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:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or <em>20%</em> is alcohol. So let's just say that x=alcohol and y=water, this means that: 
where c is the total amount in the glass. This means that: 
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: 
and that: 
.
So if we're going to add the two glasses, we simply add the two sides, and get: 
. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: 
Now we can add like terms to get the equation: 
. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Answer: 3• D 4• B (why does this require me to put 20 characters) anyway this is my guess
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
<h3>What is the Angle of Intersecting Chords Theorem?</h3>
According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.
Applying the angle of intersecting chords theorem, let's find x first:
73 = 1/2(96 + x)
Multiply both sides by 2
2 × (73) = 1/2(96 + x) × 2
146 = 96 + x
Subtract both sides by 96
146 - 96 = 96 + x - 96
50 = x
x = 50°
Therefore:
x + z + 96 + 114 = 360° [full circle measure]
Plug in the value of x
50 + z + 96 + 114 = 360
z + 260 = 360
Subtract both sides by 260
z + 260 - 260 = 360 - 260
z = 100°
The answer is: D. 100°.
Learn more about the angle of intersecting chords theorem on:
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