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3 years ago

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Find the volume of a pyramid with a square base where the perimeter of the base is 18.4 cm in the height of the pyramid is 20.6

cm round your answer to the nearest 10th of a cubic centimeter

1 answer:

Igoryamba3 years ago

7 0

Answer:

45

Step-by-step explanation:

Find the volume of a pyramid with a square base, where the perimeter of the base is 18.4\text{ cm}18.4 cm and the height of the pyramid is 20.6\text{ cm}20.6 cm. Round your answer to the nearest tenth of a cubic centimeter.

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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

FIND THE AREA OF THE SHADED REGION. SHOW ALL YOUR WORK.

erik [133]

Answer:

he area that is un-shaded is (x-3)(x-6).

The entire area is (2x+2)(3x-4).

Area of the shaded region is:

(2x+2)(3x-4) - (x-3)(x-6) =

(6x2-2x-8) - (x2-9x+18) =

6x2-2x-8-x2+9x-18 =

5x2+7x-26 hopes this help btw (;

3 0

3 years ago

Read 2 more answers

Pls help for number 6

Vlad1618 [11]

A: 45x + 30y = 1350
Since we don’t know how many adults and children are in the group, we use x and y

b: x-intercept= 30 y-intercept=45
To find the x-intercept you need to isolate the variable. 45x/45 = x
Then you do the same thing to the other side. 1350/45 = 30
So x=30
Same thing with the y-intercept.
30y/30 = y 1350/30 = 45
y=45 (Not really sure what it means by “what they represent” but I thinks it’s that there are 30 adult tickets and 45 children tickets )

c: so our points are (30,0) and (0,45) so you would graph that.
To find how many children tickets were bought if there were 20 adult tickets just look at the photo I put. I don’t know how to explain this.

Hope this helps

7 0

2 years ago

Help ASAP again........

lorasvet [3.4K]

Answer: 53

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7 0

3 years ago

Read 2 more answers

Which expression is equivalent to the expression below? Select all that apply.

katen-ka-za [31]

Answer:

2 and 3

Step-by-step explanation:

To simplify this expression, you will need to use the distributive property.

Multiply -2/5 by 15 = <u>- 6</u>, -2/5 by -20d = <u>8d</u>, and -2/5 by 5c = <u>-2c</u>.

you can switch these around to get -6 + 8d - 2c and -2c + 8d - 6.

Hope this helps :)

3 0

2 years ago