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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.)
Answer:
The correct option is A.
Step-by-step explanation:
Total number of students at the school is 2,500.
In the given pi chart Pink, Yellow and Sky Blue color represent the percentage of students that under reported, accurately reported, and over reported their heights respectively.
From the graph we can conclude that the yellow portion is approximately one fifth of whole circle. It means the number of students that accurately reported their height is one fifth of total number of students.
Therefore the number of students that accurately reported their height is 500. Option A is correct.