Which are the roots of x^2-4x+4=20

Is 2.55 a irrational, rational, integer, whole number or natural number?

satela [25.4K]

So, the first thing we need to know is what is what.

So, A natural number is a whole number

A whole number is an integer

and An integer is a rational number.

Now, since there is a terminating decimal (a decimal that does not go on forever) we know it is a rational number.

Since there is a decimal, it cannot be an integer, therefore

It is a rational number

4 0

3 years ago

Luda [366]

Answer:

a) H0: There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

b) $\chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75$

c) $\chi^2_{crit}=5.991$

d) Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

High school Some College Bachelor or higher Total

Public Broadcasting 15 15 10 40

Commercial stations 5 25 10 40

Total 20 40 20 80

We need to conduct a chi square test in order to check the following hypothesis:

Part a

H0: There is no association between level of education and TV station preference (Independence)

H1: There is association between level of education and TV station preference (No independence)

The level os significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

Part b

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{20*40}{80}=10$

$E_{2} =\frac{40*40}{80}=20$

$E_{3} =\frac{20*40}{80}=10$

$E_{4} =\frac{20*40}{80}=10$

$E_{5} =\frac{40*40}{80}=20$

$E_{6} =\frac{20*40}{80}=10$

And the expected values are given by:

High school Some College Bachelor or higher Total

Public Broadcasting 10 20 10 40

Commercial stations 10 10 20 40

Total 20 30 30 80

Part b

And now we can calculate the statistic:

$\chi^2 = \frac{(15-10)^2}{10}+\frac{(15-20)^2}{20}+\frac{(10-10)^2}{10}+\frac{(5-10)^2}{10}+\frac{(25-10)^2}{10}+\frac{(10-20)^2}{20} =33.75$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(2-1)(3-1)=2$

Part c

In order to find the critical value we need to look on the right tail of the chi square distribution with 2 degrees of freedom a value that accumulates 0.05 of the area. And this value is $\chi^2_{crit}=5.991$

Part d

And we can calculate the p value given by:

$p_v = P(\chi^2_{3} >33.75)=2.23x10^{-7}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(33.75,2,TRUE)"

Since the p value is lower than the significance level we enough evidence to reject the null hypothesis at 5% of significance, and we can conclude that we have dependence between the two variables analyzed.

7 0

3 years ago

What scale factor was applied to the first rectangle to get the resulting image?

sdas [7]

Answer:

Step-by-step explanation:

In this question, it is given that, A rectangle with a short side of 6. An arrow points to a smaller rectangle with a short side of 1.5 .

The shorter side of first rectangle is of measurement 6 units and of second rectangle, is of size 1.5units .

To find the scale factor, we have to do division of the shorter sides of the first and second rectangle, that is

So the scale factor is 0.25 .

4 0

3 years ago

Read 2 more answers

In an election, Mr. Jones received 70% of the 1,500 votes cast. How many votes did Mr. Jones receive?

Len [333]

Given situation: Mr. jones received 70% of the 1500 vote casts in an election Question and solution => How many votes did Mr Jones received: => 1 500 is the total number of voters and 70% of it voted Mr. Jones. SO let’s start solving to get the number of voters who voted him. => 70% = 70 / 100 = .70 => 1 500 * .70 => 1 050 , the number of voters who voted him in an election.

3 0

3 years ago

Read 2 more answers

Aaaahhhh.

vovangra [49]

Answer:

Step-by-step explanation:

evolved=verb

from=preposition

british=noun if referring to a person that is British (That person is a British). adjective when referring to something from britain (british food/british person/british language)

6 0

3 years ago