Response:
Detailed explanation:
Hello!
Stratified sampling involves the categorization of the population into subgroups based on pre-established criteria for the study. These subgroups consist of homogeneous units concerning the relevant characteristics. In this instance, individuals in the groups will represent only one of the two potential opinions (support or not support) and not both.
The researcher determines the sample size desired, considering several factors such as finances, material availability, and accessibility to experimental subjects (for instance, if they are endangered species, larger sample sizes may not be feasible).
One might conduct proportionate stratified sampling by selecting a proportion of respondents who answered "yes" along with those who answered "no."
In this sampling method, taking a specific proportion from each subgroup allows for a more straightforward extrapolation of results to the overall populations. For example, if you needed a sample size of n = 20, each stratum would ideally contain half, meaning 10 from the “yes” group and 10 from the “no” group.
I hope this is helpful!
(a) 4 <span>(b) y = sqrt(9 - (9/16)x^2) </span>The most accurate assumption for the equation based on the general format for an ellipse is: [[TAG_3]]x^2/16 + y^2/9 = 1 [[TAG_4]](a). An ellipse is symmetrical along both its major and minor axes. Thus, if you can calculate the area of the ellipse in one quadrant, multiplying that area by 4 will yield the total area of the ellipse, confirming the factor of 4 is accurate. [[TAG_5]] (b). The standard equation for an ellipse doesn't adequately represent a general function as it results in two y values for each x value. However, if we constrain ourselves to the positive square root, that issue can be resolved easily. Here’s how: [[TAG_6]] x^2/16 + y^2/9 = 1 [[TAG_7]] x^2/16 + y^2/9 - 1 = 0 [[TAG_8]] x^2/16 - 1 = - y^2/9 [[TAG_9]] -(9/16)x^2 + 9 = y^2 [[TAG_10]] 9 - (9/16)x^2 = y^2 [[TAG_11]] sqrt(9 - (9/16)x^2) = y [[TAG_12]] y = sqrt(9 - (9/16)x^2)
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
The correct answer is that you start with no refills, paying $2 for the first drink, and when you receive a refill, you pay an additional $1, totaling $3.
Answer:
The expression representing the sum of three times a number and six, over the difference of seven times that number and nine
Step-by-step explanation:
we have
Let
p -----> the variable
we understand that
In the numerator we have (3p+6)
The statement that corresponds to this algebraic representation is "The sum of three times a number plus six"
The denominator is (7p-9)
The statement that corresponds to this algebraic representation is "The difference of seven times the number and nine"
therefore
The statement that represents this problem is "The sum of three times a number and six, divided by the difference of seven times the number and nine"
