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Snowcat [4.5K]
2 years ago
5

Use the binomial expression (p+q)^n to calculate a binomial distribution with n=5 and p=0.3.(Show all steps)

Mathematics
1 answer:
Helen [10]2 years ago
8 0

Answer:

The binomial in expanded form is (0.3 + q)^{5} = \frac{243}{100000} + \frac{81}{2000}\cdot q + \frac{27}{100}\cdot q^{2} + \frac{9}{10} \cdot q^{3} + \frac{3}{2}\cdot q^{4} + q^{5}.

Step-by-step explanation:

The Binomial Theorem states that a binomial of the form (a + b)^{n} can be expanded by using the following identity:

(a + b)^{n} = \Sigma \limits^{n}_{k = 0}\,\frac{n!}{k!\cdot (n-k)!}\cdot a^{n-k}\cdot b^{k} (1)

If we know that a = p = 0.3 and n = 5, then the expanded form of the binomial is:

(p+q)^{n} = \frac{243}{100000} + 5\cdot \left(\frac{81}{10000} \right)\cdot q + 10\cdot \left(\frac{27}{1000})\cdot q^{2} + 10\cdot \left(\frac{9}{100} \right)\cdot q^{3} + 5\cdot \left(\frac{3}{10} \right)\cdot q^{4} + q^{5}

(0.3 + q)^{5} = \frac{243}{100000} + \frac{81}{2000}\cdot q + \frac{27}{100}\cdot q^{2} + \frac{9}{10} \cdot q^{3} + \frac{3}{2}\cdot q^{4} + q^{5}

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Have a nice day :D

Step-by-step explanation:

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Please help me as fast as you can. thanks
Angelina_Jolie [31]

Answer:

<h2><DEF = 40</h2><h2><EBF = <EDF = 56</h2><h2><DCF = <DEF =40</h2><h2><CAB = 84</h2>

Step-by-step explanation:

In triangle DEF, we have:

<u>Given</u>:

<EDF=56

<EFD=84

So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)

____________

DE is a midsegment of triangle ACB

( since CD=DA(given)=>D is midpoint of [CD]

and BE = EA => E midpoint of [BA] )

According to midsegment Theorem,

(DE) // (CB) "//"means parallel

and DE = CB/2 = FB =CF

___________

DEBF is a parm /parallelogram.

<u>Proof</u>: (DE) // (FB) ( (DE) // (CB))

AND DE = FB

Then, <EBF = <EDF = 56

___________

DEFC is parm.

<u>Proof</u>: (DE) // (CF) ((DE) // (CB))

And DE = CF

Therefore, <DCF = <DEF =40

___________

In triangle ACB, we have:

<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)

HOPE \:  THIS \:  HELPS.. GOOD  \: LUCK!

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