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3 years ago

What is the solution of the equation when solved over complex numbers? x^2+27=0

1 answer:

7 0

${x}^{2} + 27 = 0 \\ {x}^{2} = - 27 \\ x = + - \sqrt{ - 27} \\ x = + - \sqrt{27 \times ( - 1) }$
$x = + - 3 \sqrt{3} \times \sqrt{ - 1}$
$x = + - 3 \sqrt{3} i$

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3 years ago

A researcher wishes to estimate, with 9090% confidence, the proportion of adults who have high-speed Internet access. Her es

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Answer: a) Required minimum sample size= 219

b) Required minimum sample size= 271

Step-by-step explanation:

As per given , we have

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Critical z-value for 90% confidence interval : $z_{\alpha/2}=1.645$

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Formula to find the sample size :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.28(1-0.28)(\dfrac{1.645}{0.05})^2\\\\=218.213856\approx219$

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b) If no estimate of true proportion is given , then we assume p= 0.5

Formula to find the sample size :-

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Required minimum sample size= 271

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3 years ago

Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probabi

r-ruslan [8.4K]

Answer:

15.85%

Step-by-step explanation:

The empirical rule states that:

68% of all data falls within 1 standard deviation of the mean
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99.7% of all data falls within 3 standard deviation of the mean

When we say 1,2,3 standard deviation of the mean, that is, it is evenly distributed in both sides of the mean. For example:

68/2 = 34% of data falls within mean - 1*standard deviation, and

also, 34% of data falls within mean + 1*standard deviation

Now, we see that 192 - 27 = 165, so this is 1 standard deviation of the mean [mean - 1*standard deviation], so 34% of data fall in that range.

But we want, data that ARE FEWER than 165. So, we use property of normal distribution.

Half of data (50%) is left of mean, of which 34% fall within 1 standard deviation So the remaining would fall fewer than 165.

That is 50 - 34 = 16 - 0.15 = 15.85%

Note: since 99.7% fall within 3 standard deviation of mean, so 100 - 99.7 = 0.3 which is distributed in both sides, so 0.3/2=0.15 is subtracted

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3 years ago

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Answer:

It is already rounded to the nearest tenth! Hope this helps!

Step-by-step explanation:

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