### The Company has purchased a 1-year software license for the use of the Sales team from Widgets

Question: The Company has purchased a 1-year software license for the use of the Sales team from Widgets, Inc. The total cost of the license is \$5,000, and it is valid from July 25, 2020 through July 24, 2021. The invoice is dated August 1, 2021, and due within 30 days. Please write the entry or entries you would use to record this transaction. Include debit(s), credit(s), and a memo for each entry.

Solution:

### Group A Question 1 The two port circuit presented in Fig. 1 can be described in terms of b-parameters as:

Question: Group A Question 1 The two port circuit presented in Fig. 1 can be described in terms of b-parameters as:

Solution:

It can be proved by advanced circuit theory that voltages and currents in Fig. can be related

by the following sets of equations :

v1 = h11 i1 + h12 v2 …(i)

i2 = h21 i1 + h22 v2 …(ii)

In these equations, the hs are fixed constants for a given circuit and are called h parameters.

Once these parameters are known, we can use equations (i) and (ii) to find the voltages and currents

in the circuit. If we look at eq.(i), it is clear that **h11 has the dimension of ohm and h12 is dimension-

less. Similarly, from eq. (ii), h21 is dimensionless and h22 has the dimension of mho. The following

points may be noted about h parameters :

(i) Every linear circuit has four h parameters ; one having dimension of ohm, one having di-mension of mho and two dimensionless.

(ii) The h parameters of a given circuit are constant. If we change the circuit, h parameters would also change.

The major reason for the use of h parameters is the relative ease with which they can be measured. The

h parameters of a circuit shown in Fig. 24.1 can be found out as under :

(i) If we short-circuit the output terminals (See Fig. 24.2), we can say that output voltage v2 = 0.

Putting v2 = 0 in equations (i) and (ii), we get,

v1 = h11 i1 + h12 × 0

i2 = h21 i1 + h22 × 0

∴ h11 = v1/i1 for v2 = 0 i.e. output shorted

and

h21 = i2/ i1 , for v2 = 0 i.e. output shorted

Let us now turn to the physical meaning of h11 and h21 . Since h11 is a ratio of voltage and current

(i.e. v1/i1), it is an impedance and is called * “input impedance with output shorted ”. Similarly, h21 is the ratio of output and input current (i.e., i 2/i 1), it will be dimensionless and is called“current gain with output shorted”.

The other two h parameters (viz h12 and h22) can be found by making i

1 = 0. This can be d doneby the arrangement shown in Fig.. Here, we drive the output terminals with voltage v2,

keeping the input terminals open. With this set up, i

1 = 0 and the equations become :

v1 = h11 × 0 + h12 v2

i 2 = h21 × 0 + h22 v2

∴ h12 = v1/v2 for i1 = 0 i.e. input open

and

h22 = i2 /v2 , for i1 = 0 i.e. input open

Since h12 is a ratio of input and output voltages (i.e. v1/v2), it is dimensionless and is called “voltage

feedback ratio with input terminals open”. Similarly, h22 is a ratio of output current and output voltage

(i.e. i 2/v2), it will be admittance and is called “output admittance with input terminals open”.

### Find the number of pumps required to take water from a deep well under a total head of 120 m

Question: Find the number of pumps required to take water from a deep well under a total head of 120 m. All the pumps are identical and are running at 800 rpm. The specific speed of each pump is given as 25 while the rated capacity of each pump is 0.16 m3/s

Solution: Given: total head h = 120 m
Speed, N = 800 rpm
Specific speed at each pump, Ns = 25
Rated capacity of each Pump, Q = 0.16 m^3/s
Let us assume, head developed by each pump is Hm
Specific speed, Ns = N (Q)^(1/2)/ (Hm)^(3/4)
25 = 800(0.16)^(1/2)/(Hm)^(3/4)
(Hm)^(3/4) = 800 (0.16)^(1/2)/25
(Hm)^(3/4) = 12.8
Hm = (12.8)^(4/3)
Hm = 29.94 m

Number of pumps required
= 120/29.94 = 4.008 = 4
4 numbers of pumps are required to lift water from deep well under a total of 120m

### What problems exist in Starsville? What needs to occur in the school and the community to make things right?

Question: What problems exist in Starsville? What needs to occur in the school and the community to make things right? Compare and contrast the events in this case with a school setting with which you are familiar. How are the issues the same and different? What is the impact of changing demographics in both settings? What are school leaders doing to address the needs of all learners?

CASE STUDY: WHAT DO YOU DO WHEN THE DEMOGRAPHICS CHANGE? Howe, W. A., & Lisi, P. L. (2017). Becoming a multicultural educator: Developing awareness, gaining skills, and taking action (2nd ed.). Los Angeles: SAGE. Key Issues to Be Explored in the Case 1. Understand the cultural influences you experienced while growing up. 2. Become aware of the obstacles sometimes faced by newcomers and people of color. 3. Adapt teaching strategies to be congruent with changing student populations. Starsville was a typical, sleepy New England town comprised almost exclusively of White, middle-class citizens whose families had lived there for generations. As is the case in many small towns, the residents seemed to appreciate the idea that they knew each other and shared similar pastimes, values, beliefs, and ways of living. Then one of the churches in town decided to sponsor a family of refugees from a South American country. Initially, the town residents rallied around this family and supported them in finding work, finding housing, and enrolling their children in the schools. The school-age children, for whom English was not the first language, posed a new challenge to the school system and to the teachers who were not accustomed to teaching non-English-speaking children. In another development, due to the close proximity of Starsville to a large metropolitan area, African American and Hispanic families from the city-upwardly mobile professionals-began buying homes in town. Starsville was quickly becoming a diverse community. As the numbers of newcomers increased and people didn’t have opportunities to get to know each other, problems arose in the schools and in town. A refugee from Bosnia was chased home by bullies throwing stones. A group of Vietnamese girls were taunted by other girls as they walked through the high school hallways. Racist graffiti began appearing around town. Fights were becoming more frequent in school, especially between the newer students and the students from more established homes. Derogatory comments about minority students became more common in the teachers’ lounge. An educator who had prided herself on being able to reach and support the neediest students became distressed by the treatment of students in her school and in the community at large. Perhaps most distressing was her realization that teachers did not know what to do to best teach the new students.

Solution:

1. The problems which exist in starsville are mainly due to the presence of diverse community; as there is an increase in population and there is an increase problem in the school as English was not the fist language. People use to bully the Bosnia by throwing stones; A girl from Vietnamese group also taunted by other girls and there was fight between old and new students. The teachers also become distress because people think that they don’t know the best methods to teach.

2. In order to resolve the above mentioned consequences it is important to make English first language and give value to this language as it is important for the career of children. In addition the community of Starsille should stop blaming the other community and they should not taunt or throw stones on others. It is important to learn their culture and should I respect every other person. It is important to interact with each other to know and develop a friendly environment.

3. In modern era, I know a school where English is compulsory language and teachers are friendly with the students. It is important to maintain a quality relation and interact with them to know then better and enhance their growth and development. However in this school the English Alan giage is not given that importance and local students used to taunt and throw stones on other community students.

### Prove that any positive rational number q is uniquely represented as q=p1^r1…pk^rk

Question: Prove that any positive rational number q is uniquely represented as q=p1^r1…pk^rk, where p1…pk are prime numbers, r1…rk are integer numbers (+ or -).

1b: Prove that sqrt(q) is rational number if and only if the numbers r1…rk are even.

1c: Let t=2cos(72degrees), prove that t^2+t-1=0.

Solution:

1a) Given
q=p1^r1.p2^r2.p3^r3…pk^rk
let us consider
q=12
prime factors are 2*2*3
So,here p1=2,r1=2
p2=3,r2=1
Here we can represent a positive rational
in the form of q=p1^r1.p2^r2.p3^r3…pk^rk
which is 12=2^2 * 3^1.
Hence we can say that any positive rational number q is uniquely represented as q=p1^r1…pk^rk, where p1…pk are prime numbers, r1…rk are integer numbers (+ or -).

1b) From the above example
we have assumed q=12 which is a rational
and if we take square root of it.

√12=2*√3
= 3.46410162..
which is a irrational number.
As r1=2(even), but r2=1 which is odd, the sqrt has become irrational number

Similarly we can take a number 16
q=16
p1=2,r1=4(even)

Here r1 is even, so does the √q=√16=4 which is rational number
Here we can conclude that, √q is rational number if and only if the numbers r1…rk are even.

1c)
t=2cos(72) cos in degrees
=2*0.309
=0.6180
=0.62

t^2+t-1=0
substitute value of t in the above equation

=0.62^2 +0.62 -1
=0.38+0.62-1
=1-1
=0
hence proved

### Create Context (Deployment) Diagram for self-driving robot car.

Question: Create Context (Deployment) Diagram for self-driving robot car. The car can do line detection and obstacle recognition

Solution:

### A 1200-kg two-wheel-drive car drives up θ-15° incline

Question: A 1200-kg two-wheel-drive car drives up θ-15° incline. If the coefficient of static friction between the tires and the ground is 0.7, find the maximum acceleration of the car as well as the normal forces on the pairs of tires at R and F in the separate cases where the car is a) rear-wheel drive and b) front-wheel drive. Neglect any rolling resistance and the mass of the wheels 0.9 m’ 1.6 m 0.76 m

Solution:

### Let Ai be any events. a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2)

Question: Let Ai be any events.

a) Show that P(A1 ∩A2 ∩A3) = P(A1 ∩A2 ∩A3) = P(A1)·P(A2 | A1)·P(A3 | A1 ∩A2) .

b) Generalize this to give a formula for the intersection of any number of events. [Hint: Use induction.]

Solution:

### Amresh is interested in estimating the company’s WACC and has collected the following information

Question:

Amresh is interested in estimating the company’s WACC and has collected the following information:

The company has bonds outstanding that mature in 20 years with an annual coupon of 7.5 percent. The bonds have a face value of \$1,000 and sell in the market today for \$950.

The risk-free rate is 7 percent.

The market risk premium is 6 percent.

The stock’s beta is 1.2.

The company’s tax rate is 40 percent.

The company’s target capital structure consists of 60 percent equity and 40 percent debt.

The company uses the CAPM to estimate the cost of equity and does not include flotation costs as part of its cost of capital. What is Amresh WACC?

Solution: So, amresh WACC = 5.28%, as calculated below:
working notes:
I. Calculation of cost of equity (through CAPM Method)
ke = Risk free rate of return + Beta x [ Market Rate of Return – Risk free rate of return]
ke = 7% + 1.2 [ 6% -7%]
so, ke = 5.8%

II. Calculation of debenture (kd) =
Interest (1 – tax rate) / Net Proceeds

Interest = \$1000 x 7.5% = \$75
Net Proceeds = \$1000 (assuming issued)

So, kd = \$75(1-40%)/\$1000 = 4.5%

Now Calculation of WACC

WACC = 1.8% + 3.48% = 5.28%

### You are a research scientist for the U.S. Department of Agriculture

You are a research scientist for the U.S. Department of Agriculture that has been asked to research the impact of permaculture and conventional farming methods on soil erosion. You identify 4 conventional farms, 4 permaculture farms, and 4 undisturbed natural areas. All of the farms and natural areas have streams that run nearby. Every week you measure the turbidity and sediment depth in the streams and compare the results after 2 years of data collection

a. Identify the independent variable(s) from the study above

b. Identify the dependant variable(s) from the study above.

c. List 2 variables that should be controlled in this study.

d. Why do you suppose 4 undisturbed natural areas were included in the study?

Solution: 8 A- the indipendant variables in the study are the numbers of different type of farms i.e. 4 conventional farms, 4 permaculture farms and 4 undisturbed areas.

Ans-B- the dependent variables include the turbidity and sediment depth of stream.

Ans-C- the two variables which should be controlled are turbidity and sediment depth of the stream.

Ans-D- four undisturbed natural area are included in this study to act as control sample.