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STA301 Assignment 2 Solution Fall 2012

Monday, November 19, 2012 Edit This
Q2:

Question no 02 part a

If coefficient of skewness is zero then distribution is symmetric or zero skewed.\
\

question no 2 part b
The least squares regression line

The least squares regression line is the line which produces the smallest value of the sum of the squares of the residuals. A residual is the vertical distance from a point on a scatter diagram to the line of best fit. Therefore the least squares regression line can be seen as the best line of best fit.
The equation of the least squares regression line of y on x is:


Where b is:


As you can see there are 3 different ways to calculate the value for b, based on what information you are given in the question
Example

Calculate the least squared regression line of y on x from the following data:
x
203040506070
y
2.492.412.382.141.972.03
Firstly draw up a table of the values you need and fill it out. In this example we'll use the third equation for b so we need all the values of x2and xiyi:
x
y
x2
xiyi
202.4940049.9
302.4190072.3
402.38160095.2
502.142500107
601.973600118.2
702.034900142.1
Sum:
27013.4213900584.7
Next step is to calculate the means of the x and y values:




Now the value of b can be calculated:
Hence the equation is therefore:


Cleaning it up:



















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PHY101 1st Assignment Solution nov 2012

Monday, November 19, 2012 Edit This

PHY101 1st Assignment Solution nov 2012


Q 1: A football player kicks a football straight up in to the air with an initial velocity of 25m/s. What is the approximate maximum height that the ball reaches? Use acceleration due to gravity (g) as 9.8m/s2. Marks = 7

Ans:-
2as = Vf2 – Vi2
Where a = g = 9.8m/s2
Vf2 = 0
Applying the values:
2as = Vf2 – Vi2
2(9.8m/s2) s = 0 – (25m/s)2
(19.6m/s2) s = 625m2/s2
s =625m2/s2 / (19.6m/s2)
s = 31.8m


Q 2: In the classic horse and cart problem, a horse is attached to a cart that can roll along on a set of wheels. Which of the following statement is true? Also explain the reason of your selected choice as well.
a) The horse pulls on the cart with a force, and the cart pulls, back on the horse with an equal force.
b) The horse pulls on the cart with a force greater than the force that the cart pulls back on the horse.
c) The horse pulls the cart forward because the force of friction forward is greater than the force of the wagon backward.
d) The horse pulls the cart forward, because of a time delay between the action and reaction forces.
e) The horse pulls the cart forward, but only if the horse has a mass greater than the mass of the cart. Marks = 6 (2+4)

Ans:-
c) The horse pulls the cart forward because the force of friction forward is greater than the force of the wagon backward.

Reason:-
The forces on the cart include the forward force the horse exerts on the cart and the backward force due to friction at the ground, acting on the wheels. At rest, or at constant velocity, these two are equal in size, because the acceleration of the cart is zero. The forces on the horse include the backward force the cart exerts on the horse and the forward force of the ground on its hooves. At rest, or at constant velocity, these two are equal in size, because the acceleration of the horse is zero. The force the horse exerts on the cart is of equal size and opposite direction to the force the cart exerts on the horse, by Newton's third law. The horse places its feet so as to change the angle of the force its hooves exert on the ground, thereby increasing the backward force of its hooves on the ground.

Q 3: Is it true to say that a projectile has zero acceleration at its peak? If yes explain if not give a reason. Marks = 4

Ans:-
The acceleration due to gravity is constant at 9.8 m/sec^2. One of the variables in projectiles is its speed --- it slows down as it goes up and gains speed as it goes down. When the projectile reaches its maximum height, its velocity is always zero. Acceleration has nothing to do with instantaneous velocity. Acceleration shows the relationship between the velocities of the projectile at 2 different points in time. If acceleration was zero, the difference in velocity of the projectiles between any two points of its trajectory would be 0. However, with an acceleration, even if the velocity of the projectile at one point was 0, but the acceleration would not be zero because the acceleration of a projectile is always equal to the acceleration of gravity.



Q 4: (a) Anna is pushing but the box does not move. What is the force of static friction shown in below figure? Marks = 3

Ans:-
Fs=mu*N
=1*7N
=7N

(b) What is the maximum static friction force shown in below figure? The coefficient of static friction for these materials is 0.31. Marks = 5

Ans:-

=0.31*27N

27 nai only 7 hai
or answer hai 2.17

ECO403 Assignment 1 Solution Fall 2012

Monday, November 19, 2012 Edit This
Commodities19861987
PriceQuantityPriceQuantity
Fish10501370
Milk51007100
Meat715010155
Rice6701090
Fruits7901490
Requirements:
With the help of above data, calculate Togo’s:
Nominal GDP : Y = P x y
y = quantity
P = price
a) Nominal GDP for year 1986
CommoditiesNominal GDP
Fish500
Milk500
Meat1050
Rice420
Fruits630
b) Nominal GDP for year 1987
CommoditiesNominal GDP
Fish910
Milk700
Meat1550
Rice900
Fruits1260
c) Real GDP for year 1987
Real GDP y = Y/P
Where we multiple each year’s Quantities (y) with the previous year’s Prices (P)
CommoditiesNominal GDP
Fish700
Milk500
Meat1085
Rice540
Fruits630
d) GDP deflator for the year 1987
GDP Deflator = (Nominal GDP/Real GDP) x 100
ProductGDP Deflator
Fish130
Milk140
Meat142.86
Rice166.67
Fruits200
e) Labor force for year 1986 and 1987
Labor force = employed + unemployed
1986: 90 lac employed and 7 lac unemployed
Labor Force = 97 lac
1987: 87 lac employed and 11 lac unemployed
Labor Force = 98 lac





Real GDP = Nominal GDP/CPI*100

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Nominal GDP = ∑ ptqt

Figure 6. Employment by Sector, 1987
Source: Based on information from United States, Department of State, Bureau of Public Affairs, Background Notes, El Salvador, Washington, November 1987, 1.
The Salvadoran labor force has been traditionally characterized as industrious, motivated, and reliable. Of new entrants to the labor force in 1986, it was estimated that 4 percent possessed executive, technical, or professional skills. Some 25 percent of all job seekers were classified as semiskilled , while 71 percent were unskilled laborers. The labor force was young, reflecting the demographic profile of the population; in 1985 more than 52 percent of workers were less than thirty years of age (see table 5, Appendix). The labor force remained largely agrarian and rural in the late 1980s (see fig. 6).
Labor suffered because of a variety of economic and institutional circumstances: real wages declined, unemployment rose, and efforts to unify the fragmented labor movement were thwarted by the failure of President Duarte to implement promised labor reforms and by the polarization of union leadership (see Interest Groups , ch. 4). The negative trend for labor continued in 1987. The legal real minimum wage fell by 28 percent, and average real private sector and public sector wages dropped by 13.3 percent. Between 1983 and 1987, real wages declined by about one-third.
The Salvadoran Constitution details the right to organize unions and associations, but the establishment of "closed shops" (enterprises employing only union workers) was forbidden by law. The law also required the use of collective bargaining, conciliation, and arbitration before a strike could be called.
In 1986 there were approximately 150 recognized unions, employee associations, and peasant organizations, which represented 15 percent of the total work force. Although union membership stabilized in the 1980s, union activism fluctuated with prevailing economic and political conditions. For example, in 1982, while membership remained fairly constant in relation to past years, the number of workers involved in strikes fell from 13,904 in 1981 to just 373. In 1984 the number jumped to 26,111.
In 1987 the labor movement vocalized its frustrations as economic conditions stagnated and the civil conflict dragged on. Such frustrations were exacerbated by the perception that Duarte failed to implement the labor reforms he had promised during the 1984 presidential campaign. Labor leaders protested Duarte's failure to fulfill his end of the "social pact" after labor had put its weight behind him in exchange for pledges of increased inclusion of union members in the government and greater responsiveness to labor and peasant issues.
Between 1978 and 1984, private employment fell from 147,000 to 122,000, a 17 percent decline. Employment in the construction industry suffered the most during this period, declining almost 75 percent (see fig. ). Employment opportunities in 1987 continued the downward trend that began with the country's civil conflict. Although no official unemployment rates were available for 1986 or 1987, it is likely that counterbalancing forces stabilized the rate during these two years at the 1985 level, or 33 percent. First, the civil conflict continued to displace many workers and to limit employment growth. Second, the agricultural sector grew by 3.1 percent, recouping losses experienced in 1986. Finally, an estimated 2.5 percent economic growth rate in 1987 was insufficient to reduce the unemployment rate.
The impact of El Salvador's civil conflict was demonstrated in the evolution of the unemployment rate between 1978 and 1985. Over this period, the rate rose almost tenfold, from 3.1 percent to 33 percent. Labor's situation would have been even more grave without the emigration of an estimated 500,000 Salvadorans to the United States between 1978 and 1985. Remittances from workers abroad totaled US$350 million officially in 1987, although some estimates were as high as US$1 billion or more.
Data as of November 1988
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