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3 years ago

Solve the Quadratic Equation By Completing the Square b^2-15b-54=0

1 answer:

vladimir1956 [14]3 years ago

3 0

$b^{2}-15b-54=0. \newline
b^{2}-15b=54. \newline
b^{2}-15b+(\frac{15}{2})^{2}=54+(\frac{15}{2})^{2}. \newline
(b-\frac{15}{2})^{2}=\frac{441}{4}. \newline
b-\frac{15}{2}=\pm\frac{21}{2}. \newline
b=\pm\frac{21}{2}+\frac{15}{2}. \newline
b_1 = -3, b_2 = 18.$

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$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

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And the best option would be:

C. [17.42,20.78]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$