A rectangular floor measures $a$ feet by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half the area of the entire floor. How many possibilities are there for the ordered pair $(a,b)$?

Answers

Answer 1

The number of possibilities that are there for the ordered pair is 2.

Calculation and Parameters

Because the unpainted part of the floor covers 1/2 of the area, then the painted rectangle covers 1/2 of the area as well.

Given that the border width is 1 foot, the dimensions of the rectangle are a-2 by b-2.

Making an equation:

ab= 2((a-2)(b-2))

ab= 2ab-4a-4b+8

ab-4a-4b+8=0

If we apply Simon's Favorite Factoring Trick,

ab-4a-4b+16= 8

(a-4)(b-4)= 8

Since b > a, then we have the possibilities

(a-4) = 1 and (b-4) = 8, or (a-4) = 2 and (b-4) = 4.

(5, 12) or (6,8) which gives us 2 possibilities.

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Related Questions

The user growth rate of a social media platform decreased by 15% per month. On January 1, the platform had 20 million users. If growth decreases at 15% each month, how many will it have by year end?

Answers

Answer:

2.844835 million current users

Explanation:

20 million x .85 x .85 x .85 x .85 x .85 x .85 x .85 x .85 x .85 x .85 x .85 x .85

Theta Inc. uses normal costing and applies overhead based on direct material costs. The predetermined overhead rate for the current year is 250% of direct material costs. During the year, $3,500,000 of direct material costs and $4,000,000 of direct labor costs were incurred. Theta's applied overhead is:

a. $9,375,000.

b. $1,600,000.

c. $8,750,000.

d. $1,400,000.

Answers

Answer:

a. $9,375,000.

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Indicate the point where a monopoly will set its price.

Answers

Answer:

A monopoly will set its price at the point where marginal cost and marginal revenue intersects or meet (MC = MR).

Explanation:

A monopoly is a market structure which is typically characterized by a single-seller who sells a unique product in the market by dominance. Thus, it is a market structure wherein the seller has no competitor because he is solely responsible for the sale of unique products without close substitutes. Any individual that deals with the sales of unique products in a monopolistic market is generally referred to as a monopolist.

For example, a public power company that serves as the only power utility (electricity) provider to the public.

Generally, a monopoly will set its price at the point where marginal cost and marginal revenue intersects or meet (MC = MR). This is simply because a monopoly would derive the maximum profit at the point where MC = MR.

Answer:

The dot where green and red meet.

Explanation:

Which research tool is best suited to gathering qualitative market data?

A. Census statistics
B. In-depth interviews
C. Business records
D. Surveys

Answers

In-depth interviews is best suited to gathering qualitative market data.

What is market data?

Every business's success has been largely attributed to its use of market research techniques. Knowing the ins and outs of your target market is more important than ever in a world where competition seems to be endless.

Companies that benchmark can see 69% quicker growth and 45% higher productivity than those that don't, according to a PwC study.

Organizations have been able to learn not only some of the largest industry revelations, but also the smallest facts that most people miss, thanks to market research. Market research is crucial because it enables businesses to interpret information and make defensible judgments.

Therefore,  In-depth interviews is best suited to gathering qualitative market data.

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Answer:in-depth interviews

Explanation:

I just Took the quiz.

most stock exchanges today use electronic trading

Answers

True

(Not sure what was the question about but I’m guessing it’s a true/false?)

hope this helps :)

HELP ME PLEASE!!!
when is it usually best to choose a variable rate home mortgage?
A. if you plan to stay there many years.
B. if you plan to stay there a short time before moving again.
C. if you plan to rent it out.
D. if you plan to have a large family.

Answers

Answer:

A...............maybe D

Which of the following tips can help you avoid electrical
shock from a computer? (Select three answers.)
Unplug the computer before performing maintenance.
| Keep liquids away from the computer.
Open up the computer while it is turned on to see
what's wrong.
D Use only the keyboard and not the mouse when
performing maintenance.
Make sure the computer doesn't have worn out wiring.
Wash the inside of the computer with water to keep it clean.

Answers

Answers:


1) Unplug the computer before preforming maintenance.

2) Keep liquids away from computer.

3) Make sure the computer doesn’t have a worn out wiring.


I hope this helped :)

Click this link to view O*NET's Tasks section for Actors.
Note that common tasks are listed toward the top, and less common tasks are listed toward the bottom. According to
O*NET, what are common tasks performed by Actors? Check all that apply.
creating artwork for use in stage sets
collaborating with other actors
working closely with directors, other actors, and playwrights to find the interpretation suited to the role
studying and rehearsing roles from scripts
learning about characters in scripts and their relationships to each other
teaching college classes and training other people how to become actors

Answers

Answer: B C D E

Explanation:

Did the assignment

To find the interpretation suited to the role, studying and rehearsing roles from scripts, learning about characters in scripts and their relationships to each other and teaching college classes and training other people how to become actors are common tasks performed by Actors. Hence, options B, C, D and E are correct.

Who is a director of a movie?

The directors are the movie's creative leaders. They uphold the artistic vision throughout pre-production and final editing. They are employed by the executive producer or producer, who is ultimately in control of a production.

A film director's responsibilities include reading and editing scripts, overseeing the cast and crew, and putting the final product together. The actors and other crew members will work with you to ensure that the movie ultimately reflects the aesthetic vision for the finished result.

Thus, options B, C, D and E are correct.

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Understanding the legal ramifications what types of policies should organizations implement when using social media tools for recruitment

Answers

Answer:

Social media is a vital tool for online recruitment in the large MNCs now-a-days.

Explanation:

In the recent, there is a trend of recruiting the new professionals through various online platforms and other social media tools.

With social media many legal consideration comes into account. The organizations while handling social media tools for recruitment has to look on various important points while posting their advertisement and collecting the data of the candidates online. There are severe legal ramifications on using social media in a wrong way, so organization have to be ethical while using them.

Firstly, they should respect the privacy of the social media communities.Professionalism and rules of ethics should be applied.They should respect the copyright laws.

What are three ways to discover how to involved in your chosen career field

Answers

Answer:

Research industry information. ...

Find out about professional associations. ...

Research career options using LinkedIn.

Prepare a report on environmental sanitation. Include the impacts, causes, and prevention methods​

Answers

Answer and Explanation:

Environmental sanitation is carried out through a series of public investments that seek to promote environmental control in a region. The impacts of this type of sanitation must be positive, since it is through it that a community can present adequate garbage collection, treated water supply, sewage treatment, correct disposal of human waste, cleaning of public roads, basic sanitation, among others . All of this promotes human development, the well-being of the population and environmental preservation.

The causes of environmental sanitation are the need to establish social policies that promote better living conditions and that optimize the health of citizens without degrading the environment.

review of the nigerian economy​

Answers

Answer:

amazing

Explanation:


Nigeria's economic freedom score is 57.2, making its economy the 116th freest in the 2020 Index. Its overall score has decreased by 0.1 point, reflecting a decline in the fiscal health score.

Pete and Shirley are filing a joint return. They have two dependent children. What is the total amount of their exemptions for tax year 2019? A. $0 B. $4,200 C. $8,400 D. $16,800

Answers

Answer:

A. $0

Explanation:

The Tax Cuts and Jobs Act eliminated personal exemptions starting 2018. It also increased standard deductions though. For example, the standard deduction for married filing jointly for 2019 was $24,400. This is a significant increase if you consider that the standard deduction for married filing jointly in 2017 was $12,700.

How can the government be both a producer and a consumer in respect to its relationship with business

Answers

Answer:

they gonna tinda and be kind to the coatumets

Answer:

they are gonna tinda and be nice to the caotmautes

What is the biggest business in the world right now and why.

Answers

Answer:

Apple

Explanation:

It is worth the most money. It is worth 2 trillion dollars.

Answer:

anime

Explanation:

an anime? jus cu.z i luv anime

5. Describe how Chris used networking to his advantage in getting an internship
Witter and signing new clients.

Answers

Answer:

is there more information for this question?

3. Why are people who are unemployed but not looking for work not included in
the unemployment figures? (Hint: think of teenagers)
Need help due TODAY

Answers

Answer:

Because they don't keep track on it.

Explanation:

Basically they are just included in it because they don't keep track of it. Hope that helps!

A weekly report for new agents at a vacation sales company is shown in the histogram. A histogram titled Vacation Packages has number of packages sold on the x-axis and number of salespersons on the y-axis. 9 sold 1 to 2 packages; 7 sold 3 to 4; 4 sold 5 to 6; 3 sold 7 to 8; 2 sold 9 to 10; 1 sold 11 to 12; 2 sold 13 to 14; 3 sold 15 to 16. How many of the new agents sold more than 10 vacation packages?

Answers

Answer:

6 salespersons

Explanation:

A histogram shows the graphical representation of the distribution of numerical data using bars of different lengths.

From the histogram:

The number of salespersons who sold 11 - 12 packages = 1

The number of salespersons who sold 13 - 14 packages = 2

The number of salespersons who sold 15 - 16 packages = 3

Therefore the new agents who sold more than 10 vacation packages = 1 + 2 + 3 = 6 salespersons

Answer:its 6

Explanation:i took the quiz and i know the answer

Problem 17-1A Comparing costs using ABC with the plantwide overhead rate LO P1, P3, A1, A2

Answers

Answer:

$67.50 per hour

Explanation:

Setup Cost = $312,500

Transportation Cost = $10,000

Direct Labor cost $25,500

Modification of machine cost $12,000

Insurance of Factory Premises $28,000

Raw material Cost $118,250

Machine hours = 7,500 hours

labor hours = 3,500  hours

Total manufacturing Overheads = $506,250 / 7,500 = $67.5 per hours

Question 2 (1 point)
Kelsi works in a toy manufacturing company assembling small dolls. Her job falls into
the Maintenance, Installation & Repair pathway of the Manufacturing career cluster.

1:) True

2:) False

Answers

True




I guess don’t be mad if I’m wrong

Which economic system is based on an idea of equality of result; that regardless of how well off somebody starts, all
should be guaranteed an equal success?
O A. Traditional
B. Command
OC. Mixed
D. Market

Answers

B. Command

What your describing sounds a lot like communism which would be found under a command economic system

Answer:

D.Market

Explanation:

A market economy conforms to formal equality of opportunity only if jobs offered by business firms are publicized in advance, so that anyone who might want to apply has a reasonable opportunity to do so.

Explain incentives and opportunity cost. Also give an example of both.

PLEASE ANWSER THIS AS A QUESTION YOU HAVE BEEN GIVING SO I CAN COPY AND PASTE PLEASE.

Answers

Answer:

Incentives are the rewards or punishments that shape people's choices. Incentives can be either monetary or non-monetary. When opportunity costs change, incentives change, and people's choices and behavior change. Changes in incentives cause people to change their behavior in predictable ways.

Explanation:

I think that is correct

DO you like Anne with an E?​

Answers

Answer:

meh

Explanation:

it's okay. I kind of don't like how they stayed from the book but all the scenes were shot beautifully, and the actors did great. I only watched a few so I cant give more than a "meh" but I do like what I'm seeing so far

On 3/1/X1 Landlord Co. received a $36,000 cash payment from Renter Co. to pay for a total of 17 months, starting in the current month. How much revenue should Landlord Co. recognize in the year ending 12/31/X1? Round your answer to the nearest penny.

Answers

Answer: $21177

Explanation:

First and foremost, we should note that since the revenue that Landlord Co. wants to recognize in the year ending 12/31/X1 will be for a period of 10 months that is, from 1st of March to 31st of December.

Therefore, the revenue that Landlord Co. should recognize in the year ending 12/31/X1 will be:

= $36000 × 10/17

= $21176.471

= $21177

Burning of candle is which change?(chemical change or physical change)​

Answers

Burning a candle is a physical change
Hope that helped

Answer:

physical as it is getting smaller, but I would also say chemical as it's changing into melted wax? more of a physical change for me. hope this gelps

Besides individuals, who else pays taxes in our country?

Answers

Answer:

Aliens?

Explanation:

Which of the following explains how revenue is determined?

A. The total amount of money brought in by sales.

B. Gross domestic product is calculated.

C. Costs are subtracted from revenues.

D. The maximum level of benefits is figured.​

Edit: Its not C

Answers

Answer:

A. The total amount of money brought in by sales.

Critical reading is a
a Theory
b. Process
C. Summarization strategy
d. None of these
Please select the best answer from the choices provided
A
В
C
D

Answers

Answer:C

Explanation:

Answer:

The correct answer for this question is B

Here is selected financial statement data regarding a company's property, plant, and equipment. Balance Sheet: Dec. 31, 2018 Dec. 31, 2017 Property, plant, and equipment $ 563,000 $ 294,000 Accumulated depreciation 286,000 237,000 Income Statement: 2018 Depreciation expense $ 105,000 Gain on sale of property, plant, and equipment 26,000 During the year, PPE with a book value of $23,000 were sold. In the statement of cash flows, the investing activities section should show a cash disbursement for "purchases of property, plant, and equipment" for $ _________.

Answers

Answer:

$292,000

Explanation:

price of old equipment sold = $26,000 + $23,000 = $49,000 (cash inflow)

new equipment purchased = $563,000 - $294,000 + $23,000 = $292,000 (cash outflow)

cash flow from investing activities:

cash disbursed for purchasing new equipment = ($292,000)

cash received from sale of old equipment = $49,000

net cash flow from investing activities = ($243,000)

Which of the following does not fall into the field of marketing?
-restaurant management
-education
-e-commerce
-professional sales

Answers

Answer:

professional sales

Explanation:

sales

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