Answer:
120960
Step-by-step explanation:
Given that a librarian has a set of ten different books, including four different books about Abraham Lincoln.
The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six different books.
First arrnage the 6 other books in the shelf.
This can be done in 
Now arrange the 4 books of Lincoln
This can be done in 
Now we have 7 places to insert Lincoln books including two corners and in between.
Thus this can be done in 7 ways
Total no of ways = 
Answer:
64
Step-by-step explanation:
First, you divide 416 by 65. This gets you 6.4. But it's not 1 in 65 eating pizza, it's 10 out of 65, so then you multiply 6.4 by 10, getting 64.
Answer:
58 feet.
Step-by-step explanation
Since the angle given is across from the length we need to find and we are given the hypotenuse, we use sine.
Sin(46)=x/80 where x is the height of the triangle and 80 is the hypotenuse.
80sin(46)=x
x=57.55 or 58 feet.
Both expression have the same denominator: 9x²-1. Thus it must not be 0.
9x²-1=(3x-1)(3x+1)=0, resulting x=+-1/3.
Restrictions: x in R\{-1/3, 1/3}
Adding those expressions:
E=(-x-2)/(9x²-1 ) + (-5x+4)/(9x²-1)=
(-x-2-5x+4)/(9x²-1)=(-6x+2)/(9x²-1)=
(-2)(3x-1)/(9x²-1)=-2/(3x+1)
E=-2/(3x+1)