Mathematics: Given: f(x)=0.7x^2+3.2x+1.5, find all roots to the nearest 0.001. what does find all roots mean in this instance?

Given: f(x)=0.7x^2+3.2x+1.5, find all roots to the

Ответ:

xander252577

10.06.2020

Mathematics

(0.0772,0.1688)

Step-by-step explanation:

We are given the following data set:

0.12, 0.08, 0.18, 0.07, 0.12, 0.14, 0.15

n = 7

a) Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where x_i are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{0.86}{7} = 0.123$

Sum of squares of differences = 0.000008163265305 + 0.001836734694 + 0.003265306122 + 0.002793877551 + 0.000008163265305 + 0.0002938775509 + 0.0007367346937 = 0.008942857142

$S.D = \sqrt{\frac{0.008942857142}{6}} = 0.0386$

Confidence interval:

$\mu \pm t_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at}~\alpha_{0.02}\text{ and degree of freedom 6} = \pm 3.142$

$0.123 \pm 3.142(\frac{0.0386}{\sqrt{7}} ) = 0.123 \pm 0.0458 = (0.0772,0.1688)$

b) No, this requirement is not met because the interval contains value greater than 0.165 g as well.

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Given: f(x)=0.7x^2+3.2x+1.5, find all roots to the nearest 0.001. what does find all roots mean in this instance?

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