Answer:

Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 40 dollars
Standard Deviation, σ = 7 dollars
Sample size,n = 51
We are given that the distribution of cost of shrimp is a bell shaped distribution that is a normal distribution.
Formula:

Standard error due to sampling =

P(sample mean would differ by true mean by more than 0.6)



0.5404 is the required probability.
Part A:
x=5
4x-1 ≤19
4(5)-1 ≤19
20-1 ≤19
19 ≤19
x=5
4x-1<19
4(5)-1<19
19<19
Explanation:
In problem one the greater then symbol has a line under it, this means that the symbol now means greater then or equal to. Since 19 is equal to 19 it is correct. In problem to the greater then symbol has no line under it meaning it only means greater then. Since 19 is not greater then 19 it is false.
So basically the difference is:
≤ = greater then or equal to
< = greater then
Part B:
5x+2=47
-2 -2
5x=45
/5 /5
x=9
Explanation:
Since when you solve the equation x=9 the value 9 from the set makes the equation.
Hope this helped :)
Answer:
The minimum y-value is
or 
Step-by-step explanation:
we have

This is the equation of a vertical parabola open up
The vertex is the minimum y-value on the graph
Convert the equation into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side


Rewrite as perfect squares

------> equation in vertex form
The vertex is the point (-0.5,-7.75)
therefore
The minimum is the point (-0.5,-7.75)
The minimum y-value is 
see the attached figure to better understand the problem
I'd arbitrarily begin by writing the factors 10 and 16. These, in turn, factor to 2 and 5. That's all we need to do here to form the product 160, using 5 once and 2 several times:
160 = 5 * 2^5