Answers
Answer 1
Answer: y = -cos2x
Explanation:
Its a sine wave. Or a cosine wave. Theyre the same depending on how you phase shift it.
I see it as a reflection of the cosine wave over the x axis. this way there are no ugly phase changes. this makes the whole function negative though.
The amplitude can be seen as 1. so there is no vertical stretch.
However, there is a period change. in 2pi, we can see 2 full cycles of this graph, which suggests the period has been shrunk, (by a factor of 2).
so b = 2.
plugging all this information into the cosine function, our equation is going to be:
y = -cos2x
ask questions in the comments if you dont get it :)
Related Questions
What is permissive mean
Answers
The term "permissive" generally means granting permission or allowing something to be done without objection or interference. It implies a degree of flexibility or leniency in terms of rules or regulations. For example, a permissive parent may allow their child to make their own decisions without strict rules or discipline. In contrast, an authoritarian parent may have strict rules and expect strict obedience from their child. In a legal context, a permissive law or regulation allows something to be done, but does not necessarily require it.
According to the Bureau of Labor Statistics, 71.9% of Young women enroll in college directly after high school graduation. Suppose a random sample of 200 female high school graduates is selected and the proportion who enroll in college is obtained.
a. What value should we expect for the sample proportion?
b. What is the standard error?
c. What effect would increasing the sample size to 500 have on the standard error?
Answers
a. The expected value for the sample proportion can be calculated as the population proportion: 71.9%, so we expect that approximately 71.9% of the 200 female high school graduates will enroll in college directly after high school graduation.
Expected value = population proportion * sample size = 0.719 * 200 = 143.8
Therefore, we expect approximately 144 female high school graduates to enroll in college directly after high school graduation.
b. The standard error of the sample proportion can be calculated as:
SE = sqrt[p(1-p)/n], where p is the population proportion and n is the sample size.
SE = sqrt[0.719(1-0.719)/200] = 0.033
Therefore, the standard error is 0.033.
c. The standard error is inversely proportional to the square root of the sample size. Increasing the sample size from 200 to 500 would reduce the standard error:
SE = sqrt[0.719(1-0.719)/500] = 0.023
Therefore, the standard error would decrease to 0.023 if the sample size increased to 500.
Expected value = population proportion * sample size = 0.719 * 200 = 143.8
Therefore, we expect approximately 144 female high school graduates to enroll in college directly after high school graduation.
b. The standard error of the sample proportion can be calculated as:
SE = sqrt[p(1-p)/n], where p is the population proportion and n is the sample size.
SE = sqrt[0.719(1-0.719)/200] = 0.033
Therefore, the standard error is 0.033.
c. The standard error is inversely proportional to the square root of the sample size. Increasing the sample size from 200 to 500 would reduce the standard error:
SE = sqrt[0.719(1-0.719)/500] = 0.023
Therefore, the standard error would decrease to 0.023 if the sample size increased to 500.
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