If x = 1 -√2, find the value of ( x -1/x)^3

In early 2012, the Pew Internet and American Life Project asked a random sample of U.S. adults, "Do you ever ... use Twitter or

8090 [49]

Answer:

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

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0

3 years ago

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a

levacccp [35]

Answer:

$P(x>12) = 0$

Step-by-step explanation:

Given

$x = \{1,2,3,4,5,6,7,8,9,10,11,12\}$ --- outcomes

$n(x) = 12$ -- sample size

Required

$P(x > 12)$

This is calculated as:

$P(x > 12) = \frac{n(x > 12)}{n(x)}$

$n(x>12) = 0$ because none of the outcomes is greater than 12:

So:

$P(x > 12) =\frac{0}{12}$

$P(x>12) = 0$

6 0

2 years ago

Which of the following sets of transformation provides sufficient information to prove the two circles described are similar?

Reika [66]

<h2>Explanation:</h2><h2></h2>

A circle is simply a curve made up of all the points that are the same distance from the center. This distance is called the radius of the circle. It's important to know that <em>all circles are similar to each other</em>, but what is similarity? It's simply, shapes are similar if we can turn one into the other by moving, rotating, flipping, or scaling. So every circle can match any other circle by moving it, rotating it, flipping it, or scaling it.

Then circles O and Q shown below are similar no matter what's the radii of them.

4 0

3 years ago

Please answer these questions.(please include work/explanation)(1)

ohaa [14]

Answer:

Hi there!

I will help you answering the questions, if you do not understand what I'm working about, you can ask me on comment section.

<h3>Number 1</h3>

First of all, we need to multiple the separated function.

$\sf2(3x + 4)(x - 1)(x - 3) \\ = \sf(6x + 8)(x - 1)(x - 3) \\ \tt multiple \: the \: first \: equation \\ \tt(6x + 8) \: with \: (x - 1) \\ \sf = (6x \times x + 6x \times - 1 + 8 \times x + 8 \times - 1)(x - 3) \\ = \sf({6x}^{2} + 2x - 8)(x - 3) \\ \tt then \: multiple \: the \: last \: one \\ \tt (6 {x}^{2} + 2x - 8) \: with \: (x - 3) \\ \sf = \boxed{ \bold{ \red{ {6x}^{3} - 16x {}^{2} - 14x + 24}}}$

So the right answer is <u>A</u>

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<h3>Number 2</h3>

the graph has four zeros at :

-4
-2/3
0
9

After that we make them equal with 0, here is the thing:

x = -a is equal with x + a = 0

So we can conclude that :

-4 → x + 4 = 0
-2/3 → 3x + 2 = 0
0 → x = 0
9 → x - 9 = 0

Then we substitute them to a function :

x(x + 4)(3x + 2)(x - 9) = 0

3x⁴ - 13x³ - 118x² - 72x = 0

Then we looking on the option which one is equal with the answer above.

The right answer is <u>B</u>

━━━━━━━━━━━━━━━━━

Hope It Helps!

3 0

2 years ago

Show your work and the answer please

Fofino [41]

Answer:

-0.375

Step-by-step explanation:

Writing -3/8 as a decimal using division method:

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Here, the fraction is -3/8 which means we need to perform 3 ÷ 8.

This gives the answer as -0.375. So, -3/8 as a decimal is -0.375

7 0

2 years ago