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Blizzard [7]
3 years ago
12

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Mathematics
1 answer:
Sloan [31]3 years ago
5 0

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

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Answer:

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Step-by-step explanation:

total amount paid if offer 1 is accepted:

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total amount paid if offer 2 is accepted:

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Compounding interest refers to interest that earns more interest itself, e.g. in the first offer, the $180 of interests charged for the first year will earn $5.40 in extra interests. While offer 2 only charges $60 in interests during the first year which will in turn earn $3 of interests. The difference between both offers is that interest charges in offer 1 earn more interests than the interest in offer 2 = $5.40 - $3 = $2.40

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Which one doesn’t belong? Why? Explain. please help me
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Determine the truth value of the statement if the domain for all variables is the set of nonnegative integers.
Nadya [2.5K]

The domain for all variables of the set of nonnegative integers given is true.

<h3>How to explain the truth value?</h3>

From the information given, we are given ∃n∀m(m< n). This implies that for all m, there exists n such that m × n where m and n are non negative integers.

This statement is true because for any non negative integer, the least value is zero and the set is unbounded.

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2 years ago
Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential el
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Answer:

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Step-by-step explanation:

we have

n = 25

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