A professor gives a multiple choice exam where each question has five choices. The professor decides not to count a question against students if the class as a whole does significantly worse on the question than they would have done simply by guessing. In other words, the teacher tests H_0: p=0.20versus H_\text{a}: p<0.20 for each question, where p is the proportion of students who would correctly answer the question.

Suppose that 14 of 100 students correctly answer a particular question.
Assuming that the conditions for inference have been met, calculate the test statistic for the professor's significance test.

4 puzzles in 3 hours

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30

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idk

i hope i

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1