this question is related to numbers and the solution is as follows,
Rover eats 3/4 can of cat food in a day.
given
in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food
3 cans cost = $5 and a pack contains 3 cans
45 cans is equivalent to= 45/3
= 15 packs
15 packs cost = 15 x $5 = $75
So it will cost $ 75 to feed Rover for 60 days
Bobo eats 1/2 of a can of cat food per day
in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food
3 cans cost $5 and a pack contains 3 cans
30 cans are equivalent to 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So it will cost $50 to feed Bobo for 60 days
In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.
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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.
We are given that in 60 days he will consume ,
60 x 3/4 cans
= 45 cans of cat food
The cost of 3 cans cost = $5
and one pack has 3 cans in it.
Therefore, 45 cans is equivalent to
= 45/3
= 15 packs
So , the cost of 15 cans will be ,
15 packs cost = 15 x $5 = $75
Therefore ,$75 is used for 60 days of cat food for Rover.
Now , we know that Bobo eats 1/2 of a can food in a day.
Therefore, in 60 days he will eat,
60 x 1/2 cans
= 30 cans of food
As we know, 3 cans cost $5 and a pack contains 3 cans
Therefore, 30 cans = 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So , $50 is spend to feed Bobo , in a month.
Therefore , if will combine their cost we will get that ,
$75 +$ 50 = $125 is required to feed both the cats in one month.
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find the value of 15/4 divided 5/8.show you reasong
[tex]\dfrac{15}{4} \div\dfrac{5}{8}[/tex]
In order to divide two fractions, you will need to use the KCF method.
Keep
Change
Flip
This means that we will keep the first fraction, change the division to multiplication, and flip the second fraction(reciprocal).
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
Multiply:
[tex]\dfrac{15}{4} \times\dfrac{8}{5}[/tex]
[tex]\dfrac{15\times8}{4\times5}[/tex]
[tex]=\dfrac{120}{20}[/tex]
Simplify:
[tex]120\div20[/tex]
[tex]=\fbox{6}[/tex]
Answer: 6
Step-by-step explanation:
1. 15/4 divided by 5/8 = 120/20
15/4 / 5/8 = 15/4 times 8/5 = 15 time 8 over 4 time 5 = 120/20
2. 120/6 = 6
Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week
The minimal number of employees who did not get their preferred shift that week was 20.
Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.
But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.
We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.
But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.
Thus, 20 is the minimum number of staff members who failed to receive her preference of shift that week.
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In the figure below, side AC of ABC lies on line l.
A. 25
B. 30
C. 22
D. 24
As you can see, 5y is an external angle of triangle ABC
we know that 5y=180-x
since angle B is 40, and angle A=x and C=x, we have
x%2Bx%2B40=180
2x=180-40
x=140%2F2
x=70
so, angle A=70 and C=70
then
5y=180-70
5y=110
y=110%2F5
y=22
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The data set represents the total number of tickets each person purchased for a play.
0,0,1,1,1,2,2,2,4,
What is the median of the daya?
Answer:
The median of the data is 1
One of the roots of the equation x^2-5x+q=0 is 2. Find the other root and the value of the coefficient q.
The value of q in the given equation x²- 5x + q = 0 will be 4.
What is a polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.
given an equation x²- 5x + q = 0 and the question states that it has a root that is equal to 2
Since 2 is the root of this quadratic equation it will satisfy the equation
Substituting the values in the equation
4 - 5*2 + q = 0
q = 6
Equation will be
x²- 5x + 6 = 0
The root of the given equation using the fraction method
x²- 3x - 2x + 6= 0
(x -2)(x - 3) = 0
The root of the given equation are 2 and 3
Therefore, In the given equation x²- 5x + q = 0 the value of q will be 4.
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Math Subject: Symmetry.
Question is attached below.
The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.
What is Symmetry?A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.
Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.
The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.
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Answer:
1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.
2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.
3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.
4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.
5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.
6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.
7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.
8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.
Please help im not smart
Can a polynomial have no real roots?
Odd degree polynomials can have no real roots.
A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.
polynomials
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Real root
A real root is a solution to an equation which is also a real number.
Real number
Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
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Help ASAP!!!!!!!!!!!!!!!!
The correct order of match is 1-a, 2-b, 3-d and 4-c.
What are conic sections?The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.
A plane crosses the cone, and the resulting section is referred to as a conic section.
Given the equations,
the equation for parabola is given by
(y - b)² = 4p(x - a)
Vertex is (a,b)
equation 2 follows the same
x = -2(y - 4)² + 3
this is the equation for parabola.
Equation for ellipse is
(x − a)²/h² + (y − b)²/k² = 1
the equation x²/4 + (y - 8)²/144 = 1
(x/2)² + ((y - 8)/12)² = 1
the equation is same is equation for ellipse,
Equation for circle
(x - h)² + (y - k)² = r²
fourth equation
(x - 9)² + (y + 2)² = 7²
is same as equation of circle
Equation for hyperbola
(x − a)²/h² − (y − b)²/k² = 1
equation (x - 3)²/5 - (y + 4)²/25 = 1
is same as equation of hyperbola.
Hence the correct order is a, b, d, and c.
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2 Dylan needs 2.5 liters of water for an experiment. He has 1.125 liters.
How much more water does Dylan need?
Show your work.
Dylan needs how many
liters of water.
So Dylan needs 1.375 liters of water more for his experiment.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.
2.5 - 1.125 = 1.375 liters
So Dylan needs 1.375 liters of water more.
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Given that $13^{-1} \equiv 29 \pmod{47}$, find $34^{-1} \pmod{47}$, as a residue modulo 47. (Give a number between 0 and 46, inclusive.)
The value would be [tex]34^{-1} \pmod{47}=30[/tex]
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
Given that 13^-1 ≡ 29 (mod 47), we can use this information to find the inverse of 34 mod 47. The inverse of a number modulo m is a number x such that the product of the number and its inverse is congruent to 1 mod m.
In the case of the given equation, [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex] is saying that 29*13 = 377 is congruent to 1 mod 47.
We can use this congruence to find the inverse of 34 mod 47. The inverse of 34 mod 47 is the number x such that 34*x = 1 mod 47. So we can write this congruence as [tex]$34x \equiv 1 \pmod{47}$[/tex]
We can use the given congruence of 13^-1 ≡ 29 (mod 47) to find the inverse of 34 mod 47.
Since [tex]$13^{-1} \equiv 29 \pmod{47}$[/tex], we can multiply both sides of the congruence by 34 as:
[tex]$13^{-1} * 34 \equiv 29 * 34 \pmod{47}$[/tex]
Now we can substitute the right side of the equation:
[tex]$13^{-1} * 34 \equiv (13*29) \pmod{47}$[/tex]
And now we can substitute the left side of the equation:
[tex]$34^{-1} \equiv (13*29) \pmod{47}$[/tex]
And since [tex]$13*29 = 377$[/tex] this is congruent to 30 (mod 47) the inverse of 34 mod 47 is 30.
Therefore, the value would be [tex]34^{-1} \pmod{47}=30[/tex]
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The value would be 13.
What is the modulus in mathematics?
In mathematics, the modulus is the remainder of the division of one number by another. It is denoted by the symbol %, or in some cases, by the symbol mod.
We can use the property of modular inverse that
[tex]$(ab)^{-1} \equiv b^{-1}a^{-1} \pmod{m}$[/tex]
So, [tex]$(13*34)^{-1} \equiv 34^{-1} \cdot 13^{-1} \pmod{47}$[/tex]
[tex]$13^{-1} \equiv 29 \pmod{47}$\\$(13*34)^{-1} \equiv 34^{-1} \cdot 29 \pmod{47}$So, $34^{-1} \equiv (13*34)^{-1} \cdot 13 \pmod{47}$$34^{-1} \equiv 1 \cdot 13 \pmod{47}$$34^{-1} \equiv 13 \pmod{47}$[/tex]
Hence, The value would be 13.
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Write two expressions (with at least two terms each) that when added together have a sum of -4n 6.
On solving the provided question, we can say that the sum of the two expressions will be -4n + 6
what is expression ?It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.
Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.
let the two expression be
-4nand 6 and the sum will be -4n + 6
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What is the mole of o2?
The number of mole O₂ is 2. Since the subscript of oxygen denotes the number of moles.
What is a diatomic element?
Diatomic molecules—so named because they only contain two atoms of the same or different chemical elements—are molecules that are made up of two atoms. A diatomic molecule is considered to be homonuclear if it contains two atoms of the same element, such as oxygen (O₂) or hydrogen (H₂).
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
The subscript part of a chemical compound represents the number of moe of the chemical compound. The subscipt of O₂ is 2. Thus the number of mole is 2.
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What is a shape called with 1000000000 sides?
Answer:
Regular megagon
Step-by-step explanation:
Regular megagon is a shape called with 1000000000 sides.
Solution for 4x+3y=11 over 2x+y=7
Answer
x=-1/2,=29/4
explanation
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the image below for Part A, Part B, and Part C.
Two triangles: GHI and JKL
Both have one similar angle but different side lengths
Part A: Sharon says the triangles above are similar using the AA Postulate. Is she correct?
Part B: Explain the answer from Part A.
Part C: If HI=7, find KL. Show your work.
Please Help!
Answer:
see explanation
Step-by-step explanation:
A
for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.
In this case we are only given 1 pair of congruent angles.
Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.
B
the sides are of different lengths but the ratios of corresponding sides are equal, that is
[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2
If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so
Δ GHI and Δ JKL are similar by the SAS postulate
C
the ratios of corresponding sides are equal , then
[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]
[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
KL = 14
5
Isabella wants to create 23 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of two lotions.
One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on the inequality
below, how much of the 21% lotion, x, will she need?
O A. x≥ 14.375
O B.
x2 15.33
OC.
x2 20.125
O D. x2 11.5
0.21x+0.05(23-x) ≥ 3.45
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
What are Inequalities?The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.
In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.
An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.
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∠A and \angle B∠B are upplementary angle. If \text{m}\angle A=(7x-11)^{\circ}m∠A=(7x−11)
∘
and \text{m}\angle B=(x-25)^{\circ}m∠B=(x−25)
∘
, then find the meaure of \angle B∠B
The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
What are supplementary angles?
Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.
When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:
m∠A + m∠B = 180
Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:
(7x - 11)° + (x - 25)° = 180
Simplifying this equation by combining like terms:
8x - 36 = 180
Adding 36 to both sides:
8x = 216
Dividing both sides by 8:
x = 27
Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
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The measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
What are supplementary angles?
Supplementary angles are two angles that add up to 180 degrees. They are angles that when placed together will form a straight line. They are called "supplementary" because they "supplement" each other to form a straight angle.
When two angles are supplementary, their measures add up to 180 degrees. So, if ∠A and ∠B are supplementary, then:
m∠A + m∠B = 180
Given that m∠A = (7x - 11)° and m∠B = (x - 25)°, we can substitute these values into the equation:
(7x - 11)° + (x - 25)° = 180
Simplifying this equation by combining like terms:
8x - 36 = 180
Adding 36 to both sides:
8x = 216
Dividing both sides by 8:
x = 27
Hence, the measure of ∠B is (x - 25)° = (27 - 25)° = 2°.
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What does 4 mean in maths?
The meaning of the 4! ( factorial ) in mathematics is equal to ( 4 × 3 × 2 × 1 ).
As given in the question,
Given expression in mathematics is written as :
4! ( factorial )
In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.
It is expressed as:
n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).
Apply this formula for 4! ( factorial ) we get,
4! ( factorial )
= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)
= 4 × 3 × 2 × 1
= 12
Therefore, the meaning of 4! ( factorial ) in mathematics is given by
4 × 3 × 2 × 1 .
The above question is incomplete , the complete question is :
What does 4! ( factorial ) mean in mathematics?
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PLS HELP ASAP 50 POINTS!!!!
Triangle ABC is congruent to triangle PDF. Dude AC corresponds to what side in triangle PDF
Answer:
PF
Step-by-step explanation:
Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.
Hope this helped!
Why is the longest side of a triangle always opposite the largest angle?
The longest side of a triangle is always opposite to the largest angle because the endpoints of the lines on either side are going to be further apart if the angle is wider .
What is Triangle ?
The triangle can defined as a three-sided polygon that consists of three edges and three vertices.
Let the angle opens up to its opposite side.
So , the larger the angle, the wider will be it's opening. which means that the endpoints of lines on either side of the angle are going to be further apart if angle is wider.
If the endpoints are further apart, then the line connecting them, which makes up the side opposite will be going to be more longer.
So , the longest side will always be opposite to the largest angle
Similarly , the smallest angle will result in shortest side opposite side for the same reasons.
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Make the mathematical expressions. Simplify them and find the correct answers. a) The total cost of 4 pens at Rs 20 each, 5 pencils at Rs 5 each and 2 boxes at Rs 60 each.
Answer:
Step-by-step explanation:
Cost of 1 pen = 20 rupees
Cost of 4 pens = 20 x 4 = 80 rupees
Cost of 1 pencil = 5 rupees
Cost of 5 pencils = 5 x 5 = 25 rupees
Cost of 1 box = 60 rupees
Cost of 2 boxes = 60 x 2 = 120 rupees
therefore, total cost = 80 + 25 + 120 = 225 rupees
Type the correct answer in each box.
Compete the statement about these similar cylinders.
The circumference of the base of figure 2 is____ pi inches, and the area of the base of figure 2 is____ pi square inches
(Hint: The circumference of a circle = 2nt and the area of a circle = 12, where r is the radius)
The circumference of the base of figure 2 is 5π inches, and the area of the base of figure 2 is 6.25π square inches
You can presume that the cylinders are proportionate because they are comparable.
9/5 = 4.5/x would be the equation to be used for the calculation.
The radius of 2.5 is obtained by dividing and multiplying by crosses.
Figure 1's circumference will be:
Circumference = 2 * 2.5 = 5π
The area for figure 2 is as follows:
Area = (2.5)² = 2.5 * 2.5 = 6.25π
As a result, the base of figure 1 has a 5π inches circumference.
The base of figure 2 has a 6.25π square inch area.
The base of figure 1 has a 5π inch circumference.
The base of figure 2 has a 6.25π square inch area.
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Does a hyperbola have an inverse?
If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
What is a hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
A hyperbola is made up of two mirror images of one another that resemble two infinite bows.
These two sections are known as connected components or branches.
The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.
The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).
The section of a line that a hyperbola's vertices form.
The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.
Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
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You have 140 tomatoes and 13 onions left over from your garden. You want to use these
to make jars of tomato sauce and jars of salsa to sell at a farm stand. A jar of tomato
sauce requires 10 tomatoes and 1 onion, and a jar of salsa requires 5 tomatoes and 1
onion. You will make a profit of $2 on every jar of tomato sauce and a profit of $1.50 on
every jar of salsa sold. The owner of the farm wants at least three times as many jars of
tomato sauce as jars of salsa. How many jars of each should you make to maximize
profit?
3. A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts
of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce
the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000
hours are available for producing the parts, 4000 hours for assembling the parts and 5500
hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110.
How many of each type of tables should be produced in order to maximize the total
monthly profit?
1. To maximize the profit :
28 jars of salsa and
0 jars of tomato sauce should be made.
which make maximum profit of $42.
2. In order to maximize the total monthly profit
2300 units of T₁ type table and and
600 units of T₂ type table should be made
which provide maximum profit of $273000.
What is an Inequality?In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa. If the relationship between two algebraic expressions is defined using the inequality symbols, then it is called literal inequalities.
1. Let x be the numbers of jars of tomato sauce
Let y be the number of jars of salsa sauce
Profit P(x, y)=2x+1.5y
x≥0
y≥0
10x+5y≤140
x + y ≤13
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,13)
B at (0,28)
C at (14,0)
D at (15,0)
E at (15, -2)
Evaluate profit P(x, y) at each vertex
A at (0,13):P(0,13)=$19.5
B at (0,28):P(0,28)=$42
C at (14,0):P(14,0)=$28
D at (15,0):P(15,0)=$30
E at (15, -2):P(15,-2)=30-3=$27
The maximum profit of $42 is at vertex B.
Which means production of 28 jars of salsa and 0 jars of tomato sauce provides maximum profit of $42.
2. Let x be the number of tables of type T₁
and y the number of tables of type T₂
Profit P(x, y)=90x+110y
x≥0
y≥0
2x+4y≤7000
x+2.5y≤4000
2x+1,5y≤5500
The solution set of the system of inequalities above the vertices of the feasible solution set obtained are shown below.
A at (0,0)
B at (0,1600)
C at (1500,1000)
D at (2300,600)
E at (2750,0)
Evaluate profit P(x, y) at each vertex
A at (0,0):P(0,0)=0
B at (0.1600):P(0,1600)=90(0)+110(1600)=176000
C at (1500,1000):P(1500,1000)=90(2500)+110(1000)=245000
D at (2300,600):P(2300,600)=90(2300)+110(600)=273000
E at (2750,0):P(2750,0)=90(2750)+110(0)=247500
The maximum profit of $273000 is at vertex D.
which means production of 2300 tables of type T₁ and 600 tables of type T₂ makes maximum profit.
1. Hence, maximum profit is made by making
28 jars of salsa and
0 jars of tomato sauce getting
$42 of profit.
2. Hence the company needs to produce
2300 tables of type T₁ and
600 tables of type T₂,
in order to maximize its monthly profit which is equal to $273000.
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What are the 7 steps in problem solving examples?
The 7 stepd in problem-solving examples are:
Step 1: Read through the problem
Step 2: Draw diagram
Step 3: Assign variable to each unknown
Step 4: Translate information into an equation
Step 5: Check the equation
Step 6: Use algebra rules to solve the equations
Step 7: Check the final answer.
We know that the word problems are required to translate the real world problem into mathematical terms.
Everything mentioned in the word problem is important.
The seven necessary steps in problem solving examples:
Step 1: Read the problem throughly
Step 2: Draw picture / diagram / arrow diagram related to example
Step 3: Assign an alphabate to each unknown value
Step 4: Translate information into an equation
Step 5: Check the types equation
Step 6: solve the equations using algebra rules
Step 7: Check the final answer.
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For what value of k is 4x 2 8xy k * y 2 9 The equation of a pair of straight lines?
The value 'k' for which '4x^2 + 8xy + ky^2 = 9' is the second degree equation of a pair of straight lines is 4.
Therefore the answer is 4.
A general second-degree equation of a pair of straight lines is given by:
ax² + 2hxy + by² + 2gx + 2fy + c = 0
Where a, b, c, d, e, and f are constants, x and y are variables.
For the equation to represent a pair of straight lines, the following conditions must be met :
abc + 2fgh - af² - bg² - ch² = 0
In the equation 4x^2 + 8xy + ky^2 = 9, a = 4, h = 4, b = k, g = f = 0 and c = -9.
That is 4×k×(-9) + 2×0×0×4 - 4×0² - k×0² + 9×4² = 0
4×k×9 = 9×4²
k = 4
--The question is incomplete, complete question is given below--
"For what value of k is 4x^2 + 8xy + ky^2 = 9 the equation of a pair of straight lines?"
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4. Nicole uses 2.5 meters of ribbon to decorate
door wreaths. There are 20 meters of ribbon on a
spool. Write an equation that could be used to
determine the number of wreaths that Nicole
could decorate using one spool of ribbon. Solve.
Equation:
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
Define Equation.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Define Algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
An equation that could be used to determine the number of wreaths that Nicole could decorate using one spool of ribbon is:
W = S / R
where W is the number of wreaths, S is the total length of ribbon on the spool, and R is the length of ribbon used per wreath.
Plugging in the given values, we get:
W = 20 / 2.5
Solving for W, we get:
W = 8
So Nicole could decorate 8 wreaths using one spool of ribbon.
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Directions: Follow the instructions for the following inequalities.
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Please Write Your Answer Below:
Answer:
1. 4x3<7×3
12×2<21×2
24×4<42×4
96×9<168×9
864<1512
2. 11+3>-2+3
14+3>1+3
17_4>4-4
13>0
3. -2/leg-2
-18/leg-18
4. -4<8
0<2
A statistics class with 30 students has 10 males and 20 females. Suppose you choose 3 of the students in the class at random. Find the probability that all three are female
The probability that all three are female is 0.281
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.2030⋅1929⋅18282030⋅1929⋅1828 = 0.281
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