Answer:
a
Step-by-step explanation:
Part a)
The simple random sample of size n=36 is obtained from a population with
and
The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of
The standard error of the means becomes the standard deviation of the sampling distribution.
Part b) We want to find
We need to convert to z-score.
Part c)
We want to find
We convert to z-score and use the normal distribution table to find the corresponding area.
Part d)
We want to find :
We convert to z-scores and again use the standard normal distribution table.
1) Graph the corresponding equation \( x = 2 \); this will split the plane into two regions. One of the region represents the solution set.
2) Select a point situated in any of the two regions obtained and test the inequality. If the point selected is a solution, then all the region is the solution set. If the selected point is not a solution, then the other (second) region represents the solution set.
3) Test: In this example, let us for example select the point with coordinates (3 , 2) which is in the region to the right of the line x = 2. If you substitute x in the inequality \( x ≥ 2 \) by 3 it becomes \( 3 ≥ 2 \) which is a true statement and therefore (3 , 2) is a solution. Hence, we can conclude that the region to the right of the vertical line x = 2 is a solution set including the line itself which is shown as a solid line because of the inequality symbol \( ≥ \) contains the \( = \) symbol. The solution set is represented by the blue hash region in the graph below including the line x = 2.
Answer:
L=P/2-W
Step-by-step explanation:
P=2(L+w) - Solve for L
1) Use the distributive property on the right side of the equation:
P=2L+2w
2) Subtract both sides by 2w:
P-2w=2L
3) Divide both sides by 2 to Isolate L:
P/2-W=L
<span>Angle 7 and 5 are vertical angles, so they're equal.
Angles 7 and 8 are supplementary, so they have to add up to 180.
2x + 15 + 3x = 180
Solve for x, then plug it into the expression for angle 7 to get you answer</span>
