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grandymaker [24]
4 years ago
15

Complex numbers, simplify the following expression; 10/1+3i

Mathematics
1 answer:
svp [43]4 years ago
8 0
\frac{10}{1 + 3i} =  \frac{10}{1 + 3i} * \frac{1-3i}{1-3i} =  \frac{10-30i}{1^{2} -(3i)^{2}} = \frac{10-30i}{1 -9 i^{2} } = \frac{10-30i}{1 -9*(-1)} = \frac{10(1-3i)}{1+9}= \frac{10(1-3i)}{10} = 1 -3i
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Find the area of an acute triangle with a base of 13 inches and a height of 5 inches.​
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A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex
Olenka [21]

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a

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     0.533  <  p <  0.64

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Considering question a

From the question we are told that

      The sample size is  n = 200

      The number of student that receives financial aid is k = 118

Generally the sample proportion is  

      \^ p = \frac{k}{n}

=>   \^ p = \frac{118}{200}

=>   \^ p = 0.59

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.10

Generally from the normal distribution table the critical value  of \frac{\alpha }{2}  is  

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Generally the margin of error is mathematically represented as  

     E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }

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Generally 90% confidence interval is mathematically represented as  

      \^ p -E <  p <  \^ p +E

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Considering question b

From the question we are told that

    The margin of error  is  E = 0.03

From the question we are told the confidence level is  99% , hence the level of significance is    

      \alpha = (100 - 99 ) \%

=>   \alpha = 0.01

Generally from the normal distribution table the critical value  of   is  

   Z_{\frac{\alpha }{2} } = 2.58

Generally the sample size is mathematically represented as      

        [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>      n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )

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3 years ago
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