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A 224 cm rope is cut so that one part is 3/4 of the other. How long is the shorter rope? The longer rope?

Answers

Answer 1

Answer:

Given that:

Length of a rope = 224 cm

Rope is cut so that one part is 3/4 of the other.

Solution:

Let one part of a rope be x cm.

So other part of the rope is $(3)/(4)x$ .

Total length $=x+(3)/(4)x$

Now,

$x+(3)/(4)x=224$

$(4x+3x)/(4)=224$

Multiply both sides by 4.

$7x=896$

Divide both sides by 7.

$x=(896)/(7)$

$x=128$

The value of one part 128 cm.

Second part $=(3)/(4)x$

$=(3)/(4)* 128$

$=3* 32$

$=96$

Therefore, the length of shorter rope is 96 cm and the length of longer rope is 128 cm.

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In a survey of 1016 ?adults, a polling agency? asked, "When you? retire, do you think you will have enough money to live comfortably or not. Of the 1016 ?surveyed, 535 stated that they were worried about having enough money to live comfortably in retirement. Construct a 99?% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.A. There is a 99?% probability that the true proportion of worried adults is between ___ and ___.

B. 99?% of the population lies in the interval between ___ and ___.

C. There is 99?% confidence that the proportion of worried adults is between ___ and ___.

Answers

Answer:

C. There is 99% confidence that the proportion of worried adults is between 0.487 and 0.567

Step-by-step explanation:

1) Data given and notation

n=1016 represent the random sample taken

X=535 represent the people stated that they were worried about having enough money to live comfortably in retirement

$\hat p=(535)/(1016)=0.527$ estimated proportion of people stated that they were worried about having enough money to live comfortably in retirement

$\alpha=0.01$ represent the significance level

Confidence =0.99 or 99%

z would represent the statistic

p= population proportion of people stated that they were worried about having enough money to live comfortably in retirement

2) Confidence interval

The confidence interval would be given by this formula

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

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=2.58$

And replacing into the confidence interval formula we got:

$0.527 - 2.58 \sqrt{(0.527(1-0.527))/(1016)}=0.487$

$0.527 + 2.58 \sqrt{(0.527(1-0.527))/(1016)}=0.567$

And the 99% confidence interval would be given (0.487;0.567).

There is 99% confidence that the proportion of worried adults is between 0.487 and 0.567

Final answer:

To build a 99% confidence interval, we first calculate our sample proportion by dividing the number of such instances by the total sample size. Next, we determine the standard error of the proportion, then our margin of error by multiplying the standard error by the Z value of the selected confidence level. Lastly, we determine the confidence interval by adding and subtracting the margin of error from the sample proportion.

Explanation:

To construct a 99% confidence interval for the proportion of adults worried about having enough money to live comfortably in retirement, we will utilize statistical methods and proportions. First, we must calculate the sample proportion. The sample proportion (p) is equal to 535 (the number who are worried) divided by 1016 (the total number of adults surveyed).

Then, we find the standard error of the proportion which we get by multiplying the square root of ((p*(1-p))/n) where n is the number of adults sampled. The margin of error is found using the Z value corresponding to the desired confidence level, in this case, 99%. Multiply the standard error by this Z value. Lastly, we construct the confidence interval by taking the sample proportion (p) ± the margin of error.

The result will give you the 99% confidence interval - meaning we are 99% confident that the true proportion of adults who are worried about having enough money to live comfortably in retirement lies within this interval.

Learn more about Confidence Interval here:

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If x3 = 8 and y3 = 125, what
is the value of y - x?

Answers

Answer:

X to power 3is=2 while y to power 3is=5so5-2=3

Step-by-step explanation:

x cubed is =8 so cube root of 8is 2

y cubed is =125so cube root of 125is 5

therefore 5-2=3

Simplify 0.05 +1.02x

Answers

0.005x + 1.02x

= ( 0.05 + 1.02 )x

= 1.07x

Hope this helps!

~LENA~

I'm assuming the 0.05 is supposed to have an x after it but you can combine like terms.

0.05x + 1.02x =x(0.05+1.02)=1.07x

When we use letters to represent unknown numbers, we call the equation

Answers

A value the replace a number that you can't see

It's called variables, that's what we see

WXYZ is a parallelogram. Name an angle congruent to ∠WZY.

Answers

Answer:

Angle congruent to ∠WZY is ∠WXY

Statistical techniques are classified into two major categories: descriptive and inferential. Describe the general purpose of each category. A-The purpose of (1)inferential (2)descriptive statistics is to simplify the organization and presentation of data.
B-The purpose of (1) inferential (2) descriptive statistics is to use the limited data from a sample as the basis for making general conclusions about the population.

Answers

Answer:

A-The purpose of (2)descriptive statistics is to simplify the organization and presentation of data.

B-The purpose of (1) inferential statistics is to use the limited data from a sample as the basis for making general conclusions about the population.

Step-by-step explanation:

The descriptive statistics is used to make large data presentable into usable short forms, without which it would look impossible to solve. We draw a sample from the population and find its mean or draw histograms for the frequency distributions. This is descriptive statistics.

The inferential statistics is used to make inferences and conclusions from limited data given from a population. We do the hypothesis testing for the random samples obtained from larger populations. The hypothesis tests or the confidence intervals help us decide whether the rseults are accepted or not.

Final answer:

Descriptive statistics is used to summarize and organize data from a sample, such as providing the average or frequency of a variable. Inferential statistics, on the other hand, uses this sample data to make broad generalizations about the population.

Explanation:

The two major categories of statistical techniques are inferential statistics and descriptive statistics. The general purpose of descriptive statistics is to simplify the organization and presentation of data. They provide simple summaries about the sample and the measures. For example, we may want to know the average, maximum, minimum, or frequency of some variable.

On the other hand, inferential statistics involve using the limited data from a sample as the basis for making general conclusions about the population. They also include the theory of hypothesis testing, which is a method for testing statistical results. For example, inferential statistics would be used to determine if a difference observed between groups is a real one or if it might have happened by chance in this study.

Learn more about Descriptive and Inferential Statistics here:

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