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3 years ago

4(1 - x) + 3x = - 2(x + 1)

Mathematics

2 answers:

s344n2d4d5 [400]3 years ago

6 0

Answer:

x=-2

Step-by-step explanation:

4 - 4x + 3x=-2x -2

4 -1x=-2x -2

4= -1x -2

2=-1x

x=-2

liubo4ka [24]3 years ago

4 0

Answer:

X=-6

Step-by-step explanation:

4(1−x)+3x=−2(x+1)

(4)(1)+(4)(−x)+3x=(−2)(x)+(−2)(1)(Distribute)

4+−4x+3x=−2x+−2

(−4x+3x)+(4)=−2x−2(Combine Like Terms)

−x+4=−2x−2

Step 2: Add 2x to both sides.

−x+4+2x=−2x−2+2x

x+4=−2

Step 3: Subtract 4 from both sides.

x+4−4=−2−4

x=−6

Answer:

x=−6

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Vikki [24]

Answer:

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

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We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,35)".And we see that $t_{\alpha/2}=2.03$