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3 years ago

Given the two vertices and the centroids of a triangle, how many possible locations are there for the third vertex?

Mathematics

1 answer:

hoa [83]3 years ago

7 0

Answer:

Step-by-step explanation:

The centroid is the average of the coordinates of the three vertices. If you know two vertices (A and B) and the centroid (Q), then the third vertex (C) is ...

C = 3Q -A -B

It has only one possible location.

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In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

b) From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

8 0

3 years ago

If you earn $48,000 per year, how much will you receive on a biweekly basis?

Harrizon [31]

$48,000 a year is $1,846.15 biweekly before taxes and approximately $1,384.62 after taxes. Paying a tax rate of around 25% and working full-time at 40 hours a week, you would earn $1,384.62 after taxes. To calculate how much you make biweekly before taxes, you would multiply $23.08 by 40 hours and 2 weeks

5 0

2 years ago

Read 2 more answers

Which are vertical angles? Check all that apply. ∠EAB and ∠BAC ∠EAB and ∠CAD ∠CAD and ∠FAE ∠CAB and ∠DAE ∠DAC and ∠DAE

Anastaziya [24]

Answer:

<CAB and <DAE are vertical angles

<EAB and <CAD are vertical angles

Step-by-step explanation:

this is because they are formed by the prolongation of the sides of the other angles and are opposite to them on the other side of the vertex.

8 0

3 years ago

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The simple formula for the nth term of an arithmetic sequence is an = 5n + 15. What is the explicit formula corresponding to the

Nikitich [7]

Sequence will look like this:
Term 1: 20 --------- 20 + 5(0)
Term 2: 25 --------- 20 + 5(1)
Term 3: 30 --------- 20 + 5(2)
Term 4: 35 --------- 25 + 5(3)
ETC.

It cab noted that the numbers in the bracket (that is, 0, 1, 2, 3, 3, etc) = n-1

Then, the explicit formula will be;
an = 20 + 5(n-1).

The correct answer is D.

7 0

3 years ago

Brainliest to correct answer

aksik [14]

Answer:

No, zack will finish first.

Step-by-step explanation:

I would rather not write it out but zack should finish first

4 0

2 years ago

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