What is the solution to the following system?? A) (2.5,0) B) (5,1) C) (0,2) D) (1,5)

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:

a

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

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

The null hypothesis is rejected

b

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 $P(z > 3.08)= 0.001035$

So

$p-value = 2* 0.001035$

$p-value = 0.00207$

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

Which answer is correct? It wouldn’t let me click mathematics btw

Bad White [126]

6)
KM bisects on <NKL so m<MKN = m<MKL = 3x + 5

2(m<MKL) + m<JKN = 180
2(3x+5) + 8x + 2 = 180
6x + 10 + 8x + 2 = 180
14x + 12 = 180
14x = 168
x = 12

so
m<MKN = m<MKL = 3x + 5 = 3(12) + 5 = 36 + 5 = 41

answer
b. 41

7)

2 supplementary has sum = 180
x + x + 14 = 180
2x + 14 = 180
2x = 166
x = 83
x + 14 = 83 + 14 = 97

2 angles are 83 and 97

answer
b. 83, 97

7 0

3 years ago

If f(x) = 2x² – 2. what is f(-6)? If -78 30 18 0 78 PLS HELP

blondinia [14]

Answer:

70

Step-by-step explanation:

Substitute x with -6:

2(-6)²-2

2(36)-2

72-2

70

4 0

2 years ago

Read 2 more answers

Points (−3, 5) and (3, 5) on the coordinate grid below show the positions of two players on a tennis court:

Goshia [24]

Answer:

D

Step-by-step explanation:

-3 and 3 are opposites but 5 (y), is the same

6 0

3 years ago

Help find length of ac n explain please thanks

Debora [2.8K]

Answer:

AC = 12.5 cm

Step-by-step explanation:

use cosine law c^2 = a^2 + b^2 − 2ab cos(C)

c^2 = 6^2 + 10^2 - 2(6)(10)(cosin100)

c^2 = 156.84

c= √156.84

c= 12.5 cm

The cosine rule is used when we are given either three sides or two sides and the included angle.

6 0

3 years ago

Read 2 more answers

What is the solution to the following system??A) (2.5,0)B) (5,1)C) (0,2)D) (1,5)​

What is the solution to the following system??A) (2.5,0)B) (5,1)C) (0,2)D) (1,5)