A clothing business finds there is a linear relationship between the number of shirts, n ,it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price of $66, while 10000 shirts can be sold at a price of $48. Give a linear equation in the form p

Answers

Answer 1

Answer: p = [tex]\frac{-n}{500} +68[/tex]

Step-by-step explanation:

Let n represent the number of shirts and p represent the price, the there is a linear relationship between n and p, then the model equation is given as:

p = mn + b, where

m = slope and b is the intercept

From the question, when n = 1000, p = $66

And, when n = 10,000 , p = $48

The formula for finding slope is given as:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

[tex]y_{1} = 66[/tex]

[tex]y_{2} = 48[/tex]

[tex]x_{1} = 1000[/tex]

[tex]x_{2} = 10000[/tex]

substituting the values,

m = [tex]\frac{48-66}{10000-1000}[/tex]

m = [tex]\frac{-18}{9000}[/tex]

m = [tex]\frac{-2}{1000}[/tex]

m = [tex]\frac{-1}{500}[/tex]

The linear equation thus becomes

p = [tex]\frac{-n}{500}+b[/tex]

To find the value of b, substitute  p = 66 and n =1000 into the equation

That is,

66 = [tex]\frac{-1000}{500}+b[/tex]

66 = -2 + b

68 = b

Therefore b = 68

The linear equation is therefore

p = [tex]\frac{-n}{500} +68[/tex]


Related Questions

what is green and blue? HELP

Answers

Answer:

green horizontal asymptote: y = -2

blue horizontal asymptote: y = -4

Step-by-step explanation: Exponential functions have a horizontal asymptote

Leala can write a 500- word essay in an hour. If she writes an essay in 10 minutes, approximately how many words do you think the essay contains?

Answers

Answer:

about 83

Step-by-step explanation:

The table shows a set of values for x and y

Answers

a) Assume y = [tex]x^{2}[/tex]

[tex]1b=\frac{k}{1^{2} }[/tex] k = 1b

[tex]y=\frac{1b}{x^{2} }[/tex]

b) y = 25

[tex]x^{2}=\frac{16}{25}[/tex]

[tex]x=\sqrt{\frac{4}{5} ^{2} }[/tex]

x = ±[tex]\frac{4}{5}[/tex]

x > 0, x = 4/5

{ Equation }

y=16/x² is required equation for y in terms of x and x=4/5 when y=25.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The table of values are

x         1         2         3         4

y        16        4        16/9      1

Given that y is inversely proportional to square of x.

y=k/x²

Let us consider

y=16 and x=1

16=k/1

k=16.

y=16/x²

So y=16/x² is equation for y in terms of x

b) We need to find value of x when y=25

25=16/x²

Use cross multiplication

x²=16/25

Take square root on both sides

√x²=√16/25

x=±4/5

If x>0 , so x=4/5

Hence y=16/x² is required equation for y in terms of x and x=4/5 when y=25.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Which of the following statements must be true based on the diagram below.please help

Answers

Answer:

A: ST is a segment bisector

Step-by-step explanation:

ST is a segment bisector. Point S cuts in between segment QP. While Point T cuts between segment PO.

FIND THE FACTORS OF THE FOLLOWING POLYNOMIAL 3y²-2y-1

Answers

Answer:

y

[tex] y2 - 2y - 3[/tex]

[tex](y - 1)(y + 3) [/tex]

[tex](3y - 1)(3y + 3)[/tex]

Step-by-step explanation:

you multiple the 3 with the 1

then factor

then divide by 3 again but the denominator goes in front of the y.

I'm having a bit of trouble finding out how to find the Domain of this function. Help please!

Answers

In general, the domain is the set of all x-values for the graph.  

The issue here is that this isn't the graph of a function.  A function has at most one y-value for each x-value and this graph has an infinite number of y-values for the single x-value of 1.

So, either your teacher is wanting you to say the domain is {1}, because that's the only x-value used by the graph, or they're wanting you to say this is a trick question, because this isn't the graph of a function.

The range is the set of all y-values, which is -9<y<9, but again, do they intend this to be a trick question?

helpppppppppppppppppppppppppppppppppppppppppppmmmmmmmeeeeeeeeeeeeeeeeeeeeeeeeeeeemeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

It is correct because the smallest one is 3 the second one all together is 15 and the last one is 60.

Step-by-step explanation: Basically you can divide the 60 with 15 and you can divide 60 with 3.

60/15 = 4

60/3 = 20

and 4 can go in to 20 5 times so yeah.

And I hope I helped you out.

What are two numbers whose product is 81 and their sum is -18?

Answers

Answer:

-9

Step-by-step explanation:

-9  * -9 = 81

-9 + -9 = -18

Answer: -9

Leo bought 6 glasses and 6 mugs. Leo knows that he was charged $3.99 for
each
mug
and that the total bill before tax was $65.88. Write and solve an
equation to determine how much Leo was charged for each glass

Answers

Answer:

filedownload.ashx

do all straight lines that are functions have inverses?

Answers

Answer: Not all Functions have a inverse

Happy To Help :)

Step-by-step explanation:

The length of a rectangle is three more than twice it’s width. The perimeter of the rectangle is 246 cm. Write an equation to find the perimeter and then find the length of the rectangle.

Answers

Answer:

83 cm

Step-by-step explanation:

Let the length of the rectangle be L cm and the width be W cm.

L= 2W +3 -----(1)

Perimeter of rectangle= 2(length) +2(width)

2L +2W= 246 -----(2)

Substitute (1) into (2):

2(2W +3) +2W= 246

Expand:

4W +6 +2W= 246

Simplify:

6W +6= 246

Divide both sides by 6:

W +1= 41

W= 41 -1

W= 40

∴ width of the rectangle is 40cm.

Substitute value of W into (1):

L= 2(40).+3

L= 80 +3

L= 83

Thus, the length of the rectangle is 83 cm.

.Triangle ABC is right angled at B,  AB= 8 cm, BC = 15 cm, find AC​

Answers

Answer:

17

Step-by-step explanation:

Part A: Rhett made $250 washing cars with his mobile car wash company. He charges $70 per car and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car wash. Write an equation to represent this situation. (4 points)


Part C: Explain how the equations from Part A and Part B differ. (2 points)

Answers

Answer:

Part A 70x+50=250

Part B(75x + 35) = 250 - 5x

Step-by-step explanation:

Here to form an equation you must add all the money that she earned and subtract the money that she had to spend We dont know how many car washes she did, so we must represent it with a variable, or x.

Answer:

Step-by-step explanation:

Part A: Rhett washed 3 cars and earned $50 in tips. y=70x+50

Part B: $75 - $5 = $70 (this is the amount charged minus the amount needed to get the job done per car wash)

the +35 is the tips extra/ constant that will be added after the jobs are done.

x is the number of car washes done

y would be the profit received.

so y = 70x + 35 (profit = value of car wash * number of cars washed + tips)

Guinea made a scale drawing of a window she is making for her house.

1 centimeter = 3 inches. Triangle A B C. Side A is 4 centimeters, side B is 3 centimeters, and side C is 5 centimeters.
Which proportion could Guinea use to find the length of side B?

Answers

Answer:

The answer is c: 1cm/3in = 3 cm/Xin

Step-by-step explanation:

1000 Chevrolet times 1000 Lamborghini

Answers

Answer:

1000000 chevginis

Step-by-step explanation:

Answer:

1000000 sports cars (Chevrolet and Lamborghinis)

Step-by-step explanation:

1000x1000

Someone help me I will mark you as brain

Answers

Answer:did u get it right

Step-by-step explanation:

I'm pretty sure that the answer to the question is 2, or D, since the slope of f(x) is 3, and the slope of g(x) is 6. Since g(x) = f(k*x), and g(x) has twice the slope. I could be wrong, but I hope this helps.

Find the line of best fit for the relationship between calories and fat.

y=0.0714x-9.2682
y=1.2653x+14.452
y=2.5612x+4.9045
y=1.139x-6.7093

Answers

Answer: Choice A

y=0.0714x-9.2682

==============================================

Explanation:

I used GeoGebra (free graphing software) to find the line of best fit, aka the regression line. You can do so by hand, but I think it's tedious busywork and prefer to use technology whenever possible. Other graphing and spreadsheet programs are able to compute the regression line as well.

Check out the diagram below.

what is 5x plus 2 equals 4x -9

Answers

Answer:

x=-11

Step-by-step explanation:

5x+2=4x-9

5x-4x=-9-2

x=-11

The length of a 10-minute video is decreased by 45% when the video is edited. What is the length of the edited video?

Answers

Answer:

The edited video would now be 5 Minutes 50 Seconds

Step-by-step explanation:

10-4.5=5.5

To subtract any percentage from a number, simply multiply that number by the percentage you want to remain. In other words, multiply by 100 percent minus the percentage you want to subtract, in decimal form. To subtract 20 percent, multiply by 80 percent (0.8).

Step-by-step explanation:

its 5.5 mins

here are the methods

1-0.45= 0.55  0.55*10= 5.5

or

its

45/100= 0.45  0.45*10min= 4.5  10mins-4.5mins= 5.5 mins

Rachna borrowed a certain sum at the rate of 15% per annum. if she paid at the end of the two years Rs.1290 as interest Compounded annually, find the sum she borrowed.​

Answers

Given info:

Compound Interest = Rs.1290

Rate of Interest = 15% p.a

Time = 2 years

Formula we have to know:-

[tex] \dag{\underline{\boxed{\sf{C.I = P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1}}}}[/tex]

Where

C.I = Compound Interest

P = Principle

R = Rate of Interest

N = Time

[tex]\textsf{ \underline{Solution-}}\\[/tex]

Here

C.I = Rs.1290

R = 15%

N = 2 years

Principle = ?

Now,Calculating the sum (Principle) borrowed by Rachna

[tex] \quad{: \implies{\sf{C.I = \Bigg[P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1 \Bigg]}}}[/tex]

Substituting the given values

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(1 + \dfrac{15}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{(1 \times 100) + 15}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \bigg)^{2} - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \times \dfrac{115}{100} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{13225}{10000} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg( \cancel{\dfrac{13225}{10000}} \bigg) - 1 \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = \Bigg[P \bigg({1.3225 - 1} \bigg) \Bigg]}}}[/tex]

[tex]\quad{: \implies{\sf{1290 = P \times {0.3225}}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{1290}{0.3225} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{1290 \times 1000}{0.3225 \times 1000} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\dfrac{12900000}{3225} = P}}}[/tex]

[tex]\quad{: \implies{\sf{\cancel{\dfrac{12900000}{3225}} = P}}}[/tex]

[tex]\quad{: \implies{\sf{Rs.4000 = P}}}[/tex]

[tex]\quad{\dag{\underline{\boxed{\tt{\blue{Principle} = \purple{Rs.4000 }}}}}}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

Hence,

The sum (Principle) is Rs.4000.

the cost of a DVD is $29.95. Sales tax is 6%. About how much will the DVD cost, including tax? ​

Answers

Answer:

31.75$

Step-by-step explanation:

To add sales tax, you multiply the amount you start with by 1 + what the tax is.

In this case, you multiply 29,95 by 1.06%.

29.95 × 1.06% = 31.747 or 31.75$

Answer:

30.01

Step-by-step explanation:

29.95+6%= 30.01

braiblest plz:)

hope this helps

What is the greatest common factor of 8m2, 4m, and 10m4?

Answers

Answer:

2m²

Step-by-step explanation:

Apply the prime factorization method: 2³m², 2 · 5m⁴

Find the greatest common divisor: 2m²

Answer: 2m²

How many faces does a right rectangular prism have if it has 8 vertices and 12 edges?
A. 4 faces
B. 6 faces
C. 8 faces
D. 10 faces

Answers

Answer:

B

Step-by-step explanation:

I think

Which of the following customary units is the most appropriate unit to measure the capacity of a coffee pot?

A. gallon
B. pound
C. ounce
D. cup

Answers

Answer:

Cup

Explanation:

Gallon is too large, it'll spill over.

Pound is just... Obviously not. You use that to weight people...

And ounce is smaller than a cup but we're talking about the most appropriate unit therefore your answer is cup.

Hope that helps <3

I need help on this problem i dont know if the answer is: 16 or 48,but i dont know for sure so if my guess if wrong please tell me.**Thank you so much if you help me will make brain if you answer correctly!** =3
*no links!*

Answers

Answer:

You will need 32 ounces

Step-by-step explanation:

2 pounds x 16 = 32 ounces

300 cal / 3 oz = x / 32 oz

(300 * 32) / 3 = 3,200 calories

Can someone tell me the answer to this please I got this wrong on my first attempt ._.

Answers

Answer:

36

Step-by-step explanation:

FG ≅ QG

Its the same as the other side

24 and 24

so 36 and 36

:)

bill heads north driving at 55 mph and jane heads south driving at 60 mph. How long before they are 862.5 miles apart?

Answers

Answer:

bill heads;15.68

jane heads;14.38

Step-by-step explanation:

862.5÷55=15.68

862.5÷60=14.38

Danni walked 2 miles, and Wendi walked 10,500 feet. Which statement is accurate?
A) Wendi walked farther than Danni.

B) Danni walked farther than Wendi.

C) Danni walked twice as far as Wendi.

D) Danni and Wendi walked equal distances.

Answers

Answer:

B) Danni walked farther than Wendi.

Step-by-step explanation:

a mile is 5,280 feet. 5,280 + 5280 = 10,560

what color is a blueberry?

Answers

Answer: blue

Step-by-step explanation: it’s blue because when you see it, you can see the color blue. Also, blue is in blueberry :). Honestly, there isn’t a main reason why, but it’s blue.

it starts at 10 and stops at 4​

Answers

6 hours
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