Answer:The better buy Option is A
Step-by-step explanation:
Answer:
The roots are
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![x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\](https://tex.z-dn.net/?f=x%20%3D%20%20-%203%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%20i%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%20%20-%203%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20i%20%5C%5C%20)
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Step-by-step explanation:
9x² + 54x + 82 = 0
Using the quadratic formula
That's
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![x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%20b%5Cpm%20%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20%20-%204ac%7D%20%7D%7B2a%7D%20)
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From the question
a = 9 , b = 54 , c = 82
Substitute the values into the above formula and solve
That's
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![x = \frac{ - 54\pm \sqrt{ {54}^{2} - 4(9)(82)} }{2(9)} \\ x = \frac{ - 54\pm \sqrt{2916 - 2952} }{18} \\ x = \frac{ - 54\pm \sqrt{ - 36} }{18} \\ x = \frac{ - 54\pm 6i}{18}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%20-%2054%5Cpm%20%5Csqrt%7B%20%7B54%7D%5E%7B2%7D%20%20-%204%289%29%2882%29%7D%20%7D%7B2%289%29%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B%20-%2054%5Cpm%20%5Csqrt%7B2916%20-%202952%7D%20%7D%7B18%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B%20-%2054%5Cpm%20%5Csqrt%7B%20-%2036%7D%20%7D%7B18%7D%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B%20-%2054%5Cpm%206i%7D%7B18%7D%20)
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Separate the real and imaginary parts
That's
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![x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i](https://tex.z-dn.net/?f=x%20%3D%20%20-%20%20%5Cfrac%7B54%7D%7B18%7D%20%5Cpm%20%5Cfrac%7B6%7D%7B18%7D%20%20%5C%3A%20i%20%5C%5C%20x%20%3D%20%20-%203%5Cpm%20%5Cfrac%7B1%7D%7B3%7D%20i)
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We have the final answer as
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![x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\](https://tex.z-dn.net/?f=x%20%3D%20%20-%203%20%2B%20%20%5Cfrac%7B1%7D%7B3%7D%20%20i%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%3D%20%20-%203%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20i%20%5C%5C%20)
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Hope this helps you
Answer:
![706.85 {cm}^{2}](https://tex.z-dn.net/?f=706.85%20%7Bcm%7D%5E%7B2%7D%20)
Step-by-step explanation:
![area =\pi {r}^{2} \\ = \pi \times 15 \times 15 \\ = 706.85 {cm}^{2}](https://tex.z-dn.net/?f=area%20%3D%5Cpi%20%20%7Br%7D%5E%7B2%7D%20%20%5C%5C%20%20%3D%20%5Cpi%20%5Ctimes%2015%20%5Ctimes%2015%20%5C%5C%20%20%3D%20706.85%20%7Bcm%7D%5E%7B2%7D%20)
If the sample size of population is 24 then the number of degrees of freedom for reading the t value is 23 which is option c.
Given sample size of 24,mean 23.
We have to determine the number of degrees of freedom which will be used to find the critical values of t.
Degree of freedom is the number of values in the final calculation of a statistic that are free to vary means that can change their values in the formula of calculating t.
t=(X-μ)/s/![\sqrt{n}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D)
where X is sample mean ,
μ is hypothsised population mean
s is sample standard deviation
n is sample size.
Degree of freedom=n-1
In this question n is 24 so the degree of freedom =24-1=23.
Hence the number of degrees of freedom for reading the t value is 23.
Learn more about degree of freedom at brainly.com/question/17305237
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