POW 15 Growth of rat populations Problem Statement This problem is composed of the growth of a rat population over the course of one year from 2 rats. Four assumptions for this problem were made: Each new liter is composed of 6 rats; 3 males, 3 females. The original pair give birth to 6 rats on the first day and then ever 40 days after. There is a 120 day "gestation" period before a newborn rat can reproduce. After this gestation period the rats will give birth every 40 days. Also over the course of a year no rats die. The key question is how many rats are there after one year. Process In order to solve this problem I first focused on getting an answer for the number of rats. Originally I had planned to use a large sheet of poster board paper to draw out the family tree. But quickly realized that this would be quite impractical. I then settled on a similar but more efficient method. In this method I focused on the 10 liters that the original parents produced. The 10 liters comes from the fact that there is 365.25 days in a year and the parent liter produce every 40 days from day zero. Meaning that they will have a liter on day 0, 40, 80, 120, 160, 200, 240, 280, 320, and 360. I started on the day 360 liter and worked backwards. After finishing this method I compiled the data in a spreadsheet. From which I was able to sum each interval of rat births. The data collected in family tree method is shown in the following data table: Couple: Original D0 D40 D80 D120 D160 D200 D240 D280 D320 D360 Sum 0 2 6 40 80 120 160 200 240 280 320 360 Total Sum after birth 2 2 6 8 6 14 6 20 24 44 42 86 60 146 132 278 258 536 438 974 6 834 1808 6 1808

I then found the pattern that emerged in the upper data table interesting. So I decided to look into it further. At first I looked at the graph of the sum after birth to see what kind of relationship it was.

Sum vs Day
2000 1800 1600 1400 1200 1000 800 600 400 200 0 0

50

100

150

200 Series 1

250

300

350

400

As clearly shown the growth is exponential. I then tried to get a model for this data but could not get anything that fit it perfectly, which is what I was aiming for. So I moved on to looking for relationships in the data. I looked at the ratios and differences between the days and the sums, and rats born. But was unable to come up with anything. I then tried to look at other relationships between sterile rats, reproducible rats, and the sum before and after birth. Sum after birth # rats reproducable sum before birth # sterile 2 8 2 2 0 14 2 8 6 20 2 14 12 44 8 20 12 86 14 44 30 146 20 86 66 278 44 146 102 536 86 278 192 974 146 536 390 1808 278 974 696

Solution My solution for this problem was 1808 rats at the end of 1 year. I believe that this solution is correct because of the pattern noticed when looking at the compiled data table. Also because after creating the table shown above (last page) it was logical that that was how it worked out. Through the course of working on the problem I looked at various ways of solving and trying to find patterns and became familiar enough with the growth of the rats that my answer appears to be completely logical with no questions or discrepancies left open. Generalizations In order to generalize this problem I first looked into jumping straight to an explicit formula but quickly found that doing so would be highly improbable. So I then looked into a recursive function that would model the population. Looking at the growth logically I noticed that the first 3 dates 6 rats were due. Then on the 4th date (120) the number of rats born were going to be 6+ the number born 120 days earlier, or 3 dates back. Then if you continue this a recursive function emerges; such that:

2

U0 = 6 U1 = 6 U2 = 6 U n = (3(U n − 3 ) + 3(U n − 4 ) + 3(U n − 5 ) + ... + 3(U n − n ) )+ 6

...A Pow Wow is a gathering of North America's Native people. The word Pow Wow comes from the Narragansett word powwaw, which means "spiritual leader". A modern pow-wow is a specific type of event where both Native American and non-Native American people meet to dance, sing, socialize, and honor American Indian culture. There is generally a dancing competition, often with significant prize money awarded. Pow-wows vary in length from one day session of five to six hours to three days. Major pow-wow or pow-wows called for a special occasion can be up to one week long. Planning for a pow-wow generally begins months, perhaps even a year, in advance of the event by a group of people usually referred to as a pow-wow committee. Pow wows may be sponsored by a tribal organization, by an American Native community within an urban area, a Native American Studies program or American Native club on a college or university campus, tribe, or any other organization that can provide startup funds, insurance, and volunteer workers.
A pow-wow is often set up as a series of large circles. The center circle is the dance arena, the outside circle which is much larger consist of the MC's table, drum groups, and sitting areas for dancers and their families. Most of the various types of dances performed at a pow-wow are descended from the dances of...

...Like many ambitious, provocative films, "15 Minutes" is a bit of a mess. Both audacious and unwieldy, exciting and excessive, this dark thriller is too long, too violent and not always convincing. But at the same time, there's no denying that it's onto something, that its savage indictment of the nexus involving media, crime and a voracious public is a cinematic statement difficult to ignore.
For despite its traditional cops-and-killers format, "15 Minutes" (its title taken from Andy Warhol's prediction of how long everyone in the future can expect to be famous) is a polemical, apocalyptic film. Writer-director John Herzfeld is furious at the "if it bleeds, it leads" nature of our TV news culture, at the intertwined lusts for fame and gore that rule a society where publicity is more important than reality, everyone plays the victim, and everything is for sale.
Though its anger is a force to be reckoned with, "15 Minutes" finds some space to be funny, albeit in a bleak way, and even provides unexpected moments of romance. Herzfeld, whose debut film was the equally impudent if less impressive "2 Days in the Valley," has utilized an appropriately off-center sensibility for his story, taking the strands of crime melodrama and twisting them to fit his particular purposes.
A key factor in keeping "15 Minutes" involving is its look. Working with inventive French cinematographer Jean Yves Escoffier ("Les...

...F-15 Eagles vs. SU-27 Flankers Aircrafts 1
Comparison of F-15 Eagles vs. SU-27 Flankers Aircrafts
Carlos E. Quinonez
ENG 121 English Compositions I
Instructor: Tiffany Young
February 9, 2009
F-15 Eagles vs. SU-27 Flankers Aircrafts 2
Comparison of F-15 Eagles vs. SU-27 Flankers Aircrafts
At the height of the cold war, both the United States and the Soviet Union have developed aircraft to aggressively engage one another in aerial combat to dominate the skies. The United States had developed the F-15 Eagle in the early 1970 as a primer aircraft while the Soviet Union had developed its own aircraft, the little know SU-27 Flankers aircraft, but after the fall of communism, westerns have always wondered, who had the better aircraft. In 2002, it was rumored that the SU-27 Flanker aircraft could defeat the F-15 Eagle in aerial combat. In this discussion, I will be comparing...

...consumption.
下面这是错误的表达：
The consumption of bottled water in West Europe accounted for 45.5% of the world.
45.5% of the world was in West Europe.
√ West Europe was responsible for the largest proportion of the world’s bottled water
consumption
Incorrect: West Europe was responsible for the largest proportion of the world
这个图是静态，强调对比
两个图的单位不同，因此分开写，一个图写一段，总共两段
第一个图从最高值开始说起
第二个图有些值比较类似，可以归类
时态是过去时
The table below gives information about the percentage of workforce employed in six
industries between 1989 and 2009.
Industries
%
1989
Manufacturing
Retail
Healthcare
Construction
Education
Tourism
2009
15%
11.8%
9.6 %
7.6%
6.8%
5.5%
替换词
Working population, those in the workforce
如果你想描述 15% 这个数字
分子：15（制造业的劳动力） 100 （整个国家的劳动力）
9.8%
10.1%
11.3%
8.3%
7.5%
7.3%
可以说：
1 15% of the country’s working population worked in the manufacturing sector.
2 Those working in the manufacturing sector accounted for 15% of the country’s working
population.
这个图是动态，强调趋势
总共有六个行业，分开写
第一段写 retail, healthcare，因为 2009 年的数据比较高
第二段写其他四个行业的变化
时态是过去时
The table gives information about students’ opinions on different aspects of courses they
attended in a university in 2012.
Percentage of students rating aspects of their course as “very good”
Aspect/course Pre-course
information
Business
62%
Computing
61%
Maths
64%
Teaching
quality
93%
88%
64%
Tutor support
96%
85%
90%
Course
content
74%
69%
72%
譬如说你想描述 62%这个数字
分子：62 （学习 BUSINESS...

...Problem Statement
There are twelve items numbered 1 through 12. All of the values or "weights" are the same except one item whose value is either greater than or less that the other 11 by an unknown amount.
One can compare the sum of the values of a number of items in a set with the sum of the values of items in a disjoint set to see which one is greater. This comparison is also called "weighing."
Find the least number of ways to determine which item has a greater or lesser value.
Process
From the previous POW it was concluded that it would take 5 weighings as described by the equation for an unknown item value:
However, this is an overestimate as there is a way to determine the lighter of nine items with only two weighings. This was overlooked in the last POW (Eight Bags of Gold). Nine items can be weighed by dividing into three sets of size three. Comparing two sets together would determine which set contained the lighter item. With the last weighing, one can determine the lightest item.
This raises the limit of weighings meaning that it would take a mere three weighings to single out the different item out of a set of 27.
Anyway, determining the item which is either lighter or heavier out of 12 is claimed to need only three weighings. It can be done in four because the largest power of three that's within 12 is 33, hence taking three to determine which...

...: 3
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13) Which of the following tasks will you perform in a method that contains a valid reference to a timer object?
1) Notify the enterprise bean about all expired timers
2) Interrogate a timer callback notification
3) Obtain a list of outstanding timer notifications
4) Process a timer callback notification
Solution : 2
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14) By using which of the following methods the enterprise bean obtains a reference to the TimerService object?
1) ejbTimeout method
2) getTimers method
3) getNextTimeout method
4) getTimerService method
Solution : 4
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15) Which of the following options is used to implement Container Managed Transaction (CMT) to methods?
1) To apply CMT to the methods of an enterprise bean the application assembler should on a method-by-method basis consider the suitability of accepting the EJB . default transaction policy.
2) To implement CMT to methods you must code the required transaction policy in the enterprise bean method.
3) To apply CMT to methods do not specify the transactional behavior of the enterprise bean.
4) To implement CMT methods you must code the required transaction policy in the session bean method.
Solution : 1
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16) What will you do when a client method...

...Abstract
Following the Paris Peace Accords, Operation Homecoming returned 591 American prisoners of war (POWs) to the US. At the time, over 1,300 prisoners were listed as missing in action (MIA). An additional 1,200 were killed in action (KIA) and body not recovered. In the ensuing 20 years, activist groups pushed the American government to look into the matter, and several investigations were launched. While no governmental investigation has determined that AmericanPOWs were left behind, there remains considerable evidence that the POW MIA issue contains validity.
The Agreement on Ending the War and Restoring Peace in Vietnam was signed on January 27, 1973. This document, finalized during the Paris Peace Accords, signaled the end of the United States’ involvement in the Vietnam War. The Democratic Republic of Vietnam (North Vietnam), the Republic of Vietnam (South Vietnam), and the Provisional Revolutionary Government (representing various South Vietnamese insurgents) joined the US in signing this historic treaty. The agreement called for the release of US prisoners of war, along with assistance in recovering and transporting home the remains of deceased soldiers. Due in large part to a lack of reliable intelligence in North Vietnam, the US government never knew truly how many prisoners of war were held.
In the years since the war ended, there has been substantial evidence to indicate that many prisoners were left...

...Pow 2
Problem Statement:
There’s a standard 8 x 8 checkerboard made up by 64 small squares. Each square is able to combine with others squares to make other squares of different sizes. Our job is to find out how many squares there’s in total. Once you get all the number of squares get all the number of squares and feel confident with your answer you next explain how to find the number of squares on any size checkerboard. You will know you have the answer when no matter how what size board you have you can give a clear description of to easily compute the total number of squares. So basically what you’re doing is finding the total number of squares in a 8 x 8 checkerboard and pretty much finding an equation on how to find the total number of squares on any size board.
Process:
Alright so how do you find this answer? It’s not as hard as you think it is. Although it is kind of tricky on how to get the answer. What my first concern was, “This is going to take forever. I’m never going to get done.” I honestly thought I was going to get the wrong answer. So my first method was counting all the squares. I knew this was going to take forever. Then I literally was so close to giving up until I looked at the problem...