Explanation:
a)
![{3 \choose 2} = \frac{3!}{2!(3-2)!} = \frac{6}{2*1} = 3](https://tex.z-dn.net/?f=%20%7B3%20%5Cchoose%202%7D%20%3D%20%5Cfrac%7B3%21%7D%7B2%21%283-2%29%21%7D%20%3D%20%5Cfrac%7B6%7D%7B2%2A1%7D%20%3D%203%20)
![{3 \choose 1} = \frac{3!}{1!(3-1)!} = \frac{6}{1*2} = 3](https://tex.z-dn.net/?f=%20%7B3%20%5Cchoose%201%7D%20%3D%20%5Cfrac%7B3%21%7D%7B1%21%283-1%29%21%7D%20%3D%20%5Cfrac%7B6%7D%7B1%2A2%7D%20%3D%203%20)
b) First, we have that
![{n \choose k} = \frac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=%20%7Bn%20%5Cchoose%20k%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D%20)
On the other hand,
![{n \choose n-k} = \frac{n!}{(n-k)!(n(n-k))!} = \frac{n!}{(n-k)!k!}](https://tex.z-dn.net/?f=%20%7Bn%20%5Cchoose%20n-k%7D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-k%29%21%28n%28n-k%29%29%21%7D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-k%29%21k%21%7D%20)
Therefore, both expressions are equal. This makes sense, because selecting k elements from a group of n is the same than specify which elements you will not select. In order to specify those elements you need to select the n-k elements that will not be selected. Hence, each time you are selecting k from n, you are also selecting n-k from n, and from that reason both combinatorial numbers are equal.
X^2-2x -3 =0
a =1 b =-2 and c = -3
x = - (-2) +/- sqrt (-2)^2 - 4(1)(-3)
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2(1)
x = + 2 +/- sqrt [(4) - 4(-3)]
-------------------------------
2
x = +2 +/- sqrt [4 + 12]
--------------------------
2
x = +2 +/- sqrt[16]
-------------------
2
x = +2 +/- (4)
-------------
2
x = 2 + 4 or 2 -4
------- ------
2 2
x = 6/2 or -2/2
x = 3 or x = -1
Answer:
$5.33
Step-by-step explanation:
12 divided by 9=1.333333
6 divided by 4.5= 1.333333
4 multiplied by 1.333333=5.33
^^To solve you must use the fractional exponent rule.
I dont quite understand what the question is asking but thats what I have to help :)
1) this is simply solving it, so if you divide 16 by 3, you end up getting 5 1/3
2) 3 1/2, by multiplying 7 by 1/2
3) 224, by multiplying 14 by 16
4) 54 mph, by dividing 324 by 6
5) blue, because only the 1/4 ribbon color would be collected after 3/4 mile
6) 7/8 - 3/8 equals 4/8, or 1/2 when simplified