The walls and ceiling in your bedroom need to be painted, and the painters’ estimates to do the work are far too expensive. You decide that you will paint the bedroom yourself. Below is the information to help you solve the problem:
• The bedroom is 17 ft., 3 in. long by 18 ft. wide, and the ceiling is 9 ft. high.
• The color of paint you have selected for the walls covers 84 square feet per gallon and costs $31.50 per gallon.
• The inside of the bedroom door is to be painted the same color as the walls.
• The ceiling will be painted with a bright white ceiling paint that costs $27.50 per gallon but only covers 73 sq. ft. per gallon.
• Two coats of paint will be applied to all painted surfaces.
• The room has one window, measuring 3 ft., 3 in. by 4 ft., which will not be painted.

1. Because different paint lots of the same color may appear slightly different in color, when painting a room, you should buy all of your paint at one time and intermix the paint from at least two different cans so that the walls will all be exactly the same color. Because all ending values are given in feet, first find the room dimensions in feet that make a good model for this situation.

ANSWERS
LENGTH ft.
WIDTH ft.
HEIGHT ft.

Explain your answer here:




2. Using the measurements found above, label the sides in feet here:













                                                      
3. Using the formula concepts and dimensions from above, find the bedroom’s total painted surface area around all of the walls, including both coats. Do not forget to subtract the window’s area. Also, double the paint to account for two coats.

Show all step-by-step calculations, including the units of measurement, and round your final answers to the nearest whole measurement unit:

ANSWER
Total painted wall surface area

Explain your answer here:




4. Using the formula concepts and dimensions from above, find the ceiling’s total painted surface area, including both coats.

Show all step-by-step calculations, including the units of measurement, and round your final answers to the nearest whole measurement unit:

ANSWER
Total painted ceiling surface area

Explain your answer here:






5. Describe and discuss the strategy, steps, formulas, and procedures for how you will use Polya’s problem-solving techniques to determine how much it will cost to paint this bedroom with two coats of paint (on all walls and the ceiling).

Explain your answer here:






6. Find, individually and as a total, how much it will cost to paint this bedroom with two coats of paint (on all walls and the ceiling).

Show all step-by-step calculations, including the units of measurement, and round your final answers to the nearest whole dollar amount:

ANSWERS
Total cost painted wall surface area
Total cost ceiling surface area
Overall total cost of paint

Explain your answer here:





7. Assuming you can paint 100 sq. ft. per hour, what will be the work time needed to paint your bedroom?

Show all step-by-step calculations, including the units of measurement, and round your final answers to the nearest whole hour amount:

ANSWERS
Total painting time

Explain your answer here:

This week we study complex numbers which include an "imaginary" part. This is an unfortunate name,  because imaginary numbers can be proven to exist and they are very useful for describing certain physical phenomena. Search for one interesting fact about imaginary numbers. This can be their history, application, etc. Be sure to read through your classmates' postings first, duplicate facts will not count.

a. What is your fact?

b. In your secondary responses to your classmates' facts, endeavor to expand our knowledge or understanding of how they affect the world as we know it.

Consider the set of vectors S = {(1, 0, 1),(1, 1, 0),(0, 1, 1)}.

(a) Does the set S span R3?

(b) If possible, write the vector (3, 1, 2) as a linear combination of the vectors in S. If not possible, explain why.

find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. remember to complete the square in oder to accuartely graph the ellipse: 9x^2+6y^2-36x+12y=12

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?
$

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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.