Recursions, Recurrence Relations, Difference Equations, Equations for Population Growth, Fibonacci Sequences and Binet's Formula

1. Solve xn=axn-1+b when a=1. 2. An isotope of carbon called carbon-14 (14C) is used to establish the age of artifacts and fossils. It decays so that every 5000 years an amount of 14C is reduced to 54.44256% of its initial valued A archaeologist finds a fossil that contains 16% of the amount of 14C it contained when it was al ...continues

Construction of confidence interval for mean and population proportion.

* Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected. x1 = 57, n1 = 95 and x2 = 84, n2 = 96; Construct a 98% confidence interval for the difference between population proportions p1 - p2. .... ...continues

probability

Two adults a1 and b1, and eight children c1, c2, ... , c8 board a bus with 10 seats s1, s2, ... , s10. The adults board first and randomly select seats. The children select seats in order with c1 selecting first, c2 selecting second, and so on. Each child sits in the lowest numbered seat available to them. What is the probab ...continues

Applications of Parabolas, Hyperbolas and Probability

Conic Sections and Sequences, Series, and Combinatorics One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the brid ...continues

Conic Sections and Sequences, Series, and Combinatorics

Conic Sections and Sequences, Series, and Combinatorics Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways. 1. An employee of the National Parks Service told you about a location in Washington, DC. It is a large ...continues

Combinations

Is it possible to evaluate C(9,12)? Explain.

Finance Math : Probability and Expected Value of a Payoff

Charles and Millie Jackson (a married couple in their 40’s) have decided to invest a portion of their accumulated retirement “nest-egg” in a new business venture. It is an opportunity that Millie found while exploring one of her hobbies. Her idea is to embroider logos for small companies and organizations. They have already p ...continues

Exponential Generating Function for a Recurrence

Please see the attached file for the fully formatted problems.

Effective Annual Interest Rate

You've worked out a line of credit arrangement that allows you borrow up to $70M at any time. The interest rate is .480% per month. In addition , 5% of the amount that you borrow must be deposited in a non interest-bearing account. Assume that your bank uses compound interest on its line of credit loans. 1) What is the effe ...continues

Latin Squares

1) Show that for n less than or equal to 4, any Latin square of order n can be obtained from the multiplication table of a group by permuting rows, columns, and symbols. Show that this is not true for n=5 2) If n is an order for which mutually orthogonal Latin squares exist, does every Latin square of order n have an orthogo ...continues