Q1) In a food processing facility, a spherical container of inner radius r1 =41 cm, outer radius r2 = 43 cm, and thermal conductivity k = 2 W/m · °C is used to store hot water and to keep it at 105°C at all times. To accomplish this, the outer surface of the container is wrapped with a 510-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 100°C at all times. Assuming 80 percent of the heat generated in the heater is transferred to container
a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container,
b) Obtain a relation for the variation of temperature in the container material by solving the differential equation.
c) Determine the temperature at the center plane of the container

My device is a BOILER

Choose the working fluid (substance) for your model device

Choose the inlet substance conditions such as temperature, pressure, velocity, mass flow rate or volume flow rate, quality, etc

Choose the outlet substance conditions based on the available information, or design the outlet conditions based on your research.

DRAW the system you are analyzing, including the SYSTEM BOUNDARY,

Show ALL INTERACTIONS between the system and surroundings on your drawing

Write the Conservation of mass equation as it applies TO YOUR SYSTEM

Write the Conservation of Energy equation as it applies TO YOUR SYSTEM

List all the assumptions and idealizations for the process

Calculate the thermo efficiency of the device. Be sure clearly shows equations, calculation process, intermediate answers/results,and final results. Units are critically important in all calculations.

An article predicts that "spit," spam that is delivered via internet phone lines and cell phones, will be a growing problem as more people turn to web-based phone services. In a poll of 5500 cell phone users, 25% indicated that they had received commercial messages and ads on their cell phones. Is there sufficient evidence that the proportion of cell phone users who have received commercial messages or ads in 2004 was greater than the proportion of 0.13 reported for the previous year? (Use α = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.)

Calculate percentages for the following table. A prior Gamma analysis has indicated that the relationship is significant (p-value <0.05). Use these percentages to assess the strength (using the maximum difference method) and direction of this relationship.

Write a bullet points describing the relationship between these two variables

Q 2 - “Inflation is as violent as a mugger, as frightening as an armed robber and as deadly as a hit man.” Ronald Reagan (1911-2004)

a. There are two types of inflation. How are these different types of inflation reflected in the aggregate demand and aggregate supply (AD-AS) model? Use diagrams to illustrate your answer.

b. Governments may adopt fiscal policy to control one of these types of inflation. What type of fiscal policy can be adopted? Explain how this fiscal policy works. How would the ‘ratchet effect’ affect the effectiveness of this fiscal policy?

c. On a separate diagram, clearly illustrate your answer in (b).

A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004). The prices are for models with a DVD player and for models with a DVD player.

1. Compute the mean price for models with a DVD player and the mean price for models without a DVD player. What is the additional price paid to have a DVD player included in a home theater unit?
2. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player?

Complex finance problems using Excel.

1. Compost International issued $1000 bonds on May 12, 2000 in order to finance world-wide expansion. The bonds have a coupon rate of 8.4% with payments on a semi-annual basis (November 12, May 12) and mature on May 12, 2020. You purchased one of Compost’s $1000 bond on June 25, 2004 and plan to hold the bond to maturity. The bond has a list price of $1090 (not including accrued interest).

Compute the semi-annual coupon payment, the accrued interest, the invoice price of the bond, and the Yield to Maturity (YTM) of your bond.

1. Describe the graph of the function without drawing the graph. Use the terms increasing, decreasing, concave up, concave down, vertical intercept, and horizontal asymptote, as appropriate.

f(t) = 0.75(3)^t − 2

.the vertical intercept is (t, f(t)) =

.The function is increasing or decreasing and concave up or concave down?

2. Model the data with an exponential function, if appropriate. If an exponential function model is not appropriate for the situation, explain why. Do not use regression for this exercise.

Between 1960 and 2004, insurance company expenditures for health care increased at an ever-increasing rate. In 1960, $6 billion was spent on health care. In 2004, $659 billion was spent on health care.†

Is the exponential function model appropriate? If not, explain why.

. Yes, the exponential function model is appropriate.

. No, the exponential function model is not appropriate because there is a constant rate of change, meaning it is linear.  

. No, the exponential function model is not appropriate because the growth rate is less than 1.

. No, the exponential function model is not appropriate because the change factor is less than 1.

Give the exponential model, if appropriate. (If not appropriate, enter DNE. Let H(t) be health care expenditures by insurance companies in billions of dollars, t years after 1960. Round the change factor to two decimal places.)

H(t) = ________ billion dollars.

3. State the two integer values between which the expression falls.

log₂(40)

Smaller value:-

Larger value:-

Use the change of base formula to evaluate the expression exactly. (Round your answer to three decimal places.):- __________

In our lecture on Planning Ahead: Sampling variability, you were introduced to a set of five (5) questions that can be used to help decide upon a relevant statistical inference procedure.

1. Identify each of the five (5) questions and answer each question based on the scenario described above.
2. Based on your answers to part a, identify which of the inference procedures covered in class is most appropriate to analyse the researcher’s data?
3. Assume the researchers for the above scenario have obtained relevant simple random sample(s). Identify (by name) the sampling distribution that underlies the statistical inference procedure named in part b. Then, give the formulae for the mean and standard deviation for the sampling distribution you have identified.

my answer to a is:

1. The first question is “what is your analysis goal?”. The analysis goal based on the scenario above is to determine if student employment has an influence on their academic success. The second question is “how many ‘samples’ or groups are you comparing?”. Based on the scenario above, the researcher is comparing a single sample of university students and each student in the sample is surveyed. The third question is “are you ‘samples’ independent or paired?”. In this scenario, the sample is independent as the data is obtained from each student each case is unrelated to the other. The fourth question is “what type of data are you collecting? Quantitative or categorical?”. Based on the scenario above, the data being collected quantitative. Both the employment status and their course grades produce a numerical value to describe the dat The last question is “what parameters are of interest?”. In the above scenario, the parameters of interest are the hours worked per week and the mean of the student’s course grades.