(1) connected (2) path connected (3) locally connected (4) locally path connected (5) compact (6) limit point compact (7) locally compact Hausdorff (8) Hausdorff (9) regular (10) completely regular (11) normal (12) first-countable (13) second-countable (14) Lindelöf (15) has a countable dense subset (16) locally metrizable (17) metrizable

Show that topologically completeness is weak hereditary property.

Take an example from the media source and explain the implications of the central limit theorem and the Law of Large Numbers in your example

GMU uses a robot food delivery service which now has been utilized in the City of Fairfax. One of the potential benefits of this service is to help the busiest students eat breakfast. Research has shown that about 80% of college students skip breakfast due to busy schedules and other reasons. Initial data were collected from a random sample of 595 Mason students who utilize the robot food delivery service and are presented in StatCrunch e)  Check the three conditions of the Central Limit Theorem that allow you to use the one- proportion z-test using one complete sentence for each condition. Show work for the numerical calculation. You can assume the population is large. f)  Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing all the steps needed and the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to two decimal places. g)  Calculate the p-value using the standard Normal table and…

with solution and explanation of limit laws used

limit as h---0 for the funtion ((e^2h)-1)/h using L'Hopitals

For each part determine whether or not the success-failure condition of the Central Limit Theorem is satisfied. The proportion of super happy fun meals which contain a prize is 0.84. A random sample of 76 supper happy fun meals is selected. At a package distribution center it is known that 4% of packages have dented corners. You select 32 packages at random from the distribution center. You select 88 fish at random from a pet store where 44% of fish were caught wild. One in every 5 candy bar wrappers can be redeemed for a prize. You select 57 random candy bars.

Actually the range of possible results for a limit with a 00 indeterminate form is anywhere from 0 and ∞. Provide a specific example of a limit with the form 00 where the result is larger than 1

What is the Central Limit Theorem? What does an example of it look like?

The following is true about the limit in   Question 4 options:   The limit along the path y=0 is different from the limit along the path x=0   The limit along the path y=0 is different from the limit along the path y=x   The limit along the path x=-y is different from the limit along the path y=-x   the limit is the same along any path in xy-plane towards the origin