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1 year ago

What is the slope of the line -3y = 12x + 6?

Mathematics

1 answer:

Deffense [45]1 year ago

3 0

Answer:

-4

Step-by-step explanation:

Let us rearrange this equation by dividing both sides by (-3):

y=-4x-2

And since the equation of a line is y=mx+b, where slope=m,

then the slope of our line is -4

<em>I hope this helps! :)</em>

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A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the

velikii [3]

Answer:

$\theta=cos^{-1}(\frac{2}{3})$

Step-by-step explanation:

We are given that measurements of three points on the ground gave coordinates of (0,0,0),(1,2,0) and (0,2,1)

We have to find the angle by which the tower now deviate from the vertical

We find cross product of <1,2,0> and <0,2,1>

$\times =\begin{vmatrix}i&j&k\\1&2&0\\0&2&1\end{vmatrix}$

$\times =2\hat{i}-\hat{j}+2\hat{k}$

Now, we are finding the angle between $\times$ and vertical vector <0,0,1>

Angle between two vectors formula

$cos\theta=\frac{a.b}{\mid a\mid\cdot\mid b\mid }$

Now, using this formula

$cos\theta=\frac{2}{1\cdot 3}=\frac{2}{3}$

$\theta=cos^{-1}(\frac{2}{3})$

Hence, the tower deviate from the vertical by the angle $\theta=cos^{-1}(\frac{2}{3})$

6 0

2 years ago

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. A cereal company claims that th

Dmitrij [34]

Answer:

There is not sufficient evidence to warrant the rejection of the claim that the mean weight of cereal is atleast 14 oz

Step-by-step explanation:

The hypothesis for the test above will be stated as follows :

The claim to be tested is the alternative hypothesis, which is the negation of the Null hypothesis

H0 : μ < 14

H1 : μ ≥ 14

If the Null is rejected, then it means that the company's claim that the mean weight of its cereal being atleast 14 is valid ;

Then it means there is significant evidence to support the stance that the mean weight of cereal in the company's packet is atleast 14 oz.

3 0

1 year ago

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"† proposed using the Poisson distribution

oksian1 [2.3K]

Answer:

a. P(X ≤ 5) = 0.999

b. P(X > λ+λ) = P(X > 2) = 0.080

Step-by-step explanation:

We model this randome variable with a Poisson distribution, with parameter λ=1.

We have to calculate, using this distribution, P(X ≤ 5).

The probability of k pipeline failures can be calculated with the following equation:

$P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k!$

Then, we can calculate P(X ≤ 5) as:

$P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999$

The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:

$P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080$