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2 years ago

Simplify the following expression 7 y + 2x - 10 y + 3 x^2 -10x

Mathematics

2 answers:

tiny-mole [99]2 years ago

4 0

Answer:

$3x^{2} -3y-8x$

Step-by-step explanation:

Combine like terms

7y + -10 y = -3y

2x + -10x = -8x

$3x^{2} -3y-8x$

Serggg [28]2 years ago

4 0

Answer:

3x^2 - 8x - 3y

Step-by-step explanation:

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a) $\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

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Now we just take square root on both sides of the interval and we got:

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b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

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Part a

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
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The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

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The Confidence interval is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and the critical values are:

$\chi^2_{\alpha/2}=20.09$

$\chi^2_{1- \alpha/2}=1.65$

And replacing into the formula for the interval we got:

$\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}$

$363.90 \leq \sigma^2 \leq 4430.80$

Now we just take square root on both sides of the interval and we got:

$19.08 \leq \sigma \leq 66.56$

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

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3 years ago

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2 years ago

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2 years ago

Simplify the following expression 7 y + 2x - 10 y + 3 x^2 -10x​

Simplify the following expression 7 y + 2x - 10 y + 3 x^2 -10x