Answers:
- a) Stratified random sampling, or simply stratified sampling. Each group individually is known as a stratum. The plural is strata. The key here is that each stratum is sampled, though we don't pick everyone from every stratum. We randomly select from each unit to have them represent their unit. Think of it like house of representative members that go to congress. We have members from every state, but Be sure not to mix this up with cluster sampling. Cluster sampling is where we break the population into groups or clusters, then we randomly select a few clusters in which every individual from those clusters is part of the sample.
- b) Simple random sampling (SRS). This is exactly what it sounds like. We're randomly generating numbers to help determine who gets selected. Think of it like a lottery. A computer is useful to make sure this process is quick, efficient and unbiased as possible. Though numbers in a box or a hat work just as well.
For each of the methods mentioned, they aren't biased since they have randomness built into their processes.
Answer:
1/4x^2 - 1/4x - 1/4
Step-by-step explanation:
I multiplied the two binomials at the top to get 6x^2 + x -2 and I divided it by 24x^2 - 4x - 8 and simplified it to get 1/4x^2 - 1/4x - 1/4
4y^2 - 8y + 25x^2 +150x - 171 = 0
4y^2 - 8y + 25x^2 +150x - 171 = 0 Rearrange and regroup.
(25x^2 + 150x) + (4y^2 - 8y) = 0+171. Group the xs together and the ys together.
25(X^2 + 6x) + 4(y^2-2y) = 171. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 6.
Half of it = 1/2 * 6 = 3. (Note this value)
Square it = 3^2 = 9. (Note this value)
Coefficient of y in the second expression = -2.
Half of it = 1/2 * -2 = -1. (Note this value)
Square it = (-1)^2 = 1. (Note this value)
We are going to carry out a manipulation of completing the square with the values
9 and 1. By adding and substracting it.
25(X^2 + 6x) + 4(y^2-2y) = 171.
25(X^2 + 6x + 9 -9) + 4(y^2-2y + 1 -1) = 171
Note that +9 - 9 = 0. +1 -1 = 0. So the equation is not altered.
25(X^2 + 6x + 9) -25(9) + 4(y^2-2y + 1) -4(1) = 171
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1) Transferring the terms -25(9) and -4(1)
to other side of equation.
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1)
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 400
We now complete the square by using the value when coefficient was halved.
25(x+3)^2 + 4(y-1)^2 = 400
Divide both sides of the equation by 400
(25(x+3)^2)/400 + (4(y-1)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x+3)^2)/16 + ((y-1)^2)/100 = 1
((x+3)^2)/(5^2) + ((y-1)^2)/(10^2) = 1
Comparing to the general format of an ellipse.
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Coordinates of the center = (h,k).
Comparing with above (x+3) = (x - h) , h = -3.
Comparing with above (y-1) = (y - k) , k = 1.
Therefore center = (h,k) = (-3, 1).
You can easily draw the ellipse...Cheers.
Answer: b and d
Step-by-step explanation:
Since the roots are x=2 and x=6, we can write the equation as
Substituting in the coordinates of the vertex,
So, the equation is
On expanding, we get