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mrs_skeptik [129]

2 years ago

15

Points D, E, and F are collinear and DE:DF= 2/5. Point E is locate at (-3,2), point F is located at (-3,-4). What is the coordin

ate point of point D?

1 answer:

nikitadnepr [17]2 years ago

7 0

DE : DF = 2 : 5

So, DE = 2 parts and DF = 5 parts

EF = DF - DE

= 5 - 2

= 3 parts

DE : EF = 2 : 3

Let D be (x, y).

Then, the point E divides the line segment DF internally in the ratio 2 : 3.

So, E is $(\frac{2(-3)+3x}{2+3}, \frac{2(-4)+3y}{2+3} )$

$=(\frac{3x-6}{5}, \frac{3y-8}{5} )$

But, it is given that E is (-3, 2).

Therefore,

$\frac{3x-6}{5} = -3 and \frac{3y-8}{5}=2$

3x - 6 = -15 and 3y - 8 = 10

3x = -9 and 3y = 18

x = -3 and y = 6

Hence, D is (-3, 6)

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To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig

Keith_Richards [23]

Answer:

1. Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

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 1

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

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

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

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

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

And we have this property

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

We need to find the mean for each group first and the grand mean.

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

If we apply the before formula we can find the mean for each group

$\bar X_A = 27$ , $\bar X_B = 24$ , $\bar X_C = 30$ . And the grand mean $\bar X = 27$

Now we can find the sum of squares between:

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

Each group have a sample size of 4 so then $n_j =4$

$SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72$

The degrees of freedom for the variation Between is given by $df_{between}=k-1=3-1=2$ , Where k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

$MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36$

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

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

$SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306$

And the degrees of freedom are given by:

$df_{within}=N-k =3*4 -3 = 12-3=9$ . N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

$MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34$

C. 34

Part 4

The test statistic F is given by this formula:

$F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059$

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is $F_{crit}=8.02$

B. 8.02

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Answer:

Step-by-step explanation:

x = roses, y = tulips, z = lillies

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12y + 12z + 4y + 3z = 610

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--------------------

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-------------------

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