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1. Create a C++ program that let the user input his/here grade on the following subjects: Programming, Web Application, Oral Communication, Multimedia and Physics and calculate the average. 


Note : the program must also display/output the subjects with grades from the user and the average. 



2. What will happen to the equilibrium price and quantity of butter in each of the following cases? You should state whether demand or supply or both have shifted and in which direction using the appropriate diagrams:

a) A rise in the price of margarine

b) A rise in the price of bread

c) A rise in the demand for bread

d) An expected increase in the price of butter in the near future

e) A tax on butter production


A course in mathematics is taught to 15 students by explicit method. Another group of 17 students was given the same course by means of another method. At the end of the semester, the same test was administered to each group. The 15 students under method A made an average of 85 with a standard deviation of 4, while the 17 students under method B made an average of 81 with a standard deviation of 5. Test



the null hypothesis of no significant difference in the performance of the two groups of



students at 5% level of significance.



Solution:



1. H0:



H1:



2. Level of Significance:



3.Test:



4. Critical Region:



5. Solution:



Make a decision and draw a



conclusion based from the results.



1. Decision:



2. Conclusion:

A manufacturer of a brand of designer jeans has pitched her advertising to develop an


expensive and classy image, the suggested retail price is Rs 750. However, she is concerned


that retailers are undermining her image by offering jeans at discount prices. To better


understand what is happening, she randomly sampled 15 retailers who sell her product and


determines the price. The data collected is as follows:


670 720 700 570 780 770 670 720 730 770 720 810 730 790 750


Find the 95% confidence interval estimate for the prices.

A sample of students from an introductory psychology class were polled regarding the


number of hours they spent studying for the last exam. The data was used to make


inferences regarding the other students taking the course. There data are below:


8, 22.7, 14.5, 9, 9, 3.5, 8, 11, 7.5, 18,


20, 7.5, 9, 10.5,15, 19, 9, 8.5, 14,20


Compute a 99% confidence interval.

A 4.00 L rigid vessel (see figure below) holds 2.00 L of pure water. The remaining volume holds N2 at 45.0°C. At this stage the pressure gauge on the vessel reads 85.0 kPa. You then load 13.2 g of Be(NO3)2(s) and 15.4 g of N2H5Cl(s) to the container. The salts dissociate completely and a reaction occurs producing both NO(g) and more N2(g). After the reaction has completed, the temperature increased by 5.00°C, with no change in the liquid volume.

Assume that:

o No gas escaped or entered the vessel during the loading of the reagents.

o The liquid phase is free of any gaseous species.

o The ideal gas law applies.

o The reaction is irreversible with a yield of 88.0%.

i. Show that the balanced reaction in alkaline (basic) medium is given by:

4𝑁𝑂3 − (𝑎q) + 3𝑁2𝐻5 + (𝑎q) → 4𝑁𝑂(𝑔) + 3𝑁2(𝑔) + 7𝐻2𝑂(l) + 𝑂𝐻(𝑎q) −

(Show all balancing steps clearly)

ii. Calculate the number of moles of N2(g) and NO(g) after the reaction.

iii. Calculate the partial pressure of N2(g) and NO(g) in kPa after the reaction


Suppose we observe that the equilibrium price of a particular good has decreased significantly over the past 5 years, with virtually no change in the equilibrium quantity. Which of the following is the most likely explanation? Over the past 5 years:







A. both supply and demand have decreased.







B. supply has increased but demand has decreased







C. both supply and demand have increased







D. demand has increased but supply has decreased.

A 20degC water flows to 50cmx60cm flat plate with velocity of 6.5m/s . The flat plate surface temperature is maintained at 40deg C. The air flows parallel to the 50cm side of the plate. If the kinematic viscosity of water is 78x10-8 m2/s, at what length the flow become turbulent?


Write a java program for Tlhogi’s Car Care Shop that shows a user a list of available services: oil change, tire rotation, battery check, or brake inspection. Allow the user to enter a string that corresponds to one of the options, and display the option and its price as R25, R22, R15, or R5, accordingly. Display an error message if the user enters an invalid item. Save the file as CarCareChoice.java.




It might not be reasonable to expect users to type long entries such as “oil change” accurately. Modify the CarCareChoice class so that as long as the user enters the first three characters of a service, the choice is considered valid. Save the file as CarCareChoice2.java.




Finally write a test class to test both classes. Save the file as TestCarCareChoice.java

What are the truth values of these statements?


[3 marks]


a) ∃!xP(x)→∃xP(x)


b)


∀x P(x) → ∃!xP(x)


c)


∃!x¬P(x)→¬∀xP(x)

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