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barxatty [35]

3 years ago

absmiddle" class="latex-formula">

Mathematics

1 answer:

sergeinik [125]3 years ago

4 0

Answer:

The answer is 72

Step-by-step explanation:

3x(4 + 8)x2

=3 x 12 x 2

=36 x 2

=72

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A t-shirt is in sale for 33% off the original price of the shirt is $24.50 how much will you pay for the shirt after the discoun

S_A_V [24]

Answer:

$8.085

Step-by-step explanation:

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4 years ago

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Suppose a random sample of 100 observations from a binomial population gives a value of pˆ = .63 and you wish to test the null h

irakobra [83]

Answer:

We conclude that the population proportion is equal to 0.70.

Step-by-step explanation:

We are given that a random sample of 100 observations from a binomial population gives a value of pˆ = 0.63 and you wish to test the null hypothesis that the population parameter p is equal to 0.70 against the alternative hypothesis that p is less than 0.70.

Let p = population proportion.

(1) The intuition tells us that the population parameter p may be less than 0.70 as the sample proportion comes out to be less than 0.70 and also the sample is large enough.

(2) So, Null Hypothesis, $H_0$ : p = 0.70 {means that the population proportion is equal to 0.70}

Alternate Hypothesis, $H_A$ : p < 0.70 {means that the population proportion is less than 0.70}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion = 0.63

n = sample of observations = 100

So, the test statistics = $\frac{0.63-0.70}{\sqrt{\frac{0.70(1-0.70)}{100} } }$

= -1.528

The value of z-test statistics is -1.528.

Now at 0.05 level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

Since our test statistics is more than the critical value of z as -1.528 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the population proportion is equal to 0.70.

(c) The observed level of significance in part B is 0.05 on the basis of which we find our critical value of z.

4 0

3 years ago

A closed cylindrical vessel contains a fluid at a 5MPa pressure. The cylinder, which has an outside diameter of 2500mm and a wal

Julli [10]

Answer:

1) Increase in the diameter equals 3.5 mm

2) Increase in the length equals $0.0003724L_{i}$ where $L_{i}$ is the initial length of the vessel.

Step-by-step explanation:

The diametric strain in the vessel is given by

$\epsilon_{D} =\epsilon_{diam}-\nu \epsilon _{axial}$

We have

$\epsilon _{diam}=\frac{\sigma _{hoop}}{E}\\\\\sigma _{hoop}=\frac{\Delta P\times D}{2t}\\\\\therefore \epsilon _{diam}=\frac{\Delta P\times D}{2t\times E}$

Applying values we get

$\therefore \epsilon _{diam}=\frac{5\times 10^{6}\times 2.5}{2\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{5}{3088}$

Similarly axial strain is given by

$\epsilon _{diam}=\frac{\sigma _{axial}}{E}$

$\sigma _{axial}=\frac{\Delta P\times D}{4t}\\\\\therefore \epsilon _{axial}=\frac{\Delta P\times D}{4t\times E}$

Applying values we get

$\therefore \epsilon _{axial}=\frac{5\times 10^{6}\times 2.5}{4\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{2.5}{3088}$