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2 years ago

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What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Squar

e. 5, and -3. C. D. None, because there is no solution. 2x-5--3?

1 answer:

jekas [21]2 years ago

8 0

Hi :)

I'd start by adding 5 to both sides of the equation. That would make the equation easier.

$\boldsymbol{\sqrt{2x}-5=3}}$

$\boldsymbol{\sqrt{2x}=2}$

The next step is to get rid of the radical sign.

Which operation will undo the square root? Squaring.

So that's why we square both sides:

$\boldsymbol{2x=4}$

And Now we just divide both sides by 2

$\boldsymbol{x=2}$

<em>~</em> $\textit{\textbf{Learn More; Work Harder}}$ <em>~</em>

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Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random

Katyanochek1 [597]

Answer:

a) Null hypothesis: $\mu_A =\mu_B =\mu C$

Alternative hypothesis: $\mu_i \neq \mu_j, i,j=A,B,C$

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667$

And we have this property

$SST=SS_{between}+SS_{within}$

The degrees of freedom for the numerator on this case is given by $df_{num}=df_{within}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=3*6-3=15$ .

And the total degrees of freedom would be $df=N-1=3*6 -1 =15$

The mean squares between groups are given by:

$MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166$

And the mean squares within are:

$MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544$

And the F statistic is given by:

$F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326$

And the p value is given by:

$p_v= P(F_{2,15} >11.326) = 0.00105$

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

b) $(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}$

The degrees of freedom are given by:

$df = n_B +n_C -2= 6+6-2=10$

The confidence level is 99% so then $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ and the critical value would be: $t_{\alpha/2}=3.169$

The confidence interval would be given by:

$(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321$

$(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345$

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part a

Null hypothesis: $\mu_A =\mu_B =\mu C$

Alternative hypothesis: $\mu_i \neq \mu_j, i,j=A,B,C$

If we assume that we have $3$ groups and on each group from $j=1,\dots,6$ we have $6$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667$

And we have this property

$SST=SS_{between}+SS_{within}$

The degrees of freedom for the numerator on this case is given by $df_{num}=df_{within}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=3*6-3=15$ .

And the total degrees of freedom would be $df=N-1=3*6 -1 =15$

The mean squares between groups are given by:

$MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166$

And the mean squares within are:

$MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544$

And the F statistic is given by:

$F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326$

And the p value is given by:

$p_v= P(F_{2,15} >11.326) = 0.00105$

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

Part b

For this case the confidence interval for the difference woud be given by:

$(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}$

The degrees of freedom are given by:

$df = n_B +n_C -2= 6+6-2=10$

The confidence level is 99% so then $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ and the critical value would be: $t_{\alpha/2}=3.169$

The confidence interval would be given by:

$(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321$

$(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345$

7 0

3 years ago

Which expression gives the solutions of -5+2x^2=-6x

pashok25 [27]

I hope this helps you

4 0

4 years ago

Exampls of counting circle

Luda [366]

This a counting circle that I found online.

8 0

3 years ago

wel

Answer: the y intercept is -5

You can use the slope intercept form to find the answer. Aka y = mx + b

In this equation m is equal to the slope and b is equal to the y-intercept.

We already know the slope, 4. And we have two different point we can choose from. I’ll show how to solve with the first (1,-1) point.

8 0

3 years ago

What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?

s344n2d4d5 [400]

Answer:

The roots are

<h3> $x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\$ </h3>

Step-by-step explanation:

9x² + 54x + 82 = 0

Using the quadratic formula

That's

<h3> $x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a}$ </h3>

From the question

a = 9 , b = 54 , c = 82

Substitute the values into the above formula and solve

That's

<h3> $x = \frac{ - 54\pm \sqrt{ {54}^{2} - 4(9)(82)} }{2(9)} \\ x = \frac{ - 54\pm \sqrt{2916 - 2952} }{18} \\ x = \frac{ - 54\pm \sqrt{ - 36} }{18} \\ x = \frac{ - 54\pm 6i}{18}$ </h3>

Separate the real and imaginary parts

That's

<h3> $x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i$ </h3>

We have the final answer as

<h3> $x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\$ </h3>

Hope this helps you

5 0

3 years ago