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3 years ago

!!!!PLEASE HELP!!!

Mathematics

1 answer:

DaniilM [7]3 years ago

5 0

Answer:

a^2 + b^2 = c^2

a^2 + 32^2 = 58^2

a^2 + 1024 = 3364

a^2 = 2340

a = 48.37

Step-by-step explanation:

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3. A new process has been developed for applying pho toresist to 125-mm silicon wafers used in manufac turing integrated circu

dlinn [17]

Answer:

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

The null hypothesis is rejected

The 99% confidence level is $13.3930 < \mu < 13.3994$

Step-by-step explanation:

From the question we are told that

The sample size is n = 10

The population mean is $\mu = 13.4 000 \ angstroms$

The level of significance is $\alpha = 0.05$

The sample data is

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

$\= x = \frac{13.3987+ 13.3957\cdots +13.4002 }{10}$

=> $\= x = 13.3962$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }$

=> $\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }$

=> $\sigma =0.0039$

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }$

=> $z = 3.08$

Generally the p-value is mathematically represented as

$p-value = 2P( z > 3.08)$

From the z-table $P(z > 3.08)= 0.001035$

$p-value = 2* 0.001035$

$p-value = 0.00207$

So from the obtained value we see that

$p-value < \alpha$

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is 99% then the level of significance is

$\alpha = (100 -99)\%$

=> $\alpha = 0.01$

Generally from the normal distribution table critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 2.58 * \frac{0.0039}{\sqrt{10} }$

=> $E = 0.00318$

Generally the 99% confidence interval is mathematically represented as

$13.3962 - 0.00318 < \mu < 13.3962 + 0.00318$

=> $13.3930 < \mu < 13.3994$

7 0

3 years ago

One bus leaves a stop

tatuchka [14]

Answer:

They will leave at 14:25 (2:25) at the same time

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Shown below is a blueprint for a rectangular kennel at a pet hotel.

yulyashka [42]

Answer:

The total length of fencing needed to enclose the kennel 74 feet.

Step-by-step explanation:

Given:

The blueprint of the rectangular kennel shows one side is 23 feet and another side is 14 feet.

As it is a rectangular shape, let the two sides be the length and the breadth of the rectangular kennel. i.e

$length = L = 23\ feet\\breadth = B = 14\ feet\\$

To find:

Total length of fencing needed is to enclose the kennel. i.e

Perimeter of a rectangular kennel = ?

Solution:

we have the formula for perimeter of a rectangle as giving below.

$\textrm{perimeter of rectangle} = 2(length + breadth) \\\textrm{total length of fencing} = 2( L+B)\\ \textrm{substituting the values of length and breadth we get}\\ \textrm{total length of fencing} = 2(23+14)\\=2\times37\\= 74\ feet$

Therefore,the total length of fencing needed to enclose the kennel 74 feet.

8 0

3 years ago

What is the value of x?

V125BC [204]

The value of X is 1

7 0

3 years ago

She took $20 with her to the movies. When she come back with $6. How much money did she spend

mihalych1998 [28]

Answer:

$14

Step-by-step explanation:

$20 minus the $6 she came back with equals $14, which is what she spent.

(20-6=14)

7 0

3 years ago

Read 2 more answers