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3 years ago

Solve the inequality 3x-1>-6x

Mathematics

1 answer:

Ghella [55]3 years ago

3 0

Answer:

x > 1/9

Step-by-step explanation:

Given that:

3x-1>-6x

Adding 6x + 1 on both sides we get

3x-1 + 6x + 1>-6x + 6x +1

3x + 6x > 1

Adding both variables

9x > 1

Dividing both sides b 9 we get

9x/9 > 1/9

x > 1/9

I hope it will help you!

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the function f is defined by f(x)=150/x-z where z is a constant. find z if the value of f at x=1/5 is equal to 250

malfutka [58]

Answer:

x = -1 $\frac{1}{20}$

Step-by-step explanation:

f( $\frac{1}{5}$ ) = 120, therefore we can create this equation:

120 = 150 ÷ ( $\frac{1}{5}$ - z)

cross-multiply to get: 24 - 120z = 150

-120z = 126

z = -1 $\frac{3}{60}$

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3 years ago

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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

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

=> $13.3930 < \mu < 13.3994$

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3 years ago

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confid

katrin [286]

Answer:

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 865, \pi = \frac{408}{865} = 0.4717$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 - 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.4384$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4717 + 1.96\sqrt{\frac{0.4717*0.5283}{865}} = 0.5050$

The 95% confidence interval for the true proportion of all voters in the state who favor approval is (0.4384, 0.5050).

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3 years ago

Megan is sitting in her car in a parking lot. The car next to her pulls forward. If Megan is looking only at the car next to her

Zina [86]

Answer:Backward

Step-by-step explanation:

If the car next to Megan is being Pulled Forward and Megan is seeing only the pulled car then her car appears to be moving backward.

This can be said by using the concept of relative velocity which states that the speed of the body with respect to the other is considered to be at rest.

Here Megan's car appears to move backward with respect to the car next to her due to the existence of relative velocity.

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2 years ago

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Alex17521 [72]

1) 0.009

2) 0.294

3) 0.0612

4) 33.62

5) 26.46

6) 1.824

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3 years ago

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Solve the inequality 3x-1>-6x​

Solve the inequality 3x-1>-6x