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aliina [53]
1 year ago
6

3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20n%5C%5C%20evaluate%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%5C%3A%20%CE%A3%20%20%5C%3A%20%28nCi%29%5C%5C%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20i%20%3D%200" id="TexFormula1" title=" \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0" alt=" \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0" align="absmiddle" class="latex-formula">
Evaluate the summation​
Mathematics
1 answer:
Sedaia [141]1 year ago
7 0

Assuming you mean

\displaystyle \sum_{i=0}^n {}_nC_{i}

where

{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}

we have by the binomial theorem

\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}

so that the given sum has a value of \boxed{2^n}.

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son4ous [18]
<h2>Hello!</h2>

The answer is:

The second option,

Zackery, because AB=BC

<h2>Why?</h2>

To identify which type of triangle is the triangle formed by the given points, first, we need to calculate the distance between the points.

So, finding the distances we have:

From A to B: (2,3) and (4,4)

distance=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}\\\\distance=\sqrt{(4-2)^{2} +(4-3)^{2}}=\sqrt{2^{2} +1^{2} }=\sqrt{4+1}=\sqrt{5}=2.24units

From B to C: (4,4) and (6,3)

distance=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}\\\\distance=\sqrt{(6-4)^{2} +(3-4)^{2}}=\sqrt{2^{2} +(-1)^{2} }=\sqrt{4+1}=\sqrt{5}=2.24units

Hence, since the distances AB and BC are equal, the triangle is an isosceles triangle, so the answer is:

Zackery, because AB=BC

Have a nice day!

7 0
3 years ago
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Viefleur [7K]

Answer:

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Answer:

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To find greatest common factor , we write each term in factor form

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