4. A lattice point is a point (ax, y) in the plane, both of whose coordinates are integers. It is easy to see that every lattice point can be surrounded by a small circle which excludes all other lattice points from its interior. It is not much harder to see that it is possible to draw a circle which has exactly two lattice points in its interior, or exactly 3, or exactly 4, as shown in the picture below. :O: :: ● Do you think that for every positive integer n there is a circle in the plane which contains exactly n lattice points in its interior? Justify your answer.

4. A lattice point is a point (ax, y) in the plane, both of whose coordinates are integers. It is easy to see that every lattice point can be surrounded by a small circle which excludes all other lattice points from its interior. It is not much harder to see that it is possible to draw a circle which has exactly two lattice points in its interior, or exactly 3, or exactly 4, as shown in the picture below. :O: :: ● Do you think that for every positive integer n there is a circle in the plane which contains exactly n lattice points in its interior? Justify your answer.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. and and Very very grateful!
So there was a video for this online and i looked through it and analyzed it basically step by step and stilll got it wrong 3 times.
I have tried these, but it keeps saying I have the wrong answer.
A marketing firm wishes to test the effectiveness of the audio/visual presenation of certain information as opposed to the purely audio presentation of information. To this end250 volunteers were given a 10 minute presentation in which the information was presented in an audio/visual format. A second group of 250 volunteers was presented the same information in a purely audio format. Each person in each of the two groups was asked the same 20 questions related to the infomrstion in the presentation. The audio/visual grouo had an average of 10.2 correct responses with a sample standard deviation of 4. The purely audio group had an average of 9.4 correct responses with a standard deviation of 3. The marketing firm believes this means that the audio /visual format leads to better retention of the information. We test the hypothesed H1: µ1 - µ2 = 0 versus Ha: µ1-µ>0 at a 2% level of significance. Here µ1 denotes the population average number of correct responses for individuals…
please help me, I have asked that question a lot of times, and anyone is able to do it please help
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Kindly do it with explaination and don't copy from any other sources Thanks!!!!
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