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3 years ago

Solve the following equation. 2x - 1 ≤ x 5

1 answer:

5 0

2x−1≤x5

Let's find the critical points of the inequality.

2x−1=x^5

2x−1−x^5=x^5−x^5 (Subtract x^5 from both sides)

−x^5+2x−1=0

(−x+1)(x^4+x^3+x^2+x−1)=0 (Factor left side of equation)

−x+1=0 or x^4+x^3+x^2+x−1=0 (Set factors equal to 0)

x=1 or x=0.51879 or x=−1.290649

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The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed t

Lady bird [3.3K]

Answer:

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =0.1$ represent the population standard deviation

n 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)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=10.08$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

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

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

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3 years ago

Can someone please explain to me how to do this I don't understand it at alll!

elena-s [515]

Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

In right triangle ABC shown below, what is the degree measure of ZC ?

Luden [163]

Answer:

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3 years ago

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Jlenok [28]

Answer:

1200 more beats in 3 seconds or

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Step-by-step explanation:

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2 years ago