Answer: 0.9444
Step-by-step explanation:
Given: The proportion of politicians are lawyers : <em>p </em>=0.56
Sample size : n = 564
Let q be th sample proportion.
The probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4% will be :-

Hence, the required probability = 0.9444
Answer:
The correct answer is A.
Step-by-step explanation:
The area of a rectangle can be calculated using the following formula:

If we know that the area measures
and one side of the figure measures 4.2 m, we can say that:

We isolate the side we don't know:

So I = 9 m
To know the perimter of a rectangle, we use the following formula:



Answer: D. 0.306
Step-by-step explanation:
Assuming a normal distribution for the annual salary for intermediate level executives, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = annual salary for intermediate level executives
u = mean annual salary
s = standard deviation
From the information given,
u = $74000
s = $2500
We want to find the probability that the mean annual salary of the sample is between $71000 and $73500. It is expressed as
P(71000 lesser than or equal to x lesser than or equal to 73500)
For x = 71000,
z = (71000 - 74000)/2500 = - 1.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.1151
For x = 73500,
z = (73500 - 74000)/2500 = - 0.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.4207
P(71000 lesser than or equal to x lesser than or equal to 73500) is
0.4207 - 0.1151 = 0.306
Answer:
2
Step-by-step explanation:
bet
Compute the gradient of
.

Set this equal to the zero vector and solve for the critical points.








The last case has no real solution, so we can ignore it.
Now,


so we have two critical points (0, 0) and (2, 2).
Compute the Hessian matrix (i.e. Jacobian of the gradient).

Check the sign of the determinant of the Hessian at each of the critical points.

which indicates a saddle point at (0, 0);

We also have
, which together indicate a local minimum at (2, 2).