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miss Akunina [59]
2 years ago
14

A piece of cloth costs birr 200. If the piece was 5m longer and the cost of each metre of cloth was birr 2 less ,the cost of the

piece would have remained unchanged. How long is the piece and what is its original price per metre?​
Mathematics
1 answer:
Paha777 [63]2 years ago
8 0

The length of the original piece of cloth was <u>20 meters</u>.

The cost of per meter cloth initially was <u>birr 10 per meter</u>.

In the question, we are given that a piece of cloth costs birr 200.

Also, we are told that if the piece was 5m longer and the cost of each meter of cloth was birr 2 less, the cost of the piece would have remained unchanged.

We are asked to find the length of the cloth piece and what is its original price per meter.

We assume the initial length of the cloth to be x meters.

The cost of the cloth is given to be birr 200.

Thus, the per meter cost of the cloth initially was birr 200/x per meter,

In the new case, we are given that:

The piece was 5 meters longer.

The initial length = x m.

The new length = x + 5 m.

The cost of each meter of cloth was birr 2 less.

The initial cost of each meter of cloth = birr 200/x per meter.

Thus, the new per meter cost = birr 200/x - 2 per meter = birr (200 - 2x)/x per meter.

Thus, the cost of the piece = birr (x + 5)(200 - 2x)/x.

Now, we are given that the cost of the piece in both cases is the same, which can be shown as:

(x + 5)(200 - 2x)/x = 200,

or, 200x + 1000 - 2x² - 10x = 200x,

or, x² + 5x - 500 = 0,

or, x² + 25x - 20x - 500 = 0,

or, x(x + 25) - 20(x + 25) = 0,

or, (x - 20)(x + 25) = 0, which gives that:

Either x - 20 = 0 ⇒ x = 20,

or, x + 25 = 0 ⇒ x = -25.

Since x cannot be negative, x = 20.

Thus, the length of the original piece of cloth was x meters = <u>20 meters</u>.

The cost of per meter cloth initially was birr 200/x per meter = <u>birr 10 per meter</u>.

Learn more about costs at

brainly.com/question/13964154

#SPJ9

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In a random sample of 75 American women age 18 to 30, 26 agreed with the statement that a woman should have the right to a legal
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Answer:

a) z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236  

p_v =2*P(Z>0.236)=0.813  

If we compare the p value and using any significance level for example \alpha=0.01 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.  

b) We are confident at 99% that the difference between the two proportions is between -0.188 \leq p_B -p_A \leq 0.226

Step-by-step explanation:

Previous concepts and data given

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".  

p_A represent the real population proportion of women age 18 to 30  agreed with the statement that a woman should have the right to a legal abortion for any reason

\hat p_A =\frac{26}{75}=0.347 represent the estimated proportion of women age 18 to 30  agreed with the statement that a woman should have the right to a legal abortion for any reason

n_A=75 is the sample size for A

p_B represent the real population proportion for women age 58 to 70  agreed with the statement that a woman should have the right to a legal abortion for any reason

\hat p_B =\frac{21}{64}=0.328 represent the estimated proportion of women age 58 to 70  agreed with the statement that a woman should have the right to a legal abortion for any reason

n_B=64 is the sample size required for B

z represent the critical value for the margin of error and for the statisitc

The population proportion have the following distribution  

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

Part a

We need to conduct a hypothesis in order to check if the proportion are equal, the system of hypothesis would be:  

Null hypothesis:p_{A} = p_{B}  

Alternative hypothesis:p_{A} \neq p_{B}  

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

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

Where \hat p=\frac{X_{A}+X_{B}}{n_{A}+n_{B}}=\frac{26+21}{75+64}=0.338

Calculate the statistic

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

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Since is a two sided test the p value would be:  

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Part b  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

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:  

(0.347-0.328) - 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=-0.188  

(0.347-0.328) + 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=0.226  

And the 99% confidence interval for the difference of proportions would be given (-0.188;0.226).  

We are confident at 99% that the difference between the two proportions is between -0.188 \leq p_B -p_A \leq 0.226

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