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a_sh-v [17]
3 years ago
7

point M divides AB so that AM:MB 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), what are the coordinates of M?

Mathematics
1 answer:
maria [59]3 years ago
5 0

Answer:

The coordinates of point M are (2,1)

Step-by-step explanation:

Let's call the coordinates of point M by (x, y)

We have that the rate AM:MB is 1/2, so we can calculate x and y as follows:

x-coordinate of A is equal to -1, and x-coordinate of B is equal to 8, then:

AM:MB = [x - (-1)] / [8 - x] = 1/2

(x+1)/(8-x) = 1/2

2x+2 = 8-x

3x = 6

x = 2

y-coordinate of A is equal to -3, and y-coordinate of B is equal to 9, then:

AM:MB = [y - (-3)] / [9 - y] = 1/2

(y+3)/(9-y) = 1/2

2y+6 = 9-x

3y = 3

y = 1

So the coordinates of point M are x = 2 and y = 1 or (2,1)

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Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

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The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

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• The probability of obtain values within three deviation's from the mean is 0.997

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