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3 years ago

9

Twice the difference of a number and 8 is equal to three times the sum of the number and 7. Find the number.

1 answer:

Vikentia [17]3 years ago

8 0

Answer:

The number is -37.

Step-by-step explanation:

2(x - 8) = 3(x + 7)

2x - 16 = 3x + 21

x = -37

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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:

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 expression is equivalent to 3 ( x + 10)

devlian [24]

Answer:

3x + 30

Step-by-step explanation:

$3(x+10)\\\\\text{Distribute '3' into 'x + 10'}\\\\\\3(x+10)\rightarrow3x+30\\\\\left \{ {{3*x=3x} \atop {3*10=30}} \right.$

3x + 30 would be an equivalent expression.

Hope this helps.

8 0

3 years ago

If the spinner is spun 120 times, how many times would you expect it to land on red or orange?

alina1380 [7]

Answer:

D

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

What is the value represented by the digit 8 after 7,824 is divided by 10? help PLEASE 15 Point

8_murik_8 [283]

Answer: 80

Step-by-step explanation:

7824/10 = 782.4

The value represented by 8 is 80 or 8 tens.

7 0

3 years ago

1/3(22) - 1 -1\2(12)

irinina [24]

The answer is (1/3)...

6 0

4 years ago