Factorize this term: (a+b)raise to the power of 4 +4

malfutka [58]

Its f^8!!!!!!!!!!!!!!

8 0

3 years ago

A survey was conducted in the United Kingdom, where respondents were asked if they had a university degree. One question asked,

katovenus [111]

Answer:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

Step-by-step explanation:

Data given and notation

$X_{1}=45$ represent the number of correct answers for university degree holders

$X_{2}=57$ represent the number of correct answers for university non-degree holders

$n_{1}=373$ sample 1 selected

$n_{2}=639$ sample 2 selected

$p_{1}=\frac{45}{373}=0.121$ represent the proportion of correct answers for university degree holders

$p_{2}=\frac{57}{639}=0.0892$ represent the proportion of correct answers for university non-degree holders

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportions are different between the two groups, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{45+57}{373+639}=0.101$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.121-0.0892}{\sqrt{0.101(1-0.101)(\frac{1}{373}+\frac{1}{639})}}=1.620$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =2*P(Z>1.620)=0.105$

If we compare the p value and using any significance level for example $\alpha=0.05$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the two proportions are not statistically different at 5% of significance

7 0

3 years ago

A portion of the Quadratic Formula proof is shown. Fill in the missing statement.

Zielflug [23.3K]

Answer:

Option A.

Step-by-step explanation:

we have

$x+\frac{b}{2a} =\pm\sqrt{\frac{b^2-4ac}{4a^2}}$

Simplify the right side of the equation

we know that

$\pm\sqrt{\frac{b^2-4ac}{4a^2}}=\pm\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}=\pm\frac{\sqrt{b^2-4ac}}{2a}$

so

The expression is

$x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}$

therefore

x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a

4 0

3 years ago

Using the graph at the left, it shows the height h in feet

soldi70 [24.7K]

Answer:

1 second

Step-by-step explanation:

h(+-)16+power 2+128+

5 0

3 years ago

Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang.

Kaylis [27]

Answer:

height: 9 chi 6 cun
width: 2 chi 8 cun

Step-by-step explanation:

The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.

Let x and y represent the width and height, respectively. In terms of zhang, we have ...

y - x = 0.68

x^2 +y^2 = 1^2

Substituting y = 0.68 +x into the second equation gives ...

x^2 + (x +0.68)^2 = 1

2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1

Using the quadratic formula, we have ...

x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4

x = 0.28 . . . . . the negative root is of no interest

y = 0.28 +0.68 = 0.96

In units of chi and cun, the dimensions are ...

height: 9 chi 6 cun

width: 2 chi 8 cun

6 0

3 years ago

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