Matrix addition is both commutative and associative for addition?

Linear Programming A candy company makes three types of candy, solid-center, fruit-filled, and cream-filled, and packages these candies in three different assortments. A box of assortment I contains 4 solid-center, 4 fruit-filled, and 12 cream-filled candies, and sells for $17.95. A box of assortment II contains 12 solid-center, 4 fruit-filled, and 4 cream-filled candies, and sells for $18.45. A box of assortment III contains 8 solid-center, 8 fruit-filled, and 8 cream-filled candies, and sells for $20.85. The manufacturing costs per piece of candy are $0.01 for solid-center, $0.02 for fruit-filled, and $0.03 for cream-filled. The company can manufacture 4,800 solid-center, 4,000 fruit-filled, and 5,600 cream-filled candies weekly. How many boxes of each type should the company produce each week in order to maximize their profits? What is the maximum profit? *Will thumbs up for correct answer, thank you*

State whether the following statements are true of false. If they are true, give a short justification. If they are false, give a counterexample. For each of the following, P(x) is a polynomial.

(a) If P(x) has only even powers, and P(a) = 0 then x^2 ? a^2 divides P(x).

(b) If P(x) has only odd powers, and P(a) = 0 then x^2 ? a^2 divides P(x).

(c) If P(x) has only even powers, then P(x) has at least one real root.

(d) If P(x) = a7x^7 + a6x^6 + a3x^3 + a0, where ai ? R, ai is not equal to zero, then P(x) has at least one real root.

(e) If P(x) has only even powers, then P(x) has at least one complex root.

(f) If P(x) = a7x^7 + a6x^6 + a3x^3 + a0, where ai ? R, ai is not equal to zero , then P(x) has at least one complex root.

Give the fifth roots of z=11+10i in rectangular form with real and imaginary parts rounded to 4 decimal places. Show your work.

You want to be able to withdraw $20,000 from your account each year for 30 years after you retire. If you expect to retire in 25 years and your account earns 6.8% interest while saving for retirement and 4.4% interest while retired:
Round your answers to the nearest cent as needed.

a) How much will you need to have when you retire?
$

b) How much will you need to deposit each month until retirement to achieve your retirement goals?
$

c) How much did you deposit into you retirement account?
$

d) How much did you receive in payments during retirement?
$

e) How much of the money you received was interest?
$

License

Convert the system

3x1 +13x2 - 14x3 = -14

x1 + 4x2 -5x3 = -4

-7x1 - 25x2 +39x3 = 20

to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions.

Augmented matrix:

Echelon form:

Is the system consistent?

Solution (x1,x2,x3) =

A consonsultant wishes to invest up to a total of $25000 in two types of securities, one that yields 10% per year and another than yields 8% per year. They believe that the amount invested in the first security should be at most one third of the amount invested in the second security. What investment program should the consultant pursue in order to maximize income? (Use constraint inqualities with objective function)

Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of each.

(f+g) (x) =

(f-g)(x) =

(fg)(x) =

(f/g)(x) =

The domain of f+g is_

The domain of f-g is_

The domain of fg is _

The domain of f/g is _

Please at the end provide showed work.

Calculate a t-test for the following scenario. An engineer is designing a stationary parts bin at a work table and considers using an established... Calculate a t-test for the following scenario. An engineer is designing a stationary parts bin at a work table and considers using an established functional grip reach of 29.55 inches taken from the overall population mean, which was published in a textbook. However, the individuals who work in the facility represent a demographic that the engineer has noticed to be a bit small in stature. She decides to take a small sample to test her theory and randomly selects seven individuals and measures their reach. She comes up with the following data: 27.87, 29.49, 28.34, 28.20, 29.00, 29.56, 27.95 (inches). Calculate a mean and sample standard deviation, and use these values to perform a t-test on this data. Report all of these values. Also, discuss the concept of the p value and whether the data was significantly different from the population mean. Discuss whether the engineer was correct in assuming the reach of the worker population may be less than the population mean.

Twice last? month, Judy Carter rented a car in? Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily? fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4? days, she drove 360 ?miles, and the rental cost her ?$226.00 On her second business trip she drove 190 miles in 3? days, and paid ?$149.50 for the rental. Find the daily fee and the mileage charge.

Assume that you have a balance of $5300 on your Discover credit card and that you make no more charges. Assume that Discover charges 21% APR and that each month you make only the minimum payment of 2% of the balance.

Find how many months it will take to bring the remaining balance down to $2500. (Round your answer to the nearest whole number.)

Answer is NOT 301

1. Consider the three vectors, u and v are 10 degrees above and below the x-axis respectively, and ||u|| = 1, ||v|| = 2, and ||w|| = 3. Arrange the dot products taken among these vectors from least to greatest

2. Let A be a 4 x 6 matrix. Find the elimination matrix E that corresponds with the row operation "switch rows 1 and 3, and scale row 4 by a factor of 6.

3. Find the formula for the entry in the ith row and j column of the product AB in terms of the entries of A and B. Assume A is m x n and B is n x p.

explain why a matrice can have many row echelon forms