The graph of the sequence M , we define M recursively using function notation

Given :
the graph of the sequence M
Lets write the recursive function using the given points
First point is (1,7) and second point is (2,5) then (3,3) and so on
For recursive function , we use the initial point (1,7)
when n=1, f(n)=7
the y values of the point are decreasing by 2. Common difference is -2
Recursive function is

where n=2,3,4...
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Answer:
Option A.
Step-by-step explanation:
The given function is
Leading coefficient is positive, so it is an upward parabola. Vertex of an upward parabola is the point of minima.
Vertex of a parabola
is
In the given function a=0.15, b=-6 and x=400.
At x=20,
So, minimum value of f(x) is 340 at x=20.
From the given table it is clear that the minimum value of g(x) is 55 at x=70.
Since 55 < 340, therefore, g(x) has a lower minimum values, i.e, (70,55).
Hence, option A is correct.
Answer:
The answer is "Its results are not consistent with its three designs Yes. Its results show significant differences between both the three designs."
Step-by-step explanation:
Following are the distribution of preference:

An expected frequency(
) has 40 Null hypotheses to take n=120.to each design:
The effects of the three designs are standardized
Inaccurate.
Hypothesis Alternative:
The effects of the three prototypes are not uniform
Degrees Of freedom 

Chi-squared distribution critical value at
Since
value
table of
is determined.
So
is rejected.
The translation P<span>(x, y) → P'(x−3, y+4)
means that every point P(x, y) is shifted :
3 units left (because of the -) and 4 units up (because of the +).
We say P was "mapped" onto P'.
Point A(1,1) is mapped to </span>A'(1-3,1+4)=A'(-2, 5).
Check the picture to see where each of the points A, B and C are mapped.