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oee [108]
3 years ago
7

Find all solutions to the equation equation (x - 1)^2 = -4.

Mathematics
1 answer:
tatuchka [14]3 years ago
6 0

Answer:

x = 1±2i

Step-by-step explanation:

(x - 1)^2 = -4.

Take the square root of each side

sqrt( (x - 1)^2) = sqrt(-4)

Sqrt(ab) = sqrt(a)sqrt(b)

We know the sqrt(4) = 2 and the sqrt(-1) = ±i

x-1 = ±2i

Add 1 to each side

x-1+1 = 1±2i

x = 1±2i

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Read 2 more answers
A country's education department reported that in 2015, 70.8% of students enrolled in college or a trade school within 12 months
Gennadij [26K]

Answer:

The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

In 2017, a random sample of 154 individuals who graduated from high school 12 months prior was selected. From this sample, 94 students were found to be enrolled in college or a trade school.

This means that n = 154, \pi = \frac{94}{154} = 0.6104

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

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The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6104 + 1.645\sqrt{\frac{0.6104*0.3896}{154}} = 0.675

The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.

6 0
3 years ago
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