Explain why histograms and frequency polygons are used in business .pdf
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Explain why histograms and frequency polygons are used in business statistics. Solution 1) A picture is worth a thousand words, i.e. a visual display is a good way to summarize a large data set. 2) Histograms give some feeling for the overall shape of the data, something that reporting XBAR and S cannot give, i.e. skewness, kurtosis, range. 3) Relative histograms and frequency polygons are estimates of proba- bility functions..
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f(x) = 1 pi (1+x2), where x R Find the mean of the random variable.pdf
f(x) = 1/ pi (1+x2), where x R Find the mean of the random variable X with this probability
function
Solution
E(x) = int x.f(x) dx = int x/(1+x2) dx = 1/2 ln(x2 +1) (x from -a to a when a -> ) =
1/2 (ln(1+a^2) - ln(1+a^2)) = 0
Therefore the mean is zero:
E(x) = 0.
Explain what natural carbonate buffer system is. You may use a lake f.pdf
Explain what natural carbonate buffer system is. You may use a lake for your example.
Solution
As the name suggests the \"natural carbonate buffer system\". The carbonate is formed by the
natural carbon di oxide gas. Let us consider for a lake. Lake is a large water body whose surface
is open to the atmosphere. We already know that Buffers are the mistures of weak acid and its
conjugate bases that have withstanding capacity of the pH changes.
Here the natually available CO2 combines with H2O to form H2CO3. H2CO3 is Carbonic acid
i.e weak acid. Carbonic acid splits into
H2CO3 ---------) H+ + HCO3- Ions.
CaCO3 , Calcium carbonate is a commanly available mineral in the deposites of the lakes. it
splits into
CaCO3 ---------) Ca2+ + CO32- ions.
CO32- of Calcium carbonate combines with water to form OH - and HCO3- . H+ formed by the
Carbonic acid combines with OH- to form water. This phenomenon forms buffer of Weak acid (
Carbonic Acid) and weak base forming water thus maintaining the pH of the Lake.
This process is termed as natuall carbonate buffer system..
Explain what is meant by the height of a binary tree. Let us assume t.pdf
Explain what is meant by the height of a binary tree. Let us assume that in a fully populated
binary tree, there are 15 internal (non terminal) vertices. What is the height of the tree? Is there a
relationship between height of a tree and maximum number of nodes?
Solution
The height of a tree is the length of the path from the root to the leave of the tree. A (rooted) tree
with only one node (the root) has a height of zero.
heigh = 0, node = 1, internal vertices = 0
heigh = 1, node = 2, internal vertices = 1
heigh = 2, node = 4, internal vertices = 3
heigh = 3, node = 8, internal vertices = 7
heigh = 4, node = 16, internal vertices = 15
therefore, the height of the tree with 15 internal vertices is 4.
relationship:
max nodes = (2(Height + 1)) - 1.
Exercise 11. Let L R^4 - R^3 be the map defined as L(x,y,t, u) = .pdf
Exercise 11. Let L : R^4 - > R^3 be the map defined as L(x,y,t, u) = (t - 2x - 3y + u, 4x + 6y -
2u, t) (1) Prove that L is linear: (2) Compute dim (Im(L)). Hint: use the fact that dim(Im(L)) is
the column rank of AL) (3) Compute dim(ker(L)). (Hint: use part (2) together with the
Dimension Formula.)
Solution
For proving T is linear let us show that L(x1+x2, y1+y2, t1+t2, u1+u2) = L(x1,y1,
z1,t1)+L(x2,y2, z2,t2)
LHS = (t1+t2-2x1-2x2-3y1-3y1+u1+u2, ......)
By property of distributivity and commutativity for real numbers we get LHS =RHS
Hence t is linear.
2) dim (IML) = 3 as there are 4 linearly independent vectors
3) Ker(L) = (set of (x,y,t,u) such that
t-2x-3y+u =0
4x+6y-2u =0 and t =0
i.e. 2x+3y+u =0 and t =0 is the condition
This has solution as
(x,y, 0,-2x-3y)
Dim ker L = 2..
Each individual in a random sample of high school and college stude.pdf
Each individual in a random sample of high school and college students was cross-classified
with respect to both political views and marijuana usage, resulting in the data displayed in the
accompanying two-way table. Does the data support the hypothesis that political views and
marijuana usage level are independent within the population? Test the appropriate hypotheses
using level of significance 0.01.
Usage Level Never Rarely Frequently Political
Views Liberal476172117 Conservative2124613 Other1714789
Solution
The test statistic is
chisquare =72.07.
Establish that the Chebyshev polynomial form a basis tor P3 PO(t)=1. .pdf
Establish that the Chebyshev polynomial form a basis tor P3 PO(t)=1. Pl (t)=t. P2(t)=2t^2-1.
P3(t)=4t^3-3t
Solution
The Chebyshev polynomials of the first kind are defined by the recurrence relation.
P0(t) = 1
P1(t) = t
and further by
Pn+1(t) = 2t*Pn(t) - Pn-1(t)
so
P3(t) = 2t*P2(t) - P1(t)
= 2t*(2t^2 - 1) - t
= 4t^3 - 3t.
Economics (Multinational firms. FDI) Question1 With respect to innov.pdf
Economics (Multinational firms. FDI) Question1: With respect to innovation and transfer of
technology between Home and Host industries, compare and contrast views advanced by Vernon
and Kruman.
Solution
The pattern of world trade and the trends in such changes over time is gretly determined by the
technological innovation in developed countries (also refered as home countries) and transfer of
technology in less developed countries (also reffered as host countries).
The spread of production and technological advancement which results in world trade pattern is
backed up many theories in literature. One of the thoeory is of Vernon, in which decision to
locate production in foreign countries is studied through life cycle model. He linked the location
of production activities to the stages of life cycyle of a product, hypothising that new product
because of their higher knowledge intensity, would be produced in North, which has a relative
abundabce of skill labor and therefore a comparative advantage occurs in their prodcution. For a
while, when the product has become standard and popular, technology transfer to the South or
Southern firms.
Epidemiological data and operational information about outbreaks is.pdf
Epidemiological data and operational information about outbreaks is dynamic and changes
rapidly. You must develop a comprehensive Event Management System to manage critical
information about an outbreak (of your choice) within the Excel program that you have just
learned. This is one method to ensure accurate and timely communications between key public
health professionals and the community.
Choose from any one of the fields below.
Features of the data management system you create should include:
Solution
Case Management-
Businesses and agencies in long-term relationships with their customers, citizens or subscribers
will be judged by the accuracy of the records they hold, the consistency of the communications
that take place, and the speed, efficiency and fairness with which each case, claim or contract is
processed.
Delivery of customer service against these priorities has never been more challenging.
Customers are more mobile in their addresses, jobs and family relationships. Communications
channels seem to multiply overnight, with customers switching between them at will. Corporate
messaging demands multi-channel distribution with increasing amounts of personalization.
Mergers and acquisitions create multiple silos of customer-related data to be seamlessly joined.
And products, business rules and government regulations change with alarming frequency.
Against this backdrop, the demands on the IT systems to support smooth, efficient and integrated
delivery are considerable, particularly where case-orientated transactions are involved.
Emergency Response-
Environmental emergencies are incidents or events that threaten public safety, health, and
welfare and include hurricanes, floods, wildfires, industrial plant explosions, chemical spills, acts
of terrorism, and others. While these events range in size, location, cause, and effect, most have
an environmental component. Emergency response is the organizing, coordinating, and directing
of available resources in order to respond to the event and bring the emergency under control.
The goal of this coordinated response is to protect public health by minimizing the impact of the
event on the community and the environment.
An emergency response plan must provide the resources and information needed to evaluate the
human and environmental health impacts of the event, assess and reduce human exposures to
contaminants, and develop science-based strategies for remediation and rebuilding. One example
is the immediate response of NIEHS and other government agencies to the devastation and
hardship caused by Hurricane Katrina. This included the establishment of a field hospital in
Mississippi to meet the immediate health needs of the hurricane victims, as well as the
development of a Geographic Information System to plot the locations of chemical plants,
refineries, Superfund clean-up sites, and other potential hot spots of contamination where
flooding occurred.
Safe Drinking Water-
There are many types o.
Recommended
f(x) = 1 pi (1+x2), where x R Find the mean of the random variable.pdf
f(x) = 1/ pi (1+x2), where x R Find the mean of the random variable X with this probability
function
Solution
E(x) = int x.f(x) dx = int x/(1+x2) dx = 1/2 ln(x2 +1) (x from -a to a when a -> ) =
1/2 (ln(1+a^2) - ln(1+a^2)) = 0
Therefore the mean is zero:
E(x) = 0.
Explain what natural carbonate buffer system is. You may use a lake f.pdf
Explain what natural carbonate buffer system is. You may use a lake for your example.
Solution
As the name suggests the \"natural carbonate buffer system\". The carbonate is formed by the
natural carbon di oxide gas. Let us consider for a lake. Lake is a large water body whose surface
is open to the atmosphere. We already know that Buffers are the mistures of weak acid and its
conjugate bases that have withstanding capacity of the pH changes.
Here the natually available CO2 combines with H2O to form H2CO3. H2CO3 is Carbonic acid
i.e weak acid. Carbonic acid splits into
H2CO3 ---------) H+ + HCO3- Ions.
CaCO3 , Calcium carbonate is a commanly available mineral in the deposites of the lakes. it
splits into
CaCO3 ---------) Ca2+ + CO32- ions.
CO32- of Calcium carbonate combines with water to form OH - and HCO3- . H+ formed by the
Carbonic acid combines with OH- to form water. This phenomenon forms buffer of Weak acid (
Carbonic Acid) and weak base forming water thus maintaining the pH of the Lake.
This process is termed as natuall carbonate buffer system..
Explain what is meant by the height of a binary tree. Let us assume t.pdf
Explain what is meant by the height of a binary tree. Let us assume that in a fully populated
binary tree, there are 15 internal (non terminal) vertices. What is the height of the tree? Is there a
relationship between height of a tree and maximum number of nodes?
Solution
The height of a tree is the length of the path from the root to the leave of the tree. A (rooted) tree
with only one node (the root) has a height of zero.
heigh = 0, node = 1, internal vertices = 0
heigh = 1, node = 2, internal vertices = 1
heigh = 2, node = 4, internal vertices = 3
heigh = 3, node = 8, internal vertices = 7
heigh = 4, node = 16, internal vertices = 15
therefore, the height of the tree with 15 internal vertices is 4.
relationship:
max nodes = (2(Height + 1)) - 1.
Exercise 11. Let L R^4 - R^3 be the map defined as L(x,y,t, u) = .pdf
Exercise 11. Let L : R^4 - > R^3 be the map defined as L(x,y,t, u) = (t - 2x - 3y + u, 4x + 6y -
2u, t) (1) Prove that L is linear: (2) Compute dim (Im(L)). Hint: use the fact that dim(Im(L)) is
the column rank of AL) (3) Compute dim(ker(L)). (Hint: use part (2) together with the
Dimension Formula.)
Solution
For proving T is linear let us show that L(x1+x2, y1+y2, t1+t2, u1+u2) = L(x1,y1,
z1,t1)+L(x2,y2, z2,t2)
LHS = (t1+t2-2x1-2x2-3y1-3y1+u1+u2, ......)
By property of distributivity and commutativity for real numbers we get LHS =RHS
Hence t is linear.
2) dim (IML) = 3 as there are 4 linearly independent vectors
3) Ker(L) = (set of (x,y,t,u) such that
t-2x-3y+u =0
4x+6y-2u =0 and t =0
i.e. 2x+3y+u =0 and t =0 is the condition
This has solution as
(x,y, 0,-2x-3y)
Dim ker L = 2..
Each individual in a random sample of high school and college stude.pdf
Each individual in a random sample of high school and college students was cross-classified
with respect to both political views and marijuana usage, resulting in the data displayed in the
accompanying two-way table. Does the data support the hypothesis that political views and
marijuana usage level are independent within the population? Test the appropriate hypotheses
using level of significance 0.01.
Usage Level Never Rarely Frequently Political
Views Liberal476172117 Conservative2124613 Other1714789
Solution
The test statistic is
chisquare =72.07.
Establish that the Chebyshev polynomial form a basis tor P3 PO(t)=1. .pdf
Establish that the Chebyshev polynomial form a basis tor P3 PO(t)=1. Pl (t)=t. P2(t)=2t^2-1.
P3(t)=4t^3-3t
Solution
The Chebyshev polynomials of the first kind are defined by the recurrence relation.
P0(t) = 1
P1(t) = t
and further by
Pn+1(t) = 2t*Pn(t) - Pn-1(t)
so
P3(t) = 2t*P2(t) - P1(t)
= 2t*(2t^2 - 1) - t
= 4t^3 - 3t.
Economics (Multinational firms. FDI) Question1 With respect to innov.pdf
Economics (Multinational firms. FDI) Question1: With respect to innovation and transfer of
technology between Home and Host industries, compare and contrast views advanced by Vernon
and Kruman.
Solution
The pattern of world trade and the trends in such changes over time is gretly determined by the
technological innovation in developed countries (also refered as home countries) and transfer of
technology in less developed countries (also reffered as host countries).
The spread of production and technological advancement which results in world trade pattern is
backed up many theories in literature. One of the thoeory is of Vernon, in which decision to
locate production in foreign countries is studied through life cycle model. He linked the location
of production activities to the stages of life cycyle of a product, hypothising that new product
because of their higher knowledge intensity, would be produced in North, which has a relative
abundabce of skill labor and therefore a comparative advantage occurs in their prodcution. For a
while, when the product has become standard and popular, technology transfer to the South or
Southern firms.
Epidemiological data and operational information about outbreaks is.pdf
Epidemiological data and operational information about outbreaks is dynamic and changes
rapidly. You must develop a comprehensive Event Management System to manage critical
information about an outbreak (of your choice) within the Excel program that you have just
learned. This is one method to ensure accurate and timely communications between key public
health professionals and the community.
Choose from any one of the fields below.
Features of the data management system you create should include:
Solution
Case Management-
Businesses and agencies in long-term relationships with their customers, citizens or subscribers
will be judged by the accuracy of the records they hold, the consistency of the communications
that take place, and the speed, efficiency and fairness with which each case, claim or contract is
processed.
Delivery of customer service against these priorities has never been more challenging.
Customers are more mobile in their addresses, jobs and family relationships. Communications
channels seem to multiply overnight, with customers switching between them at will. Corporate
messaging demands multi-channel distribution with increasing amounts of personalization.
Mergers and acquisitions create multiple silos of customer-related data to be seamlessly joined.
And products, business rules and government regulations change with alarming frequency.
Against this backdrop, the demands on the IT systems to support smooth, efficient and integrated
delivery are considerable, particularly where case-orientated transactions are involved.
Emergency Response-
Environmental emergencies are incidents or events that threaten public safety, health, and
welfare and include hurricanes, floods, wildfires, industrial plant explosions, chemical spills, acts
of terrorism, and others. While these events range in size, location, cause, and effect, most have
an environmental component. Emergency response is the organizing, coordinating, and directing
of available resources in order to respond to the event and bring the emergency under control.
The goal of this coordinated response is to protect public health by minimizing the impact of the
event on the community and the environment.
An emergency response plan must provide the resources and information needed to evaluate the
human and environmental health impacts of the event, assess and reduce human exposures to
contaminants, and develop science-based strategies for remediation and rebuilding. One example
is the immediate response of NIEHS and other government agencies to the devastation and
hardship caused by Hurricane Katrina. This included the establishment of a field hospital in
Mississippi to meet the immediate health needs of the hurricane victims, as well as the
development of a Geographic Information System to plot the locations of chemical plants,
refineries, Superfund clean-up sites, and other potential hot spots of contamination where
flooding occurred.
Safe Drinking Water-
There are many types o.
dydt = y + sin2tSolution rewrite in standard.pdf
dy/dt = y + sin2t
Solution
rewrite in standard form: y\' - y = sin(2t) integrating factor is: e^(-t) e^(-t) y\' -
e^(-t) y = e^(-t) sin(2t) [e^(-t) y]\' = e^(-t) sin(2t) integrate both sides: e^(-t) y = -1/5 e^(-t)
[sin(2 t) + 2cos(2 t)] + C Solve for y: y = (-1/5)[sin(2 t) + 2cos(2 t)] + Ce^(t).
Eachibit 14.1 Sources of Income for the Average Retiree Socia Securit.pdf
Eachibit 14.1 Sources of Income for the Average Retiree Socia Security is the single largest
source of income for the average U.S. retiree. This source alone is larger than the amount the
average retiree receives from pension plans and personal wealth/investment assets combined.
Percentage distribution of sources of income for married couples and nonmarried people who are
age 65 and over, 1962-2010 Percent Percent 100 90 80 70 60 100 90 80 70 60 50 40 30 20 10
Other 10 16 Earnings 29 28 Pensions 12 Asset income 15 40 20 Social Security 31 34 10 1962
1967 1976 1980 1990 2000 2010 Note: A married couple is age 65 and over if the husband is age
65 and over or the husband is younger than age 55 and the wife is age 65 and over. The
definition of other\" includes, but is not limited to, public assistance, unemployment
compensation, worker\'s compensation, alimony, child support, and personal contributions.
Reference populationt Thesedata refer tothe civilian noninstitutionalized population.
Solution
Answer: Current expenses = $75,000 Current income = $55,000 Expenses afetr 20 year
$93,750.00 Income after 20 year 176392.451 surplus in 20 years = $82,642.45.
Emulsified water is generally present in crude oil as a result of mix.pdf
Emulsified water is generally present in crude oil as a result of mixing occurring during
production operations. The formation of emulsion leads to problems in production and also
transportation. Therefore the need to break oil/water emulsions system through demulsification
process using chemical surfactants for improved oil recovery operations. Selected cationic and
anionic surfactants were found to be effective in separating oil-water emulsions expected during
a surfactant/polymer (SP) process for improved oil recovery. Describe in detail the various
factors that contribute to crude oil emulsion stability. What are the various methods that could
be adopted to destabilize the crude oil emulsions? Identify conditions at which one method will
be more effective that the other. Is there a condition at which none of the destabilization
methods will work for crude oils? If so, please identify.
Solution
(A) various factors contributing to the stability of crude oil emulsion are as follows:-
1.Heavy polar fraction in crude oil:-
Naturally occurring emulsifiers are concentrated in the higher-boiling polar fraction of the crude
oil.These include:
These compounds are the main constituents of the interfacial films surrounding the water
droplets that give emulsions their stability.
2.PRESENCE OF SOLIDS
Fine solid particles present in the crude oil are capable of effectively stabilizing emulsions. The
effectiveness of these solids in stabilizing emulsions depends on factors such as-
3. TEMPERATURE
Temperature can affect emulsion stability significantly. Temperature affects the physical
properties of oil, water, interfacial films, and surfactant solubilities in the oil and water phases.
These, in turn, affect the stability of the emulsion. Perhaps the most important effect of
temperature is on the viscosity of emulsions because viscosity decreases with increasing
temperatures.The effect of temperature on crude oil/water interfacial films was studied in some
detail by Jones et al who showed that an increase in temperature led to a gradual destabilization
of the crude oil/water interfacial films. However, even at higher temperatures, a kinetic barrier to
drop coalescence still exists.
4.DROPLET SIZE
Emulsion droplet sizes can range from less than a micron to more than 50 microns. Fig. 5 in Oil
emulsions shows the typical droplet-size distributions for water-in-crude oil emulsion.Emulsions
that have smaller size droplets will generally be more stable. For water separation, drops must
coalesce—and the smaller the drops, the greater the time to separate. The droplet-size
distribution affects emulsion viscosity because it is higher when droplets are smaller. Emulsion
viscosity is also higher when the droplet-size distribution is narrow .
5.pH
The pH of water has a strong influence on emulsion stability. The stabilizing, rigid emulsion film
contains:
Adding inorganic acids and bases strongly influences their ionization in the interfacial films and
radically chang.
e sin t dt Solution uSE integration by parts .pdf
e sin t dt
Solution
uSE integration by parts ( sin(t) is the first function) I= sin(t) (- e^(-t)) from 1 to inf
- integral ( -cos(t) e^-t) = e^-1 sin(1) + I2 I2= cos(t)(-e^-t) from 1 to inf - integral ( -sin(t) (-e^-
t)) = e^-1 cos(1) - I => I= e^-1 (cos1 + sin1) -I => I = e^-1(cos1+ sin1)/2.
dydx=1+yx solve the ODE Solutiondydx - yx = 1dydx + (-1.pdf
dy/dx=1+y/x solve the ODE
Solution
dy/dx - y/x = 1
dy/dx + (-1/x)y = 1
Integrating factor = e^(integral of (-1/x)*dx)
IF = e^(integral of -1/x)
IF = e^-ln(x)
IF = e^ln(1/x)
IF = 1/x
So, multiply the DE all over by the IF :
(1/x) * [dy/dx - y/x = 1]
d/dx(y * 1/x) = 1/x
Integrating :
y*(1/x) = intergal of (1/x)
y/x = ln|x| + C
y = xln|x| + Cx ---> ANSWER.
Elizabeth wants to accumulate dollar 12,000 by the end of 5 years. If.pdf
Elizabeth wants to accumulate dollar 12,000 by the end of 5 years. If the annual interest rate is
7%, how much will she have to invest today to achieve her goal? A certain bond pays dollar 60
of coupon interest annually, and has a face value of dollar 1,000. What is the coupon rate of the
bond?
Solution
1.
PV= Fv/(1+i) )^n
=12,000/(1+7%) ^5
=12000/1.4025
= $8556.14
2.
Coupon Rate of the bond = annual pay/ bond face value
= $60/$1000
= 0.06= 6%.
Economics (Multinational firms. FDI Question 2 Balancing macroeconom.pdf
Economics (Multinational firms. FDI Question 2: Balancing macroeconomic environment is one
of the most important aspects for a host government. Comment on the roles of fiscal measures
(e.g. corporate income taxes and import tariffs) monetary and exchange rate policies on inward
FDI inflows.
Solution
INRODUCTION
The growth of private forign direct investment in the developing world has been extremely rapid
in decent years.MNC\'s are not in the development busines.Thier objective is to maximize their
return on the capital.They seek out best profit opportunities.MNC\'s carry with them
technologies of production,tastes and styles of living ,managerial philosophies and diverse
business practices.Although globally,FDI peaked in 2000 but fell aftermath of the 9/11 terrorist
attcks,FDI has been rebonded for several years.
MNC\'s underatke five different forms in the under developed countries.
1. Branches in the different nations
2. Subsidiaries
3. Joint-venture companies
4. Franchise holders
5. Turn Key projects
There has been rapid expansion of the activities of MNC\'s.The situation of today (2014-
2015),with WTO came into being.Now rougly 5-6 lakhs MNC\'S are operating in one form or
the other across the world.The focus of the MNC\'s is basically on the primary countries and the
extractive industries.
Macroeconomic poilcy of a host country creates both problems and opprtunities for international
firms.
FICAL POLICY MEASURES
1. Investment incentives: There are two kinds of investment incentives
a. Fiscal incentives: policies that are designed to reduce tax burden of a firm.It includes tax
concessions in the form of reduced corporate income tax, exemption from improt duties etc.
b. Financial incentives: They are direct contribution to firm by the government. It includes
subsidised loans,loan guarantees, governmnet insurance at preferential rates.
2. Removal of Restrictions: Various forms of restrictions were applied to FDI in the developing
countries in the pre liberalised era.Example:allowing only a fixed percentage of foreign owned
capital in an enterprise,restrictions on reimbursement of capital upon liquidation.However in the
WTO regime, due to enforcement of TRIMS(Trade related Investment Measures) many of these
restrictions have now been withdrawn.The types of restrictions realted to FDI has been greatly
liberalised. For example: large number of countries in Asia do not require investment approvals
or licensing except for few sectors that are closed to FDI(mainly for security reasons).
2. MONETARY POLICY
a. Funds originating in advanced economies dominate capital inflows to large emerging
economies.These flows are influenced by advanced economic policies including monetary
policy.The developments in financial markets have extended the role of large cross border
financial intermediaries and liquidity ceating instruments in global capital flows.
b. Other policy measures inclues careful monitoring of systematic non bank financial instructions
with.
During the night shift in an A&E; department (10 pm to 6 am) patients.pdf
During the night shift in an A&E; department (10 pm to 6 am) patients arrived at depart enl
requiring emergency treatment. The arrival of emergencies may be modeled as a non-
homogeneous Poisson process with hourly rate lambda (f) = 2t / 1 + t2, 0 f 8, where t is the
elapsed time in hours since 10pm Find the expected number of emergency admissions by f hours
after 10pm. log(1 + t2) logt3 log(l + t3) log(l + t)
Solution
take integration : log(1 + t*t) answer.
During the night shift in an A&E; department (10 pm to 6am) patients .pdf
During the night shift in an A&E; department (10 pm to 6am) patients arrived at department
requiring emergency treatment The arrival of emergencies may be modeled as a non-
homogeneous Poisson process with hourly rate lambda (f) = 2t / 1 + t2, 0 t 8, where t is the
elapsed time in hours since 10pm The expected number of emergency admissions by hours after
10pm is expressed as mu(t) = log(1 + t2) Find the probability that at least one emergency is
admitted between midnight 0. 0706 0. 2001 0. 7059 0. 7961
Solution
B.
During the month of February, Morrisey Corporations employees earne.pdf
During the month of February, Morrisey Corporation\'s employees earned wages of $108,410.
withholdings related to these wages were $8,293 for social security (FICA),$10,402 for fedral
income tax , and $2,784 for state income tax. Costs incurred for unemployment taxes were $161
for federal and $234 for state. prepare the febrauary 28 journal entries for salaries and wages
expenses and salaries and wages payable assuming that all Febrauray wages will be paid in
march The company\' payroll tax expenses.
Solution
Feb.28 Account heads Debit Credit 1. Salaries and Wages Expenses 108410 FICA
Taxes Payable 8293 Federal Income Tax Payable 10402 State Income tax Payable 2784
Salaries and Wages Payable 89715 FICA Taxes Payable 8293 Federal Income Tax
Payable 10402 State Income tax Payable 2784 Federal unemployment Tax 161 State
unemploynent Tax 234 Pay-roll tax expenses remittable 21479 Cash(161+234) 395.
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core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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dydt = y + sin2tSolution rewrite in standard.pdf
dy/dt = y + sin2t
Solution
rewrite in standard form: y\' - y = sin(2t) integrating factor is: e^(-t) e^(-t) y\' -
e^(-t) y = e^(-t) sin(2t) [e^(-t) y]\' = e^(-t) sin(2t) integrate both sides: e^(-t) y = -1/5 e^(-t)
[sin(2 t) + 2cos(2 t)] + C Solve for y: y = (-1/5)[sin(2 t) + 2cos(2 t)] + Ce^(t).
Eachibit 14.1 Sources of Income for the Average Retiree Socia Securit.pdf
Eachibit 14.1 Sources of Income for the Average Retiree Socia Security is the single largest
source of income for the average U.S. retiree. This source alone is larger than the amount the
average retiree receives from pension plans and personal wealth/investment assets combined.
Percentage distribution of sources of income for married couples and nonmarried people who are
age 65 and over, 1962-2010 Percent Percent 100 90 80 70 60 100 90 80 70 60 50 40 30 20 10
Other 10 16 Earnings 29 28 Pensions 12 Asset income 15 40 20 Social Security 31 34 10 1962
1967 1976 1980 1990 2000 2010 Note: A married couple is age 65 and over if the husband is age
65 and over or the husband is younger than age 55 and the wife is age 65 and over. The
definition of other\" includes, but is not limited to, public assistance, unemployment
compensation, worker\'s compensation, alimony, child support, and personal contributions.
Reference populationt Thesedata refer tothe civilian noninstitutionalized population.
Solution
Answer: Current expenses = $75,000 Current income = $55,000 Expenses afetr 20 year
$93,750.00 Income after 20 year 176392.451 surplus in 20 years = $82,642.45.
Emulsified water is generally present in crude oil as a result of mix.pdf
Emulsified water is generally present in crude oil as a result of mixing occurring during
production operations. The formation of emulsion leads to problems in production and also
transportation. Therefore the need to break oil/water emulsions system through demulsification
process using chemical surfactants for improved oil recovery operations. Selected cationic and
anionic surfactants were found to be effective in separating oil-water emulsions expected during
a surfactant/polymer (SP) process for improved oil recovery. Describe in detail the various
factors that contribute to crude oil emulsion stability. What are the various methods that could
be adopted to destabilize the crude oil emulsions? Identify conditions at which one method will
be more effective that the other. Is there a condition at which none of the destabilization
methods will work for crude oils? If so, please identify.
Solution
(A) various factors contributing to the stability of crude oil emulsion are as follows:-
1.Heavy polar fraction in crude oil:-
Naturally occurring emulsifiers are concentrated in the higher-boiling polar fraction of the crude
oil.These include:
These compounds are the main constituents of the interfacial films surrounding the water
droplets that give emulsions their stability.
2.PRESENCE OF SOLIDS
Fine solid particles present in the crude oil are capable of effectively stabilizing emulsions. The
effectiveness of these solids in stabilizing emulsions depends on factors such as-
3. TEMPERATURE
Temperature can affect emulsion stability significantly. Temperature affects the physical
properties of oil, water, interfacial films, and surfactant solubilities in the oil and water phases.
These, in turn, affect the stability of the emulsion. Perhaps the most important effect of
temperature is on the viscosity of emulsions because viscosity decreases with increasing
temperatures.The effect of temperature on crude oil/water interfacial films was studied in some
detail by Jones et al who showed that an increase in temperature led to a gradual destabilization
of the crude oil/water interfacial films. However, even at higher temperatures, a kinetic barrier to
drop coalescence still exists.
4.DROPLET SIZE
Emulsion droplet sizes can range from less than a micron to more than 50 microns. Fig. 5 in Oil
emulsions shows the typical droplet-size distributions for water-in-crude oil emulsion.Emulsions
that have smaller size droplets will generally be more stable. For water separation, drops must
coalesce—and the smaller the drops, the greater the time to separate. The droplet-size
distribution affects emulsion viscosity because it is higher when droplets are smaller. Emulsion
viscosity is also higher when the droplet-size distribution is narrow .
5.pH
The pH of water has a strong influence on emulsion stability. The stabilizing, rigid emulsion film
contains:
Adding inorganic acids and bases strongly influences their ionization in the interfacial films and
radically chang.
e sin t dt Solution uSE integration by parts .pdf
e sin t dt
Solution
uSE integration by parts ( sin(t) is the first function) I= sin(t) (- e^(-t)) from 1 to inf
- integral ( -cos(t) e^-t) = e^-1 sin(1) + I2 I2= cos(t)(-e^-t) from 1 to inf - integral ( -sin(t) (-e^-
t)) = e^-1 cos(1) - I => I= e^-1 (cos1 + sin1) -I => I = e^-1(cos1+ sin1)/2.
dydx=1+yx solve the ODE Solutiondydx - yx = 1dydx + (-1.pdf
dy/dx=1+y/x solve the ODE
Solution
dy/dx - y/x = 1
dy/dx + (-1/x)y = 1
Integrating factor = e^(integral of (-1/x)*dx)
IF = e^(integral of -1/x)
IF = e^-ln(x)
IF = e^ln(1/x)
IF = 1/x
So, multiply the DE all over by the IF :
(1/x) * [dy/dx - y/x = 1]
d/dx(y * 1/x) = 1/x
Integrating :
y*(1/x) = intergal of (1/x)
y/x = ln|x| + C
y = xln|x| + Cx ---> ANSWER.
Elizabeth wants to accumulate dollar 12,000 by the end of 5 years. If.pdf
Elizabeth wants to accumulate dollar 12,000 by the end of 5 years. If the annual interest rate is
7%, how much will she have to invest today to achieve her goal? A certain bond pays dollar 60
of coupon interest annually, and has a face value of dollar 1,000. What is the coupon rate of the
bond?
Solution
1.
PV= Fv/(1+i) )^n
=12,000/(1+7%) ^5
=12000/1.4025
= $8556.14
2.
Coupon Rate of the bond = annual pay/ bond face value
= $60/$1000
= 0.06= 6%.
Economics (Multinational firms. FDI Question 2 Balancing macroeconom.pdf
Economics (Multinational firms. FDI Question 2: Balancing macroeconomic environment is one
of the most important aspects for a host government. Comment on the roles of fiscal measures
(e.g. corporate income taxes and import tariffs) monetary and exchange rate policies on inward
FDI inflows.
Solution
INRODUCTION
The growth of private forign direct investment in the developing world has been extremely rapid
in decent years.MNC\'s are not in the development busines.Thier objective is to maximize their
return on the capital.They seek out best profit opportunities.MNC\'s carry with them
technologies of production,tastes and styles of living ,managerial philosophies and diverse
business practices.Although globally,FDI peaked in 2000 but fell aftermath of the 9/11 terrorist
attcks,FDI has been rebonded for several years.
MNC\'s underatke five different forms in the under developed countries.
1. Branches in the different nations
2. Subsidiaries
3. Joint-venture companies
4. Franchise holders
5. Turn Key projects
There has been rapid expansion of the activities of MNC\'s.The situation of today (2014-
2015),with WTO came into being.Now rougly 5-6 lakhs MNC\'S are operating in one form or
the other across the world.The focus of the MNC\'s is basically on the primary countries and the
extractive industries.
Macroeconomic poilcy of a host country creates both problems and opprtunities for international
firms.
FICAL POLICY MEASURES
1. Investment incentives: There are two kinds of investment incentives
a. Fiscal incentives: policies that are designed to reduce tax burden of a firm.It includes tax
concessions in the form of reduced corporate income tax, exemption from improt duties etc.
b. Financial incentives: They are direct contribution to firm by the government. It includes
subsidised loans,loan guarantees, governmnet insurance at preferential rates.
2. Removal of Restrictions: Various forms of restrictions were applied to FDI in the developing
countries in the pre liberalised era.Example:allowing only a fixed percentage of foreign owned
capital in an enterprise,restrictions on reimbursement of capital upon liquidation.However in the
WTO regime, due to enforcement of TRIMS(Trade related Investment Measures) many of these
restrictions have now been withdrawn.The types of restrictions realted to FDI has been greatly
liberalised. For example: large number of countries in Asia do not require investment approvals
or licensing except for few sectors that are closed to FDI(mainly for security reasons).
2. MONETARY POLICY
a. Funds originating in advanced economies dominate capital inflows to large emerging
economies.These flows are influenced by advanced economic policies including monetary
policy.The developments in financial markets have extended the role of large cross border
financial intermediaries and liquidity ceating instruments in global capital flows.
b. Other policy measures inclues careful monitoring of systematic non bank financial instructions
with.
During the night shift in an A&E; department (10 pm to 6 am) patients.pdf
During the night shift in an A&E; department (10 pm to 6 am) patients arrived at depart enl
requiring emergency treatment. The arrival of emergencies may be modeled as a non-
homogeneous Poisson process with hourly rate lambda (f) = 2t / 1 + t2, 0 f 8, where t is the
elapsed time in hours since 10pm Find the expected number of emergency admissions by f hours
after 10pm. log(1 + t2) logt3 log(l + t3) log(l + t)
Solution
take integration : log(1 + t*t) answer.
During the night shift in an A&E; department (10 pm to 6am) patients .pdf
During the night shift in an A&E; department (10 pm to 6am) patients arrived at department
requiring emergency treatment The arrival of emergencies may be modeled as a non-
homogeneous Poisson process with hourly rate lambda (f) = 2t / 1 + t2, 0 t 8, where t is the
elapsed time in hours since 10pm The expected number of emergency admissions by hours after
10pm is expressed as mu(t) = log(1 + t2) Find the probability that at least one emergency is
admitted between midnight 0. 0706 0. 2001 0. 7059 0. 7961
Solution
B.
During the month of February, Morrisey Corporations employees earne.pdf
During the month of February, Morrisey Corporation\'s employees earned wages of $108,410.
withholdings related to these wages were $8,293 for social security (FICA),$10,402 for fedral
income tax , and $2,784 for state income tax. Costs incurred for unemployment taxes were $161
for federal and $234 for state. prepare the febrauary 28 journal entries for salaries and wages
expenses and salaries and wages payable assuming that all Febrauray wages will be paid in
march The company\' payroll tax expenses.
Solution
Feb.28 Account heads Debit Credit 1. Salaries and Wages Expenses 108410 FICA
Taxes Payable 8293 Federal Income Tax Payable 10402 State Income tax Payable 2784
Salaries and Wages Payable 89715 FICA Taxes Payable 8293 Federal Income Tax
Payable 10402 State Income tax Payable 2784 Federal unemployment Tax 161 State
unemploynent Tax 234 Pay-roll tax expenses remittable 21479 Cash(161+234) 395.
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environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
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like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
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centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
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Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
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Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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