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4 years ago

Find the angle θθ between the vectors v=2i+kv=2i+k, w=j−3kw=j−3k.

1 answer:

4 0

Hello :
v . w = | | v | | × | | w | | cos(θ) ....(1)
v(2,0,1) w(0,1,-3)

v . w = (2)(0)+(0)(1)+(1)(-3) = - 3
| | v | | = √((2)²+(0)²+(1)²) = √5
| | w | = √((0)²+(1)²+(-3)²) = √10
by (1) :
cos(θ) = (v . w ) / | | v | | × | | w | |

cos(θ) = = - 3/√50
θ =..... calculate by 2ind function ( calculator)

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Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

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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.

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$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

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meriva

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Step-by-step explanation:

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