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Is function f defined by f = {(1, 2), (3, 4), (5, 6), (8, 6), (10, -1)}, a one to one function?



A species of fish grows 1.2 cm in first year. Each year it grows by 2% more than it did the year before. Using geometric sequence find, how much does it grow in 10th year.



In a computer science department, a student club can be formed with either 10 members from first year or 8 members from second year or 6 from third year or 4 from final year. What is the minimum no. of students we have to choose randomly from department to ensure that a student club is formed?



Determine the functions f: R -> R are onto, f(x) = |x| + x



Let A = {1, 2, 3, 4} and B = {0, 3, 6, 8, 12, 15}. Consider a rule f (x) = x² - 1, x∈A, then show that f is a mapping from A to B.



The following sets have been defined using the | notation. Re-write them by listing some of the elements.


i. {p | p is a capital city, p is in Europe}


ii. {z | 3z = n2, z and n are natural numbers}



Draw Dienes block to show how to find solution to:

b) 102 - 45


A listed company on the ZSE has the stock price six months from expiration of

an option as $95, risk free interest rate is 4% per annum and an exercise price of $90. The volatility is 30% per annum. Calculate the price of the European put option using the Black-Scholes option pricing model. Using the put-call parity relationship, calculate the call price. Sketch the call and put payoff graphs defined in the question. Use R





In the given table on the below, solve for Pearson r and interpret the result

X 80,84,86,87,89,90,91,93,94,96

Y 78,83,80,84,89,90,88,91,93,96



Solve for r and interpret the result

X 2,4,6,7,10

Y 8,10,12,6,16


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