Assume that you have a balance of $9000 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 5% of the balance.

Find how many months it will take to bring the remaining balance down to $400. (Round your answer to the nearest whole number.)

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 131 pounds in weight, and earns $20 in revenue. Each crate of cargo II is 7 cubic feet in volume and 262 pounds in weight, and earns $25 in revenue. The plane has available at most 525 cubic feet and 12,576 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

crates of cargo 1

crates of cargo 2

maximum revenue $

2. National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $30 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?

What is the optimal profit?

On May 12, 2008, a certain country had a 7.8 magnitude earthquake. What was the intensity of that earthquake? (Round your answer to two decimal places.)

The amount of outstanding consumer debt? (in trillions of? dollars) is approximated by g(t)= 0.365362 * 1.068022^t, where t=0

corresponds to 1980. Find the year in which consumer debt is

(a) $2 trillion

(b) $9 trillion

(a) The consumer debt will reach???$2 trillion in the latepart of year:

?(b) The consumer debt will reach???$9 trillion in late part of the year:

(3) Write elimination matrix representing each step in elimination process. ( not augmented matrix)

(a)

2x + y − z = 3

x + 3y − z = 6

3x − y + 7z = 8

b)

x+y−z−t=0

x + y + 2z − t = 3

2x + 2y + z + 3t = 13

x + 2y + 5z − 7t = 3

This exercise is designed to be solved using technology such as calculators or computer spreadsheets.

You borrow $18,000 with a term of four years at an APR of 8%. Make an amortization table. How much equity have you built up halfway through the term? (Round your answer to two decimal places.)

Let T₁ be the reflection about the line 4x?3y=04x?3y=0 in the euclidean plane. What is the standard matrix A of T₁ ?

What are the two eigenvalues and corresponding eigenspaces of A ?

(3) Let V be a vector space over a field F. Suppose that a ? F, v ? V and av = 0. Prove that a = 0 or v = 0.

(4) Prove that for any field F, F is a vector space over F.

(5) Prove that the set V = {a0 + a1x + a2x 2 + a3x 3 | a0, a1, a2, a3 ? R} of polynomials of degree ? 3 is a vector space over R (with respect to the usual addition and scalar multiplication of polynomials).

(2) Let Z/nZ be the set of n elements {0, 1, 2, . . . , n ? 1} with addition and multiplication modulo n. (a) Which element of Z/5Z is the additive identity? Which element is the multiplicative identity? For each nonzero element of Z/5Z, write out its multiplicative inverse. (b) Prove that Z/nZ is a field if and only if n is a prime number. [Hint: first work out why it’s not a field when n isn’t prime. Try some small examples, e.g. n = 4, n = 6.]

Prove Desargues’ Theorem for the case where AC is parallel with A′C′ on the extended Euclidean plane.

Find answer for the following floor and ceiling functions.

⌊66.6⌋ = ?

⌈66.6⌉ = ?

⌊-66.6⌋ = ?

⌈-66.6⌉ = ?

(9) Diagonalizing

4 0 1

-7 -5 5.

-12 -6 7

Decide which formula to use and than solve

A. Sara borrows $1200 at 8 % simple interest. If the loan is for 5 months, what is the total amount he pays back (This is sometimes called the maturity value)?

B.Sara later decides to deposit $9000 at 7.5% per year compounded annually, and would like to know how much she will have after 10 years.

C. Sara's husband wants to invest $1000 at the end of each quarter at 9% compounded quarterly, and would like to know (1) how much will he have after 10 years? (2) How much interest will he earn after 10 years?

D. Sara is considering depositing $600 at the end of each semi-annual period, for 5 years earning interest of 8%. She would like to know how large a one-time lump sum deposit she could make, at the same rate, to have the same amount of money after 5 years.

Determining the Selling Price of a Home Determining how much to pay for a home is one of the more difficult decisions that must be made when purchasing a home. There are many factors that play a role in a home’s value. Location, size, number of bedrooms, number of bathrooms, lot size, and building materials are just a few. Fortunately, the website Zillow.com has developed its own formula for predicting the selling price of a home. This information is a great tool for predicting the actual sale price. For example, the data to the right show the “zestimate”—the selling price of a home as predicted by the folks at Zillow and the actual selling price of the home for homes in Oak Park, Illinois. The graph below, called a scatter diagram, shows the points (291.5, 268), (320, 305), . . . , (368, 385) in a Cartesian plane. From the graph, it appears that the data follow a linear relation. 1. Imagine drawing a line through the data that appears to fit the data well. Do you believe the slope of the line would be positive, negative, or close to zero? Why? 2. Pick two points from the scatter diagram. Treat the zestimate as the value of x and treat the sale price as the corresponding value of y. Find the equation of the line through the two points you selected. 3. Interpret the slope of the line. 4. Use your equation to predict the selling price of a home whose zestimate is $335,000. 5. Do you believe it would be a good idea to use the equation you found in part 2 if the zestimate is $950,000? Why or why not? 6. Choose a location in which you would like to live. Go to www.zillow.com and randomly select at least ten homes that have recently sold. (a) Draw a scatter diagram of your data. (b) Select two points from the scatter diagram and find the equation of the line through the points. (c) Interpret the slope. (d) Find a home from the Zillow website that interests you under the “Make Me Move” option for which a zestimate is available. Use your equation to predict the sale price based on the zestimate. can i get the full answer of this question please