Answer:
μ = 1.3468
Step-by-step explanation:
Given data:
Observations
0.85
0.88
0.88
1.06
1.09
1.12
1.29
1.31
1.42
1.49
1.59
1.62
1.65
1.71
1.76
1.83
sum of the observations = 21.55
now,
the total number of the given data, n = 16
now, the mean is given as:
Mean = (Sum of all the observation) / (Total number of observations)
on substituting the values in the above formula, we get
Mean = 21.55 / 16
or
Mean = 1.3468
Since, it is given that the data follows normal distribution.
thus, the normal mean can be used as the point of estimator (μ)
i.e μ = 1.3468
The key features that are unique to the the graphs of sequences and series is that they are discrete.
That means that the graph is not a continuos line or curve that join all the points. On the contrary, the graph is a set of separated dots, because the values are valid only for specific points.
Regarding the average rate of change, there is not difference to calculate it respect to other graphs.
The average rate of change between points is yet the slope of the line (in this case imaginary line) that joined the first and the last point, and that is:
rise y2 - y1
average rate of change = slope = ------------ = --------------
run x2 - x1
Answer: 90.51 square units
Explanation:
1) The rectangle has one length on the x-axis.
2) Call x, the x-coordinate of the right lower corner of the rectangle.
And the point is (x,0)
3) The x-coordinate of the lef lower corner will be - x.
And the point is (-x,0)
4) The right upper point of the rectangle will be (x,y) where y = 24 - x²
5) The left upper point of the rectangle will be (-x,y) where y = 24 - x² .
6) The area of such rectantle is the length of the base times the length of the height.
The length of the base is 2x
The lenght of the height is y
So, the area is A = 2x(y) = 2x(24 - x²) = 48x - 2x³
7) Now to find the maximum area you have to derivate the function and make it equal to zero:
dA
---- = A' = 48 - 6x² = 0 =>
dx
4x² = 48 => x² = 48/6 = 8 =>
x = (+/-)√8
Then, y = 24 - x² = 24 - (√8)² = 24 - 8 = 16
8) Therefore the area of the rectangle is
A = 2x(y) = 2(√8)(16) = 90.51.
9) You can see if x is a greater or smaller.
For example x = 2 and x = 3
x = 2 => y = 24 - (2)² = 20 => A = 2(2)(20) = 80 which is less than 90.51
x = 3 => y = 24 - (3)² = 15 => A = 2(3)(15) = 90 which is less than 90.51
So, that tells you that your result should be right.
Answer: $2603.90
Step by step solution: See photo
Answer:
The maximum value of the function is 4
Step-by-step explanation:
