   =    480 ways

As NinjaAnswer found  !!!!

Total arrangements possible  = 10!

Arrangements where the three prints are together  =

They can occupy any of 8 positions...and for each of these, they can be arranged in 3! ways.....and the other prints can be arranged in 7! ways......so we have

8 * 3!  * 7 !

So....the total probability  is :

[ 8 * 3! * 7! ]  /  10!    =      [8 * 6] / [10 * 9 * 8 ]  = 6  / 90   =  1 / 15

The probability  = 1 − P( 0 heads)  − P(1 head)

P(0 heads)  =  (1/2)^6  =  1/64

P (1 head)  = C(6,1) (1/2)(1/2)^5 = 6 *(1/2)^6  =  6/64

So....the total probability  = 1 − 1/64 − 6/64  = 57/64