Special right traingles (30, 60, 90 45, 45, 90

The area of a regular octagon is 35 cm 2 what is the area of a regular octagon with sides three times as large

Maurinko [17]

The area of a polygon = n*side^2 / (4 * tan(180/n))
where "n" is the number of sides

Let's calculate area for side = 2
area = 8*2^2 / (4 * tan(180/8))
area = 32 / (4 * tan(22.5))
area = 32 / 4*0.41421
 area = 19.3138746047 

Now, let's calculate area for side = 6
area = 8*6^2 / (4 * tan(180/8))
area = 288 / 1.65684 
area = 173.824871442 

 173.824871442 / 19.3138746047 = 9

So, the area would be 9 times larger.

ALSO, looking at the formula
n*side^2 / (4 * tan(180/n))
we can see that the side length appears just once in the formula and we are to square it in the calculation. So, if we increase the side length is increased by 3, then the area increases by 3^2 or 9.

5 0

3 years ago

15+9/2 leave your answer in fraction

Korolek [52]

15 can be 15/1 = 30/2
30/2 + 9/2 = 39/2

6 0

2 years ago

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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

5 0

3 years ago

What should be the top item on a list of your life goals? A. A goal that's financially feasible B. A goal that's most important

Feliz [49]

The top item on a list of your life goals should be B. a goal that's most important to you. You shouldn't care much for what other people want from you - if you know what you want and need, you should make that your priority and try to achieve your life goals. It doesnt matter whether you can manage that financially, or whether it's going to be easy - if you really want it, you are going to try your best in order to achieve it.

3 0

3 years ago

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Partial quotients 36 divided by 540

den301095 [7]

1. Simply divide the 520 to 36 and that makes it 15

6 0

3 years ago