Answer:
The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2 with (h,k) being the center of the circle and r being the radius. In this case the circle's equation in standard form is (x-2)^2 + (y+3)^2 = 18. Knowing this it's easy to see that the center of the circle (h,k) is (2,-3). Finally the radius is 
or in simplified terms, 3
Step-by-step explanation:
<u>Answer</u>
3×(2×5)
<u>Explanation</u>
Multiplication of numbers is associative. For example,
(a×b)×c = a×(b×c)
This is also called grouping. We multiply more than 2 numbers by grouping.
For the equation given above, (3x2)x5, it can also be grouped as 3×(2×5).
Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
Answer:
You would do it faster
Step-by-step explanation:
48/3 is 16 minutes per bag
28/2 is 14 minutes per bag
Answer:
Step-by-step explanation:
Hello!
In stratified sampling, the researcher separates the population into subgroups according to the criteria established for his experiment. These subgroups will be made up of homogeneous observation units in terms of the characteristics of interest. In this case, each of the people who make up the groups will have only one of the two possible opinions (support, do not support) but not both.
When this type of sampling is performed, it is the researcher who decides what sample size you want to take, depending on various economic factors, availability of materials, access to experimental units (for example, if they are endangered animals, that is, finite populations , you cannot take very large sample sizes)
You can perform a proportionate stratified sampling and take a proportion of people who answered "yes" and a proportion of people who answered "no."
In this type of sampling, when taking a given proportion of each population, it is easier to extrapolate the results obtained to the populations. Then, if for example you must take a sample of size n = 20 where both strata correspond to half, that is to say that the stratum corresponding to "yes" will be 10 people and the stratum corresponding to "no" will be ten people.
I hope this helps!
