(a) Luis Mahla purchases a Porsche Boxster for $49,700 and finances the entire amount at an annual interest rate of 6.3% for 8 years. Find the monthly payment. Assume the sales tax is 6% of the purchase price and the license fee is 1% of the purchase price. (Round your answer to the nearest cent.)

(b) After becoming a commercial pilot, Lorna Kao decides to purchase a Cessna 182 for $64,975. Assuming the sales tax is 4.9% of the purchase price, find each of the following.

(1) What is the total cost, including sales tax?
(2) If Lorna makes a down payment of 18% of the total cost, find the down payment.
(3) Assuming Lorna finances the remaining cost at an annual interest rate of 7.15% for 10 years, find the monthly payment.

At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {7: 6, 5, 1}. In this voting system, the head coach A has a weight of 6, the assistant coach B has a weight of 5, and the junior varsity coach C has a weight of 1. Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.)

BPI(A) =

BPI(B) =

BPI(C) =

Let D(x, y) be the predicate defined on natural numbers x and y as follows: D(x, y) is true whenever y divides x, otherwise it is false. Additionally, D(x, 0) is false no matter what x is (since dividing by zero is a no-no!). Let P(x) be the predicate defined on natural numbers that is true if and only if x is a prime number. 1. Write P(x) as a predicate formula involving quantifiers, logical connectives, and the predicate D(x, y). Assume the domain to be natural numbers.

Hint 1: n is prime if and only if the only numbers that divide it are 1 and n.

Hint 2: You might have to use conditionals.

2. Consider the proposition “There are infinitely many prime numbers”. Express the proposition as a predicate formula using quantifiers, logical connectives and the predicate P(x). Assume the domain to be natural numbers. Note that you don’t need to use the answer from the previous part in this problem; you can write your answer in terms of P(x).

3. Write the negation of the predicate formula obtained in part 2. Make sure you take the negation all the way in so that it sits right next to P(x) in the final expression.

Only want to know what the answer for 3 should be

in 2013 the estimated world population 7.1 billion use the doubling of 70 years to predict the population 2027, 20153 and 2103?

Suppose A^2= A , where A is an n by n matrix. Use Jordan canonical form to thaw that A is diagonalizable.

B = {red,red,green,purple}
C = {red,{green},red,{red,green},purple,{green,green,red,purple}}

A.) What is the power set of C?

B.) Is B ∈ P(C)?

Draw bifurication diagram of:

(x^2-a)(x^2-4)

Again considering y'' + 4y' + 3y = 0:

(a) Solve the IVP y'' + 4y' + 3y = 0; y(0) = 1, y'(0) = α where α > 0.

(b) Determine the coordinates (tm,ym) of the maximum point of the solution as a function of α.

(c) Determine the behavior of tm and ym as α →∞.

Consider the following system of equations for all problems.
The following system of equations is designed to determine concentrations (the c’s in g/m3) in a series of coupled reactors as a function of the amount of mass input to each reactor (the right-hand sides in g/day).

8?1 − 4?2 − 2?3 = 2000

−3?1 + 18?2 − 6?3 = 1400

−4?1 − 2?2 + 12?3 = 3000

Calculate and interpret the condition number. Use the row-sum norm. Scale the coefficient matrix (A) so the absolute value of the maximum element in each row is 1 (max magnitude in each row = 1). You may use MATLAB’s inv to find the inverse of the scaled A matrix

Alternative-Fueled Vehicles The table shows the numbers (in thousands) of alternative-fueled

vehicles A in use in the United States from 1995 to 2011. (Source: U.S. Energy Information Administration)

(a) Use a graphing utility to plot the data. Let t represent the year, with t = 5 corresponding to 1995. (b) A model for the data is

4615.36t − 8726.7

1 + 15.01t − 0.542t2, 5 ≤ t ≤ 21

where t = 5 corresponds to 1995. Use the model to estimate the numbers of alternative-fueled vehicles in 1996, 2006, and 2011. How do your answers compare to the original data?

(f ) Use the model to predict the numbers of alternative-fueled vehicles in 2016 and 2017

* Need help to understand F . Should I be using a particular formula

If v is an eigenvector for a matrix A, can v be associated with two different eigenvalues? Prove your answer.

A square matrix A is said to be symmetric if its transpose A^T satisfies A^T= A, and a
complex-valued square matrix A is said to be Hermitian if its conjugate transpose A^H =
(A)^T = A^T satisfies A^H = A. Thus, a real-valued square matrix A is symmetric if and
only if it is Hermitian. Which of the following is a vector space?
(a) The set of all n xn real-valued symmetric matrices over R.
(b) The set of all n xn complex-valued symmetric matrices over C.
(c) The set of all nx n complex-valued Hermitian matrices over R.
(d) The set of all n xn complex-valued Hermitian matrices over C.
For each case, either verify that it is a vector space or prove otherwise.

Solve the following problem by Dynamic Programming:
Maximize z = (y1 + 2)^2 + y2 * y3 + (y4 - 5)^2
subject to
y1 + y2 + y3 + y4 <= 5
yi >= 0 and integer, i = 1, 2, 3, 4

Prove that the Jacobi method converges for strictly column-diagonally dominant matrices.

Let p= 11 and 13. (a) Determine all the squares modulo p in (Z/pZ)∗. (b) Using this determine the value of the Legendre symbol(a/p)for all a∈(Z/pZ)∗. (c) For all a∈(Z/pZ)∗, compute a^((p−1)/2) and confirm that a^((p−1)/2)=(a/p).