Answer:
Part (a) The value of Z is 0.10396. Part (b) The value of Z is 0.410008.
Step-by-step explanation:
Consider the provided information.
Part (a)
In order to find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.5414, simply find 0.5414 in the table and search for the appropriate Z-value.
Now, observing the table it can be concluded that the value of Z is 0.10396.
Part (b)
Consider the number 65.91%
The above number can be written as 0.6591.
Now, find 0.6591 in the table and search for the appropriate Z-value.
By, observing the table it can be concluded that the value of Z is 0.410008.
Answer:
y=-6x-2
Step-by-step explanation:
So I think the question is basically asking for the minimum y value you could get from the functions.
For the first function,
![y=4 x^{2} +8x+1](https://tex.z-dn.net/?f=y%3D4%20x%5E%7B2%7D%20%2B8x%2B1)
to find the minimum y. (Use x=-b/2a to find its vertex)
so in this case a=4 b=8
x=-8/2(4)=-1 the the minimum value will have -1 as its x coordinates,
![y=4(-1)^2+8(-1)+1=4-8+1=-3](https://tex.z-dn.net/?f=y%3D4%28-1%29%5E2%2B8%28-1%29%2B1%3D4-8%2B1%3D-3%20)
plug in x=-1 to find y.
(-1,-3) for minimum value for the first function
For the second function,
(-1,0) is the vertex of the function, which is the minimum of the function.
compare the first function with y=-3 and second function y=0.
The first function will have the least minimum value and the coordinates are (-1,-3).
Answer: the restrictions on the domain of (u°v) (x) are x ≠ 2 and which v(x) ≠ 0.
Justification:
1) the function (u ° v) (x) is u [ v(x) ], this is, you have to apply first the function v(x) whose argument is (x), and later the function u (v(x) ) whose argument is v(x).
2) So, the domain of the composed function (u ° v) (x) has to take into account the values for which both functions are defined.
3) The domain excludes x = 2 because v(x) is not defined for x = 2.
4) And the domain must also exclude v(x) = 0 because u is not defined for v(x) = 0.
5) So, in conclusion, the domain is all the real values except x = 2 and the x for which v(x) = 0.
Therefore the resctrictions are x ≠ 2 and v(x) ≠ 0