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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.
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?
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
[￢p ∧(p ∨ q)]→q
A group of students got the following scores in an achievement test:9,12,15,18,21 and 24 . consider the sample of size 3 that can be drawn from this population. Construct a sampling distribution of the resulting means and find the probability
For each of the ff. sets, determine whether 2 is an element of that set.
a. {𝑥∈ℝ|𝑥 𝑖𝑠 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 1}
b. {𝑥∈ℝ|𝑥 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 𝑎𝑛 𝑖𝑛𝑡𝑒𝑔𝑒𝑟}
c. {2,{2}}
d. {{2},{{2}}}
Determine whether each of these pairs of sets are equal.
a. {1,3,3,3,5,5,5,5},{5,3,1}
b. {{1}}{1,{1}}
c. ∅,{∅}
