To determine the size of carpets that will maximize the company's revenue, we need to find the dimensions that will generate the highest total sales. Let's analyze the situation step by step.
We know that the company can sell 200 carpets per week when the size is 3ft by 3ft. Beyond this size, for each additional foot of length and width, the number sold decreases by 4.
Let's denote the additional length and width beyond 3ft as x. Therefore, the dimensions of the carpets will be (3 + x) ft by (3 + x) ft.
Now, we need to determine the relationship between the number of carpets sold and the dimensions. We can observe that for each additional foot of length and width, the number sold decreases by 4. So, the number of carpets sold can be expressed as:
Number of Carpets Sold = 200 - 4x
Next, we need to calculate the revenue generated from selling these carpets. The price per square foot is $5, and the area of the carpet is (3 + x) ft by (3 + x) ft, which gives us:
Revenue = Price per Square Foot * Area
= $5 * (3 + x) * (3 + x)
= $5 * (9 + 6x + [tex]x^2)[/tex]
= $45 + $30x + $5[tex]x^2[/tex]
Now, we can determine the dimensions that will maximize the revenue by finding the vertex of the quadratic function. The x-coordinate of the vertex gives us the optimal value of x.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a = $5 and b = $30.
x = -30 / (2 * 5)
x = -30 / 10
x = -3
Since we are dealing with dimensions, we take the absolute value of x, which gives us x = 3.
Therefore, the additional length and width beyond 3ft that will maximize the revenue is 3ft.
The dimensions of the carpets that the company should sell to maximize its revenue are 6ft by 6ft.
To calculate the maximum weekly revenue, we substitute x = 3 into the revenue function:
Revenue = $45 + $30x + $[tex]5x^2[/tex]
= $45 + $30(3) + $5([tex]3^2)[/tex]
= $45 + $90 + $45
= $180
Hence, the maximum weekly revenue for the company is $180.
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3. The Lovely Day Fruit company makes two varieties of fruit drink, Fruit Delight and Heavenly Punch. The chart below shows how much juice goes into each type and the profit per can of juice. Each week, the company receives a shipment of 9000 ounces of pineapple juice, 24000 ounces of orange juice, and 14000 ounces of apricot juice. Fill in the question marks appropriately and then use the linear programming process to find how many cans of each should be made each week to maximize profit.
The optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.
Fruit Delight:
Pineapple juice: 3 oz
Orange juice: 6 oz
Apricot juice: 2 oz
Profit: $1.50
Heavenly Punch:
Pineapple juice: 6 oz
Orange juice: 2 oz
Apricot juice: 4 oz
Profit: $2.00
Linear Programming Process:
We can use linear programming to solve this problem. We will create two variables, x and y, to represent the number of cans of Fruit Delight and Heavenly Punch respectively. The objective is to maximize profit, which can be expressed mathematically as:
Maximize: 1.50x + 2.00y
subject to:
3x + 6y ≤ 9000
2x + 4y ≤ 14000
6x + 2y ≤ 24000
x ≥ 0
y ≥ 0
Using linear programming software, we can solve this problem and find that the optimal solution is x = 2000 and y = 4000, meaning that 2000 cans of Fruit Delight and 4000 cans of Heavenly Punch should be made each week to maximize profit.
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HURRY PLEASE!!!!!!!
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second. Diego starts with his usual 20 ounce milkshake and drinks at the same rate as before, an ounce per second.
What does the graph tell you about the situation? Specifically answer the following:
a.) How many solutions are there? (25 pts)
b.) Interpret the solution(s). (25 pts)
c.) Who finishes the milkshake first? (25 pts)
the other equation is missing, the solution cannot be found.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
Determined to finish her milkshake before Diego, Lin now drinks her 12 ounce milkshake at a rate of an ounce per second.
Rate= 1/3 ounce milkshake per second
Initial = 20 ounces
Lin's condition is thus represented by the equation:
[tex]y = \frac{1}{3} x +20[/tex]
Since the other equation is missing, the solution cannot be found.
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PLEASE HELP!!! TO THE PERSON WHO GIVES ME THE RIGHT ANSWER I WILL GIVE BRAINLIEST!!! PLEASE HELP.
Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?
Let x represent the number of students who bought a cup of orange juice and y represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:
x + 3y = 76
x + y = 36
Answer the questions to solve the problem.
1. Explain what you should do with the two equations to eliminate one of the variables. (2 points)
2. Find the value of y. (3 points)
3. Find the value of x. (2 points)
4. Interpret the solution and check the values in the system. (3 points)
Answer:
see explanation
Step-by-step explanation:
given the system of equations
x + 3y = 76 → (1)
x + y = 36 → (2)
1
subtracting (2) from (1) term by term will eliminate x
(x - x) + (3y - y) = 76 - 36
0 + 2y = 40
2y = 40 ( divide both sides by 2 )
y = 20
3
substitute y = 20 into either of the 2 equations and solve for x
substituting into (2)
x + 20 = 36 ( subtract 20 from both sides )
x = 16
4
that is 16 students bought orange juice and 20 bought a sandwich
As a check
substitute the values for x and y into the equations and if both sides are equal then they are the solution
(1) : 16 + 3(20) = 16 + 60 = 76 ← True
(2) : 16 + 20 = 36 ← True
since both equations are true, then
x = 16 and y = 20 are the solutions to the system
The biggest possible cube is taken out of a right solid cylinder of radius 15cm and height 25 cm respectively. what will be the volume of the cube
The volume of the biggest possible cube inside the right cylinder is approximately 1193.243 cubic centimeters.
What is the biggest possible cube that is taken out of a right solid cylinder?
Cubes are hexahedrons with one same side length and only right angles. In this case, the cube is constrained by cross area of right cylinder in accordance to image attached below. The maximum possible volume for a cube inside the cylinder is described by following expression:
V = (√2 / 2)³ · R³
Where:
V - Volume of the cube, in centimeters.R - Radius of the right cylinder, in centimeters.If we know that R = 15 cm, then the volume of biggest possible cube is:
V = (√2 / 2)³ · (15 cm)³
V ≈ 1193.243 cm³
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How many grams are in 3.29 X 10²5 molecules of water (H₂O)?
Water molecules with a mass of 3.34 * (10 )23 weigh 9.911 grams.
What is the mass in grams of 3.34 x 1023 molecules of H2O?Firstly, you wish to transform the quantity of water molecules you have into the quantity of moles.
Undoubtedly, you are aware
Number of Particles = Mole Ratio x Avogadro's Constant
Avogadro's constant is equal to 3.34 * (10) 23 / 6.02 * (10) 23 when the number of moles is equal to the number of particles.
=0.55
so 0.55 moles
Consequently, mass/molar mass = number of moles.
Since we must determine the mass, we can use the formula Mass = Number of Moles x Molar Mass.
H 2 O's molar mass is calculated as H - 2(1.01) = 2.02 O- 16 18.02
Consequently, 18.02 g/mol is the molar mass.
We now possess the necessary values to determine the mass because of this.
Mass = 0.55 × 18.02
Mass = 9.911
As a result, the 3.34 mass
There are 9.911 grams in 3.34 * (10 )23 water molecules.
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What is the expanded form for 45 squared?
Answer:
See below
Step-by-step explanation:
I'm guessing this is what you're looking for:
[tex]45^2=(40+5)^2=(40+5)(40+5)=40(40)+2(40)(5)+5(5)=1600+400+25=2025[/tex]
How many images are formed If two plane mirror are position at an angle of 45â°?
The number of images that will be formed when two mirrors are positioned at an angle of 45 degrees is 7.
The formula that you have provided for calculating the number of images formed by two mirrors positioned at a specific angle is (360/n) - 1, where n is the angle between the mirrors in degrees.
When two mirrors are positioned at an angle of 45 degrees, n = 45. So, using the formula, the number of images formed would be: (360/45) -1 = 8 - 1= 7
It's important to note that this formula only gives you the approximate number of images that will be formed. In reality, due to the nature of light and the reflective properties of mirrors, it is impossible to determine the exact number of images that will be formed.
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What is #6? Needhelp
Answer:
(-3,5)
Step-by-step explanation:
8x+3(23+6x)=-9
x=-3
y=23+6x(-3)
y=5
(-3,5)
Molly jogged at a rate of 6 mph, what was her speed in feet per second?
Answer:
8.8 feet per second
Step-by-step explanation:
1 mile = 5280 feet
3600 seconds = 1 hour
6 mph = 5280(6)/3600 = 528/60 8.8 feet per second
Please help quickly I have limited time!!!!!!
Cells share many cοmmon features, yet they can look wildly different. In fact, cells have adapted οver billions of years to a wide array of environments and functional rοles.
What Defines a Cell?The lοwest common element of life is a cell. Some cells function as independent entities, while οthers are a component of multicellular οrganisms.
Nucleic acids, prteins, carbohydrates, and lipids make up the four main types of οrganic molecules that all οrganisms are composed of. In part because they arrive in distinct, distinguishable packets, cells are regarded as the fundamental building blοcks of life.
The reasοn for this is that, like a hοuse's walls, the cell membrane that surrounds every cell acts as a definite border between its interiοr and exterior envirοnments. The plasma membrane is anοther name for the cell membrane. Phοspholipids are a framework οf fat-based molecules that serve as the fοundation of cell membranes.
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What is the measure of angle ACD?
Using the exterior angle theorem which involves the use of two interior angles in the polygon, the value of angle ACD in the triangle is 150 degrees
What is an Exterior AngleAn exterior angle of a polygon is an angle that is formed outside of the polygon by extending one of its sides. It is the supplementary angle of an interior angle.
Exterior angle theorem states that the sum of two interior angles is equal to one exterior angle.
Using that theorem in this problem;
∠ACD = 33 + 117
∠ACD = 150°
The value of angle ACD in the triangle is equal to 150 degrees
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Using the cosine rule calculate the magnitude of angle B when dide b=20.8cm c= 14.5cm and a= 9.3cm
Using the cosine rule calculate the magnitude of angle B when did the b=20.8cm c= 14.5cm and a= 9.3cm is [tex]\approx 37.02364^{\circ}[/tex]
What is cosine rule?c = [a2 + b2 - 2ab cos C] is the cosine formula to get the side of the triangle. a, b, and c are the triangle's three sides. When attempting to link all three sides of a triangle to a single angle, the cosine rule can be applied. You need to know the other two sides as well as the opposing angle in order to determine the length of a side. Your objective is to locate side a. With the aid of the sine rule, one can determine an angle from three sides and an angle or a side from three angles and a side.Given,
b=20.8cm c= 14.5cm and a= 9.3cm
[tex]\gamma=\cos ^{-1}\left(\frac{a^2+b^2-c^2}{2 a b}\right)[/tex]
[tex]=\cos ^{-1}\left(\frac{9.3^2+20.8^2-14.5^2}{2 \cdot 9.3 \cdot 20.8}\right)[/tex]
[tex]\approx 37.02364^{\circ}[/tex]
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Is square root of 4 a polynomial?
Square root of 4 is not a polynomial. It is a quadratic function. Functions containing other operations like square root is not a polynomial.
A polynomial need not have any square root. polynomial is a finite sequence form. it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Polynomial are sums and differences of polynomial terms. For an expression to be a polynomial term, any variables in the expression must have whole number powers. It should not have any square root, cube root or any negative values. Quadratic function can have square root cube roots and fraction values.
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Write and solve an equation or a system of equations to help you solve the following problem.
A cable 84 meters long is cut into two pieces so that one piece is 18 meters longer than the other. What is the length of each piece of cable? (show your work)
The equation written is: x + 18 + x = 84
The lengths of each piece of the cable are: 33 meters and 51 meters.
How to Write an Equation?To write an equation, let the unknown quantity be represented as a variable, which would be used in creating an algebraic expression.
For example, we are given the following:
Length of a cable = 84 meters
The length of one the pieces that the cable is cut into is represented as x.
The second pieces = x + 18 meters.
The equation that would be created for this problem would be:
x + 18 + x = 84
Solve for x:
2x + 18 = 84
2x = 84 - 18
2x = 66
2x/2 = 66/2
x = 33
The length of one of the pieces = 33 meters
Length of the second piece = x + 18 = 33 + 18 = 51 meters.
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What value breaks 100 into 4 equal pieces?
Answer:
25 :)
Step-by-step explanation:
What are the 4 triangle classifications by angle measure?
The 4 types of triangle with respect to angle measurement :
Acute Triangle
Obtuse Triangle
Right triangle
Equivalent triangle
What are the four types of triangles by angle measurement ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
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There are four different triangles for measuring angles:
sharp triangle
Sharp triangle
correct triangle
comparable triangle
What are the four different kinds of triangles according to angle?If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.
An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.
A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.
An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.
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Y=x2+2x-2 graph each quadratic function
By evaluating the quadratic equation we can get some points, and with them we can estimate the graph.
The graph can be seen in the image at the end.
How to graph the quadratic equation?Here we want to graph the function:
y = x^2 + 2x - 2
To do so, we can evaluate the quadratic equation in some values of x to get points, and then just connect the points with a general parabola.
when x = 0
y = 0^2 + 2*0 - 2 = -2
So the point is (0, -2)
when x = 1
y = 1^2 + 2*1 - 2 = 1 + 2 - 2 = 1
So the point is (1, 1)
when x = -1
y = (-1)^2 + 2*(-1) - 2
y = 1 - 2- 2 = -3
So the point is (-1, -3)
when x = -2
y = (-2)^2 + 2*(-2) - 2
y = 4 - 4 - 2 = -2
So we have the point (-2, -2)
And so on..., eventually, you will get enough points to connect, and you should get something like:
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Dante deposits $300 to open a savings account. He will earn 2% interest each year on his
money If he makes no deposits or withdrawals, how much money will Dante earn in interest
in 1 year? How much money will be in the account after 4 years?
Therefore , the solution to the given problem of interest comes out to be $324.
What is meant by interest?By dividing the original capital by the cost of borrowing, the time period, and other factors, simple interest is calculated. Simple return is calculated as follows: principal + interest + hours. This method of calculating interest is the simplest. The most typical method is to calculate it as a percent of the principal amount. For instance, if he took $100 from a buddy and promised to repay it with 5% interest, he would only be required to pay his proportion of the interest. $100 (0.05) = $5. When you make loans, you should pay interest, and you also need to when you lend money. Interest is often computed as a percentage of a loan.
Here,
Given: $300 is the principal amount
Time: 4 years,
2% interest rate
To discover the basic interest:
Using this formula
Simple interest equals
=> P*R*T/100,
=> 300*2*4/100
=> 24.
Total after four years equals 300 + 24 = 324
Therefore , the solution to the given problem of simple interest comes out to be $324.
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Clare ha $150 in her bank account. He buy for $200. What i clare' account balance now?
Claire's current account balance would be -$50.
The amount that Clare has in his bank account initially = $150
The amount that he used from his bank account to buy the bike = $200
As we can see that the amount that Clare used to buy the bike is more than the amount that he has in his account, therefore his account balance becomes negative, that is:
$150 - $200 = -$50
Here, it means that Clare has to pay the bank the amount of $50 that he used more than the amount that he had in his account.
Therefore, Claire's account balance would be -$50.
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What is the symmetric of -15??
The symmetric of -15 is 15.
Step by step explanation:When we talk about symmetric, we must remember that it means the opposite of a number, that is, we take as a basis the number line where we have zero (0) as the central number, on one side the negative infinite numbers (-) and on the other, the positive infinite number (+), see the attached image.
In order to solve this type of exercise, just change the signs of the number in question, if it is negative it will become positive and vice versa.
[tex] \bold{- 15 = + 15}[/tex]
Jon earns £90 one week. The next week, he receives a pay rise and earns £130. Write the amount of his pay rise as a fraction of his original pay. Give your answer in its simplest form.
PLEASE HELP I REALLY NEED IT FOR HOMEWORK
The fraction of Jon original pay is 4/10
How to calculate the fraction of Jon original pay?Jon earns £90 one week
The following week he earns £130
His pay rise is
130-90
= 40
The fraction of his original pay is
= 40/100
= 4/10
Hence the fraction of Jon original pay is 4/10
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The side of the quadrilateral are in the ratio 4:6:3:5. The perimeter of
the quadrilateral is 54 cm. What are the lengths of each side? Solution:
A quadrilateral is a four-sided shape. The perimeter of a quadrilateral is the sum of all its sides. If the perimeter of a quadrilateral is 54 cm, and we know that all four sides are equal, we can divide 54 by 4 to find the length of each side.
54 cm / 4 = 13.5 cmTherefore, the length of each side of the quadrilateral is 13.5 cm.
It's important to note that this is only one possibility, since quadrilaterals can have different shapes and different side lengths.
Rewrite it in for y=a(1+r)^t
Answer:
I don't get it please elaborate!
Step by Step Explanation:
Thank you!
Are rectangles and squares similar polygons?
Yes, rectangles and squares are similar polygons.
Similar polygons are two or more polygons with the same shape but different sizes. This means that the sides of the polygons are proportional, and the angles are congruent. The formula to determine if two polygons are similar is A/a = B/b = C/c = D/d = …, where A, B, C, and D are the sides of one polygon and a, b, c, and d are the sides of the other polygon. For instance, if a rectangle has sides of 4 and 8, and a square has sides of 6 and 6, the ratio of the sides of the rectangle to the sides of the square is 4/6 = 8/6. This means that the two shapes are similar.
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please help im stuck like really stuck
Answer:
[tex]14v+7=7(2v+1)[/tex]
Step-by-step explanation:
break down the equation 14v +7
Answer:
7(2v+1)
Step-by-step explanation:
7 goes into 14 twice and into itself once so its factorised as 7(2v+1) you can do the multiplication to test it .
Line A pae through the point (1,5) and (5,7). Find the equation of the line perpendicular to A that pae through point (-1,7
The equation of the line perpendicular to the line A is given by the
x-4y +29=0
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is a Line A pass through the point (1,5) and (5,7).
Find the equation of the line perpendicular to A that pae through point (-1,7)
line A is y= 1/4 x+c
x-4y +4c=0
it passes through ( -1,7)
c= 29/4
equation becomes x-4y +29=0
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Alex made a table to record how many trees were in his yard for each day that the landscapers were working. Which equation represents the data?
Which of the following is degree 2 polynomial y2 y3 +2y8?A. 2B. -1c. 3D. 8
Answer:
Step-by-step explanation: .
Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. Complete the statements.
Sally's class haven't raised $2,000 as the amount made is $958. The estimated value is $1900. The amount needed is $42.
How to illustrate the value?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, Sally's class is raising money for charity with a goal of raising $2,000. They raise $997 at a bake sale and $961 at a car wash. Sally wants to see if they raised enough money to meet their goal. The amount made will be:
= $997 + $961
= $1958
They have not made $2000. The amount left is:
= $2000 - $1958
= $42
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What are the 4 physical properties of solutions?
The 4 physical properties of solutions are:
1) Concentration
2) Solubility
3) Viscosity
4) Transparency
PHYSICAL PROPERTIES OF SOLUTIONIn chemistry, a solution is a homogeneous mixture of two or more substances. The four common physical properties of solutions are:
1) Concentration: The amount of solute present in a given amount of solvent, typically measured in molarity, molality, or mass percentage.
2) Solubility: The maximum amount of solute that can be dissolved in a given amount of solvent at a specific temperature and pressure.
3) Viscosity: The resistance of a fluid to flow, which can be affected by the presence of a solute.
4) Transparency or Opacity: The property of a solution by which it allows light to pass through it or not.
These are the 4 common physical properties of solutions, but there are many other physical properties that can be used to describe solutions depending on the context.
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