Comments Off on Another Financial Mathematics Question
Question John saved $600 and Carla saved $550 into a savings account. John found an account that would pay interest at 8% and Carla found a interest of 7% but earned interest over the interest she had. How much money would they both receive at the end of year 1 and at the end...
Comments Off on Set Theory: Show that P(A U B) = P(A) + P(Ac ∩ B)?
Answer P(A U B) = P(A) + P(Ac ∩ B)? Here is a simple but understandable approach. The method below is called the “counting argument” in combinatorics and probability. Since we have “two events” A & B, lets define the number of elements as follows : A has ‘a’ elements. We write A =...
Answer There is a “formula”. a^3 – b^3 = ( a – b ) ( a^2 + ab + b^2 ). You can multiply out the Right hand side expression and you will see that it “reduces” to the left hand side expression. In your question, just set a = x and b =...
Comments Off on A Number Theory Question: “If abcd x 4 = dcba what are the values of a b c and d?”
Answer Let us reason out completely and not just “guess” at an answer. We use base 10. abcd = a*10^3 + b*10^2 + c*10^1 + d and dcba = d*10^3 + c*10^2 + b*10^1 + a abcd x 4 = dcba implies, 4 x [ a*10^3 + b*10^2 + c*10^1 + d ]= d*10^3...
Comments Off on Counting Problem: “How many dots in the n-th rectangle?”
Question •• 1st rectangle ••• ••• 2nd rectangle •••• •••• •••• 3rd rectangle ••••• ••••• ••••• ••••• 4th rectangle (please keep in mind the dots are closer together, but I didn’t know how to illustrate it on here, thanks) The first (top) rectangle contains 2 dots. The 2nd rectangle contains 6 dots. The 3rd...
Comments Off on Solve for x and y which are both real numbers? Given that 4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i
Answer 4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i Separate the ‘real’ and ‘complex’ part as follows: (4x – 3y -12) + (3y + 12)i = ( 9-2x ) + ( 1 -2y –2x )i “equate them” [ complex coefficients with complex coefficients and real ] : For the “real” we get, (4x – 3y -12) = ( 9-2x ) 6x...
Comments Off on Math Patterns: “Can you find the rule for this sequence?”
Question 10, 22, 36, 55, … Answer One answer is (n^3 – 4n^2 + 29n – 6) / 2 for n=1 to 4. How to get it? 10 22 36 55 We have four “numbers”. We can assign a polynomial of what degree(?) in order to form simulteneous equations for which we can ‘solve’?…...
Question The amount of interest earned on $K for one year is $256. The amount of discount paid on a one year loan “for $K,” transacted on a discounted basis at a discount rate that is equivalent to the interest rate of the first transaction, is $236. Find $K! Answer Firstly, when it is...
Question Find in terms of n, the n th term of the sequence: 1/3 , 2/5 , 3/7, 4/9 , 5/11 , . . . Answer Here is a neat way to look at it… Lets count for n = 1,2,3 etc. As we “count” we “observe” how this counting “relates” to the “pattern...
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