13

Factor x^6 + 12ax^3 + 20a^2

Sedaia [141]

x^6 + 10ax^3 + 2ax^3 + 20a^2

(x^3 + 10a)(x^3 + 2a)

answer: (x^3 + 10a)(x^3 + 2a)

Hope it helps :)

8 0

2 years ago

Una escalera se apoya en una pared con un ángulo de 40º. Si se apoyase con un ángulo de 55º, se conseguiría una altura 35 cm may

sdas [7]

Answer: L ≈ 2.0 m

Step-by-step explanation:

Lsin40 = h

Lsin55 = h + 0.35

Lsin55 = Lsin40 + 0.35

Lsin55 - Lsin40 = 0.35

L(sin55 - sin40) = 0.35

L = 0.35 / (sin55 - sin40)

L = 1.98452 ≈ 2.0 m

3 0

2 years ago

A zoologist is studying four very closely related feline species. She wishes to compare their gestation periods. An observationa

diamong [38]

Answer:

$p_v= 0.01$

Since the significance level is 0.05 we see that $pv$ so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different, NOT to conclude that the all the means are different.

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"

Solution to the problem

The hypothesis for this case are:

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

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

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 $p=4$ 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

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

And in order to test this hypothesis we need to ue an F statistic and for this case the p value calculated is

$p_v= 0.01$

Since the significance level is 0.05 we see that $pv$ so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different NOT to conclude that the all the means are different.

8 0

3 years ago

Granite counter tops cost $40 for every square foot. The base pay to install the counter top is $750. Set up a Linear Model repr

vladimir1956 [14]

Answer:

31.5 square feet of counter top

Step-by-step explanation:

x represents the number of square feet

40x + 750 = 2010 subtract 750 from both sides

40x = 1260 divide both sides by 40

x = 31.5

3 0

2 years ago

help Kyle trying to explain to her friend why the placement of an ange and the concept of rigid motions can be used in determini

ivann1987 [24]

Angle b = 31

b=8

c=13

not 100% sure

6 0

2 years ago