If 6x and 9x are the complementary angles to each other, then find these angles
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<h3>Answer:</h3>
Yes. The pattern is predicted by the formula ...
f(x) = -0.465x +11.68 +0.015·mod(x, 2)
<h3>Step-by-step explanation:</h3><em>Initial investigation</em>
The predictions from a line of best fit alternate being too low and too high. That is to say, every other point fits perfectly on a line, and the alternate points fit perfectly on a parallel line.
<em>Line through alternate points</em>
If we use x=1, 2, 3, ... for the number of the member of the sequence, then we have ....
(x, f(x)) = (2, 10.75), (4, 9.82), (6, 8.89)
These points describe a line that can be found using the two-point form of the equation for a line:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
y = (9.82 -10.75)/(4 -2)·(x -2) +10.75 . . . . . using the values from the first two even-numbered points
y = (-0.93/2)·(x -2) +10.75 . . . . . . . . . . simplify a bit
y = -0.465x +11.68 . . . . . . . . . . . . . . . . simplify to slope-intercept form
<em>Correction for other points</em>
We know that this predicts a value too low when x is odd. We can find the amout the prediction is low and add a conditional term to make up the difference.
For x = 1,
y = -0.465·1 +11.68 = 11.215
The actual value is 11.23, or 11.23 -11.215 = 0.015 higher than the equation predicts. We can use the modulo function to give a value that is 1 for odd numbers and 0 for even numbers. For odd values of x, we can add this difference to make the formula predict every number in the sequence.
f(x) = -0.465x +11.68 +0.015·mod(x, 2) . . . . equation for the given points
_____
The table attached shows the given points (y1) and the values predicted using the above formula (f(x1)). (The x1 and y1 used in the attachment are the names of the lists of x-values and y-values. They are not related to the x1 and y1 used above in the 2-point form of the equation for a line.)
The value of minimum usual value is,
The value of maximum usual value is,
Given the values of the parameters of Binomial Distribution are,
Total number of trials (n) = 1490
probability of success in one trial is (p) = 2/5
The probability of failure in on trial is given by,
For Binomial distribution we know that,
Mean
and Standard Deviation
Now, calculating the required measurement we get,
The minimum usual value is given by,
Mean -2 Standard Deviation
The maximum usual value is given by,
Mean + 2 Standard Deviation
Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.
Learn more about Binomial Distribution here -
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