Recent orders
Federal Budget Exercise
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Budget
Federal Budget Exercise
The proposed budget is $1,319 billion for the year 2015 and a tax rate of 24%; the projected budget has a deficit of $ 583 billion. This deficit is a bit lower for the 2015 federal budget by $42 billion implying that some changes need to be made to come up with a viable value. The changes were made on the following; the defense budget was reduced from $752 billion to $721 billion, homeland security was positively adjusted from $47 billion to $49billion; this is done to enforce more security to the citizens. Since US forces have been gradually coming home; it was prudent to reduce the defense budget to allow citizens enjoy more security in their country. As much as it would be difficult avoiding tax increase because it is used to increase government expenditure, the $1.2 trillion dollars proposed in the federal budget was a bit high for the citizen. It would be prudent if the tax increase was set at a maximum of $1 trillion dollars or below.
Federal Budget Challenge
There are specific changes that were made to come up with the budget. The first policy was to increase the allocation of social funds from $47 billion to $ 49 billion for the homeland security to improve the social welfare of the citizens. Medicare also got a boost to have a minimum funding of $65 billion; education sectors and the research institutions got an increments in the budget allocation to help the various agencies involved to improve service delivery to the citizens. However, the defense allocation was slightly reduced since the war in Afghanistan has relatively gone down and the US army has been coming home thereby reducing the expenditure on military and defense. The method used in the budget allocation was based on the economic situation of the US and the entire globe hence making it more realistic. In addition, a number of factors have been considered in the budget such as political stability of the country, the general hunger, and global warming, thereby making the proposed budget a popular one. To ensure that the economy grows and the deficits become shrank, it is important to formulate a comprehensive immigration reform to stabilize the country’s broken immigration system. To reduce the debt and deficit levels of the country, it is important to finance new investments and tackle the fiscal challenges. This would ensure a fall in deficit levels to approximately 1.6% of the GDP and thus stabilize the economy’s debt share.
The Budget Hero
The budget policies that were implemented to achieve the results majorly focused on diverting more funds for national security. The advancement to giving priorities to national security and increasing payment for the armed forces ensured security for the United States while at the same time protecting its interests across the world. Good salaries for the armed forces gave them the motivation to advance towards achieving the country’s military mission in Afghanistan and enable Afghanistan become responsible for its own future. Giving priority to security matters also ensured the country maintain a modern, ready, and able defense forces to counter any form of threat including cyber attacks and terrorism. Part of the funds diverted to armed forces was also used to support medical care for the veteran soldiers, assist the soldiers to transition to civilian life, and reduce the veteran’s homelessness. The federal budget challenge led to a reduction in the country’s debts and a shrink in deficit levels. Most voters do not know how revenue and spending choices are influenced at the federal level because they are never involved in decision making on budget matters. The federal budget is normally formulated at the interest of political leaders and implementation of certain budget priorities will most likely get compromised if such priorities are moving against their wishes.
Finite mathematics
Finite mathematics
A. Rounding and Truncation: In a classroom, students will receive a letter grade based on the percentage of points gained in the term out of the total points possible. There are 334 points possible. To get an A in the class, the student must have a percentage that, when properly rounded to a whole number, is at least 90%.1. Determine whether the teacher will give Student 1 an A for the class if the student has earned 299 points, justifying your answer.
229/334 x 100=68%, the teacher would not give the student an A because the score of the student is only 68%, if the teacher rounded the figure to the nearest 10, it would be 70%, this is below the 90% pass mark.
2. Use your answer in part A1 to explain whether Student 1 will receive an A for the class if the teacher truncates the percentage to a whole number.
To truncate, we drop or cut of the numbers after the decimal. This is done to reduce the figure to make it easy to operate. For example, the number is 0.6856287425 or 68.56287425%, this is a very long number which is not easy to multiply or divide with another number. So If If the teacher truncates the number to a whole number, the student would not get an A as the figure would be 89.52%, five is truncated down to 89%.
3. Explain the following (suggested length of 1 page) as if you were teaching a middle school mathematics classroom (grades 5–9): a. Why a taxpayer whose income tax rate is 27.8% would hope that the rate could be truncated to a whole number when calculating the amount of tax owed on the tax form.
In this way the amount of tax on him is reduced to a lower value, this might mean him paying only 27%. For example, if the taxpayers salary is $20000, he would have to pay $5560, however, if the tax rate is truncated to 27%, he will only pay: $5400, this is less compared to $5560. This means that the tax burden is lessened.1. Why the government prefers and requires the taxpayer to round the tax rate:
This is done to increase the accuracy of the result or to get an accurate tax rate
b. Your mental math process in calculating the above situation and how you would use rounding and truncating in real-world scenarios.
If i wanted to multiply an array of number, i would round of the decimal places and remain with the whole numbers only, which are relatively easy to operate1. Provide two examples of each rounding and truncation (four total examples) to illustrate mental math skills.
34.6545 truncated into =34
23745.823 truncated into =23745
34.345 rounded off into= 35
23745.823 rounded off into 23746
B. Primes and Composites: There are 20 boys and 24 girls in an Algebra I class. The class is so large that the teacher wants to divide the students by gender into cooperative groups composed of the same number of students.
1) Explain the process the teacher will use to determine how many students will be in each group using appropriate mathematical terms from number theory by gauss
The theory of finite maths was postulated by gauss, according to him one has to find the greatest common Factor (GCF) of both numbers, for example, he would divide both genders into same portions. By this he finds the greatest common factors of both groups
The greatest common factor of 24=6
And the greatest common factors of 20=5
2). Determine the largest number of students that can be placed in a group, showing all work
4 boys per group and 6 girls per group
Boys: 4×5
Girls=6×4
3). given your answer in B2, determine how many groups will be created from the Algebra I class, providing support
Girls= (6×4) =24
Boys= (5×4)
The total number of groups that can be created from the algebra class is 114. Explain how to prove that there is an infinite number of primes.
Prime number has only two divisible factors, because they are only divisible by one and itself, example of prime number are 7 and 11. Prime number was postulated by Euclid. He proved that there are an infinite number of primes, according to him, if a number of primes are finite, and then there can be other primes to it, which generates other primes
Example:
Starting with a list of number of primes known x1, x2, …, xn.
Multiply the number together and adding one, the product is X X = x1x2…xn. Let q = X + 1.
We know that X X + 1 = q.
X divides the differences between the two numbers (X + 1) − X =1
There is no divisors of which is a prime number This number would run up to infinity as there would always be prime number in the list to
This proves that in each list containing prime number, there will always be other prime number.
C. Modular Operations: You want to explain the concept of modular operations to a middle school mathematics classroom, starting with a demonstration from clock arithmetic. Your explanation should include the following support: • Appropriate examples for modular addition using positive integers of the following sum:
Find a unit digit of the sum= 2403+791+688+4339
Total 8221,
Unit digit 1
Same way the unit digit that results from the addenda 3+8+1+9
This can be solved by use of modular arithmetic
2403 3(MOD 10)
791 1(MOD 10)
688 8(MOD 10)
4339 9(MOD 10)
TOTAL 21 OR 1(MOD 10)_
• Appropriate examples for modular addition using negative integers
When you subtract 601 from 60002 and divide the result by 6
60002 =2 (mod 6)
601 =1 (mod 6)
60002-601 =2-1 mod 6
=1 mod 6
• A sentence or two about the use of modular operations in real-world scenarios
Modular operation is used in calculating time, espcialy amongst the military people, in the airline industry, when the say that flight x was supposed to arrive at 9.00 am and is delayed by 14 hours it is easy to calculate the time.
However, modular mathematics is only easy tom use when calculating simple mathematical problem, at higher level it get complicated because, it relies on very many assumptions key amongst them is the principle of infinity of primes, discussed above. This concept is not practical in real world situation. For example at an advanced level of structural engineering, there is no need to use modular mathematics while there are system and machines for determining the stress factors in system instead of doing complex calculation.
1. Explain how you would discuss the following (suggested length of 1 page) in the classroom setting:a. Modular arithmetic and its relation to time
The modular arithmetic’s is closely related to time in that it considers repetitive cycles of numbers such as the clock face which has 12 cycles, each cycle represents 12 hours which are represented by 60 minutes and each minutes ois represented b 60 seconds. After the 12 hour cycles, one has to start from 1. If you look closely you realise that it is a mod 12 mathematics
If the hands of the clock cycles from 0 to 11 it makes 12 hours. For example, in our case we take an example of 16 mod 12, we realise that the answer is 4. This is also applicable when one is using the military time as it involves 24 cycles round, this mould mean having a mod 24, or a year which has a mod 12 months. This is possible with all the finite cycles’ numbers.
Another example, include the calculation of time , for example one can calculate time on the following grounds, if it is 7 am, and one would like to determine the position of the hour hand in 7 hours time.
Intuitively this is 7+7=14 then
Therefore: 14 mod 12=2, this is a practical even in the 24 hour clock another example on the 24 hour clock is
If the time now is 8.00, and one want to determine the position of the hour hand at 25 hours,
This is 25 mod 24=1
=1+9 ≡ (8) mod 12 + (25) mod 12 ≡ (8) mod 12 + (1) mod 12 ≡ 9 mod 12
b. What is meant by 10 mod 6?
The remainder when 10 is divided by 6
10(mod 6) =4.
c. How to add or multiply in mod 7
Add or multiply the figures ordinarily and divide the answer by 7. For example, if one is given the question below.
Add 6 and 12 in mod 7=6+12 (mod 7) =18(mod 7) =4, here we first add the figures 6 and 12, to get 18, then divide by 7. If we divide 18 by 7 the answer is 2 remainder 4, because 7 goes into 18 twice giving us 14, remaining 4. The four is the answer as it is the remainder after the operations.
The same figures can be used for operation when one is asked to multiply the figures and get the modulus. Multiply 6 and 12 in mod 7=6 X 12 (mod 7) = 72(mod 7) = 2, here we first multiply the figures 6 and 12, to get 72, and then divide by 7. If we divide 72 by 7 the answer is 10 remainder 4, because 7 go into 72, Ten times giving us 70, remaining 2. The 2 is the answer as it is the remainder after the operations.
Early human communities
Early human communities
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Many archaeologists in conjunction with scientists have tried to describe and discover the origin of human beings. Several questions remain pending with no accurate answer; where did man come from? From what did we evolve? These are some of the questions that remain unanswered and without proof. From studies made and research done by various people such as Charles Darwin, man is said to have evolved from apes. Over the years, through natural selection, survival for the fittest and adaptation man has been able to develop and evolve to what is seen today. In many ways it is rather hard for us to imagine that at a certain point in life our ancestors were solely hunters and gatherers, they lived in caves and that there was no major settlement instead they moved around the globe in search of food.
In the Palaeolithic era, there was less food which forced the people to move from place to place in search of food; men would hunt in groups while women would gather the roots and fruits. Many people died due to the scarcity of food and harsh weather conditions. In terms of relationships, women were generally exchanged sexually for reproduction, this went on until 600 BC in Mesopotamia where reproduction was considered a private thing; a man would choose a woman who would bear children and raise a family together. Women were given less power positions in the community and they were only allowed to stay at home and to reproduce; the children would provide labour and security for the community.
As early man began to settle and start agricultural activities such as farming and keeping animals, other aspects of life emerged such as religion. In the past, people believed in spirits and in gods, Egypt had a number of gods (Osiris, Isis, Anubis, and Horus) (Roosie, 111). Each god had a purpose with aspects such as war, fertility, and various weather seasons represented. Both Egyptians and Mesopotamians believed that power and authority came from gods; gods controlled every aspect in life. Priests, who were advisors of the king, would interpret to the kings what the gods want done and the laws that should be stipulated. Kings and priests were also viewed as holy beings chosen by gods as a link between them and the whole empire.
The communities also had to come up with a form of government that would implement law and order in the community. The man was considered the head of the family, while elders in the community provided advice and maintained general order in the community. As years went on, early human beings chose kings that would rule over the kingdom. Egypt was served by pharaohs while Mesopotamia was ruled by kings but all had similar roles such as setting laws (Hawkes 77). The hierarchy of authority was as follows; the king, priests, commanders, soldiers and finally the police. The middle class included the merchants, artisans, and labourers while the low class included the slaves and peasants.
Early human beings are considered the pioneers of present day’s agriculture. Egypt which was located close to the Nile was able to develop irrigation channels that enabled crop production. Mesopotamia on the other hand was located between the river Euphrates and Tigris (Roosie, 97). The rivers supplied them with water for farming and domestic use. They grew seeds and kept animals such as the dog, cats, goats and cows that provided them with food, security and also labour. The plough for example was developed around this time. Mining and the use of metal artefacts also started with the early human communities, for example, garden equipment, swords and other domestic equipments.
Early human beings fought one another for power and resources, wars were prone hence security was required. The geographical features provided security for the regions; Egypt was surrounded by the red sea and the Mediterranean which protected it from its enemies (Hawkes, 179).
It was unjust how women in the past were treated as minorities in the community. Almost equal opportunities and positions as men would have been appropriate and just. However, the governments formed were an important step for the communities to ensure law and order was maintained in the community. Religion was also an appropriate step as it allowed unity among the members of the community and it helped maintain the morals and customs of the people.
The reason for choosing this question was to show and to describe how early human communities were and how they developed. As a way to explain the origin of several aspects in the current human life, the discussion was relevant to show how man has evolved through the social, political, economic, and religious life. The current human life is almost a complete reflection of the past in terms of religion and politics.
It is important to learn and to understand the early human life, how man evolved to be what he or she is in the present. Through the study of early ways of religion enables us to embrace our culture and religion and get to know what significance it holds to respect and accept religion in our lives. Through the study of politics and how early governments were formed and their functions, people are able to respect what position leaders have and their responsibilities. People are also able to learn how agriculture came to be and how it grew. Through the study of all these aspects human beings can reflect on the important factors and come up with solutions to customs and ways that were inappropriate such as gender inequality.
References
Hawkes, Jacquetta. The First Great civilizations; life in Mesopotamia, the Indus Valley, and Egypt. (1st ed. New York: Knopf; [redistributed by Random House], 1973. Print.
Rossi, Renzo, and Andrea Due. Cradles of civilization: ancient Egypt and early Middle Eastern Civilizations. New York: Macmillan Library References USA, 1996. Print.