Find the equation for the line that passes through -1,-2 and 4,3. Is the point 3,1 on the line
1 answer:
Answer:
- y = x -1
- no
Step-by-step explanation:
A graph quickly answers this question.
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The given points have a horizontal difference of 4-(-1) = 5 and a vertical difference of 3-(-2) = 5, so the slope of the line between them is ...
m = Δy/Δx = 5/5 = 1
The point-slope form of the equation for a line can be written ...
y = m(x -h) +k . . . . . for slope m through point (h, k)
Using the first point and the slope we found, we can write the equation as ...
y = 1(x -(-1)) +(-2)
y = x -1 . . . . . . . . . simplify; this is the equation of the line
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When we try the third point in this equation, we get ...
y = 3 -1 = 2 ≠ 1 . . . . . the third point is not on the line
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1) Mean: 6.5
2) Standard deviation: 3.2
Step-by-step explanation:
1)
A uniform random distribution is the distribution of a variable that can assume n different values, and each of these values is equally likely to occur.
This means that the probability of occurring of each of these values is the same:
For a uniform random distribution, the mean of the distribution is simply equal to the median value of the distribution, which is exactly at the center of the distribution itself. It can be calculated as
where
a is the lowest value of the distribution
b is the highest value of the distribution
Here the distribution consists of all values ranging from 1 to 12, so:
a = 1
b = 12
Therefore the mean value is
2)
For a uniform random distribution, it can be dimostrated that the variance of the distribution is
For the distribution in this problem, we have:
a = 1
b = 12
Therefore the variance is
The standard deviation is the square root of the variance, therefore for this distribution it is:
Learn more about mean and standard deviation:
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