Paul bakes raisin bars in a pan shaped like a rectangular prism. The volume of the pan is 252 cubic inches. The length of the pa
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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:
2670 square feet. Option e.
Step-by-step explanation:
Dan and Betty can paint 2,400 square feet in 4 hours.
They can paint in one hour = 600 square feet.
Since given that Betty paints twice as fast as Dan. Let us take an equation:
Let Betty = B, Dan = D and Sue = S
B = 2D
4(B+D) = 2400
4B + 4D = 2400
12D = 2400
D = 200 sq. ft.
B = 2D = 400 sq. ft.
Therefore, Dan can paint 200 square feet in 1 hour and Betty paints twice 400 square feet in 1 hour.
Now given three of them can paint 3,600 square feet in 3 hours.
3( B+D+S) = 3600
3B + 3D + 3S = 3600
3(400) + 3(200) + 3(S) = 3600
1200 + 600 + 3S = 3600
S = 600 Sq. ft.
Sue can paint 600 square feet in one hour.
So sue can paint in 4 hours and 27 minutes.
× 600
= 2670 square feet. Option e.