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A landlord wants to know the average income of his tenants. He selects three of his eight apartment complexes and collects income information from several randomly chosen tenants within the selected complexes.
A health agency needs to assess the performance of hospitals in a region but does not have the resources to evaluate each hospital. To reduce costs, the agency selects 5 of the 23 hospitals in the region and samples data related to performance from randomly chosen days and times.
Answer: Options D and E.
<u>Explanation:</u>
Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups and a simple random sample of the groups is selected.
Stratified sampling is a probability sampling technique wherein the researcher divides the entire population into different subgroups or strata, then selects the final subjects proportionally from the different strata.
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We know that if two lines are Perpendicular then Product of Slopes of both of these Perpendicular lines should be Equal to -1
Given : Equation of 1st Perpendicular line is -x + 3y = 9
This can be written as :
3y = x + 9
y = x/3 + 3
Comparing with standard form : y = mx + c
we can notice that slope of 1st Perpendicular line = 1/3
Slope of 1st Line × Slope of 2nd line = -1
1/3 × Slope of 2nd line = -1
Slope of 2nd line = -3
We know that the form of line passing through point (x₀ , y₀) and having slope m is :
y - y₀ = m(x - x₀)
Here the 2nd Perpendicular line passes through the point (-3 , 2)
x₀ = -3 and y₀ = 2 and we found m = -3
⇒ y - 2 = -3(x + 3)
⇒ -3x - 9 = y - 2
⇒ -3x - y = 7
