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Which of the following statements are true and which are false? Justify your answers with
a short proof or a counter-example:
If x and y are real numbers such that x < y, then x²<y²
A shipment of five computers contains two that are slightly defective. If a retailer receives three of these computers at random,let Z represent the number of computer purchased by the retailer which are slightly defective
1. The following worksheet contains cost and revenue data for koyel Shoe Company:
Total 15,000 Pairs of Shoes
Per pair of Shoes
Sales Revenue
Tk. 600,000
Tk. 40
Variable expenses:
Invoice cost
202,500
Tk. 13.5
Sales commission
67,500
4.5
Total variable expenses
Tk. 270,000
Tk.18
Contribution margin
Tk. 330,000
Tk. 22
Fixed expenses:
Advertising
Tk. 30,000
Rent
20,000
Salaries
100,000
Total fixed expenses
Tk. 150,000
Net Income
Tk. 180,000
Required:
(a) Compute the company’s degree of operating leverage at the present level of sales.
(b) Assume that through a more intense effort by the sales staff, the company’s sales increase
by 8% next year. By what percentage would you expect net operating income to increase? Use the degree of operating leverage to obtain your answer.
(c) Verify your answer to (b) by preparing a new contribution format income statement showing an 8% increase in sales.
A researcher used a developed problem solving test to randomly select 50 grade 6 pupils. In this sample, x̄= 80. The mean μ and the standard deviation of the population used in the standardization of the test were 75 and 15, respectively. Test the hypothesis that the sample mean differ significantly from the population mean. Use level of significance 0.05. The z value is 1.96.
. Acid catalyzed dehydration-condensation reactions of carboxylic acids and alcohols produce chemicals called
esters.
i. Using carbon skeletal notation, write the dehydration-condensation reaction that occurs between ethanol
and butanoic acid.
ii. What is the name of this ester?
V.
In a job fair, 2000 applicants applied for a job. Their main age was found to be 28 with a standard deviation of 4 years.
a. Draw a normal curve distribution showing the z-scores and the raw scores
b. How many applicants are below 20 years old?
c. How many applicants are above 30 years old?
d. How many have ages between 24 and 32 years old?
An ideal Otto cycle using air has the following conditions. At point 1; p1 = 14.5 psia and 80° F. The heat added to the air is 370 BTU/lbm per cycle. If the maximum temperature is 3400 °R and K = 1.4, Compute the pressure, temperature and volume at each corner of the cycle; the compression ratio, mean effective BTU pressure and the cycle thermal efficiency if cv= 0.172 lb m-°R
A dual cycle using air operates at 14.7 psia, 70°F_and r = 7. The cylinder diameter of the engine is 10 inches and the stroke is 12 inches. The pressure at the end of isometric heating process is 800 psia. If heat is added at constant pressure during 3% of the stroke, compute the net work and cycle thermal efficiency. The atmosphere is at 14.7 psia and 70° F.
Make use of call by reference in C++, to find small, medium and large among three given integers and print true if the difference between small and medium and the difference between medium and large is same.
The probabilities that a surgeon operates on 3 4 5 6 or 7 patents and any one day are 0.15 0.20 0.25 0.20 and 0.20 respectively
#339914 on Dec 2023