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2 years ago

What is the distance between the following points?

Mathematics

1 answer:

timama [110]2 years ago

5 0

Answer:

D. d = $\sqrt{58}$

Step-by-step explanation:

Use the distance formula: d = $\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2} }$

The two points are (6, -2) and (3, -9)

Plug the values into the formula:

d = $\sqrt{(3 - 6)^{2}+ (-9 + 2)^{2} }$

Simplify

d = $\sqrt{(-3)^{2}+ (-7)^{2} }$

d = $\sqrt{9+ 49 }$

d = $\sqrt{58}$

I hope this helps :))

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2 years ago

A population has a standard deviation of 80. A random sample of 400 items from this population is selected. The sample mean is d

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Answer:

$ME= 1.8808 * \frac{80}{\sqrt{400}} =7.5232$

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".

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n=400 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)

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.8808$

The margin of error is given by:

$ME= 1.8808 * \frac{80}{\sqrt{400}} =7.5232$

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2 years ago

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Answer:

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Step-by-step explanation:

We have been given the word the word "GEOMETRY"

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Hence, The required probability is: $\frac{^5C_2\cdot ^3C_1}{^8C_3}$