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3 years ago

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The state of Colorado has roughly the shape of a rectangle that is 3.8 x 102 miles long and 2.8 x 102 miles high. What is the ap

proximate area of Colorado? Hint: The area of a rectangle is the product of its length and width.

1 answer:

Illusion [34]3 years ago

6 0

104,185 miles is the area of Colorado

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5. We want to compare two different groups of students, students taking Composition 1 in a tradition lecture format and students

RUDIKE [14]

Answer:

By knowing the standard deviation, one gets the idea of how the value is scattered or dispersed about the mean.

Step-by-step explanation:

Let us first define standard deviation.

As it is known that the standard deviation is a measure of dispersion which express the spread of observation in terms of the average of deviations of observations from some central values.

Measure of dispersion gives us an idea about homogeneity or heterogeneity of the distribution.

Standard deviation is supposed almost an ideal measure of dispersion except the general nature of extracting the square root.

Thus for the given question, if we want to compare the two different groups of students whose mean score is 85. Here the standard deviation for both the groups interprets an idea about how the individual score for each group scattered or varied about the mean score i.e. 85.

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3 years ago

Which numbers are irrational

frozen [14]

<span>"An </span>irrational number<span> can't be expressed as a ratio between 2 </span>numbers,<span> it can't be written as a simple fraction because there is not a finite </span>number<span> of </span>numbers<span> when written as a decimal. The </span>numbers<span> in the decimal would go on forever, without repeating.</span>

6 0

3 years ago

What is the simplified form of <br><br>4(2x - 5y) - 3x

koban [17]

Answer:

5(x-4y) or 5x-20y

Step-by-step explanation:

4(2x-5y)-3x

8x-20y-3x

Subtracting 8 and 3

5x-20y

6 0

3 years ago

Read 2 more answers

In a random sample of 400 items where 84 were found to be defective, the null hypothesis that 20% of the items in the populati

Murrr4er [49]

Answer:

$z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5$

$p_v =2*P(Z>0.5)=0.617$

So the p value obtained was a very high value and using the significance level given $\alpha=0.1$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=84 represent the number of items defective

$\hat p=\frac{84}{400}=0.21$ estimated proportion of defectives

$p_o=0.2$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.2 or 20%:

Null hypothesis: $p=0.2$

Alternative hypothesis: $p \neq 0.2$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.1$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z>0.5)=0.617$

So the p value obtained was a very high value and using the significance level given $\alpha=0.1$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.

3 0

3 years ago

What is the sum of the n terms of the series 6 + 24 + 96 + 384 + . . . ? Hint: cap s sub n equals start fraction a sub one left

babymother [125]

Note that each term is 6 times a power of 4, starting from 0. So you can write

$S_n=6(1+4+4^2+4^3+\cdots+4^{n-1})$

Multiplying both sides by 4 gives

$4S_n=6(4+4^2+4^3+4^4+\cdots+4^n)$

Subtracting this from the first sum reduces to

$S_n-4S_n=6(1-4^n)$
$-3S_n=6(1-4^n)$
$S_n=2(4^n-1)$

5 0

3 years ago