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Arte-miy333 [17]
3 years ago
13

Determine the center and radius of the following circle equation:

Mathematics
1 answer:
-BARSIC- [3]3 years ago
7 0

Answer:

(6, 9 ) and r = 3

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 12x - 18y + 108 = 0

Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is

x² - 12x + y² - 18y = - 108

To obtain standard form use the method of completing the square

add ( half the coefficient of the x and y terms )² to both sides

x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81

(x - 6)² + (y - 9)² = 9 ← in standard form

with centre = (6, 9 ) and r = \sqrt{9} = 3

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Standard deviation = 1.456

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The mean and variance of a binomial distribution with parameters n (number of trials) and p ( the probability of getting success in each trial) is given by :-

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Answer:

Step-by-step explanation:

Hello!

You have the following experiment, a random sample of 106 people was made and they were asked if they dreamed in color. 80 persons of the sample reported dreaming in color.

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Your study variable is a discrete variable, you can define as:

X: Amount of people that reported dreaming in colors in a sample of 106.

Binomial criteria:

1. The number of observation of the trial is fixed (In this case n = 106)

2. Each observation in the trial is independent, this means that none of the trials will have an effect on the probability of the next trial (In this case, the fact that one person dreams in color doesn't affect or modify the probability of the next one dreaming in color)

3. The probability of success in the same from one trial to another (Or success is dreaming in color and the probability is 0.21)

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