The sum of 8.8 and 5.5 is 14.3
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
To find the sum of 8.8 and 5.5 without using pen and pencil:
First, we break the term in simple manner.
8.8 = 8 + 0.3 + 0.5
And 5.5 = 5 + 0.5
And now adding the terms one by one,
0.5 + 0.5 = 1.0
0.3 = 0.3
8 + 5 = 13
Addition,
13 + 1 + 0.3 = 14.3
Therefore, the value is 14.3
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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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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 another word for undecidable?
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
Clarify algorithm.A calculation or problem-solving procedure is known as an computation or algorithm. Algorithms serve as a thorough set of instructions that direct hardware- or software-based routines through a sequence of planned actions step by step. In all areas of IT, algorithms are commonly employed.
Here,
If it is impossible to develop an algorithm that reliably returns a true or false result for each input value, the problem is said to be undecidable.
The category of inherently unknowable questions, a subtype of insoluble problems, only includes questions that ought to receive a yes-or-no response .
Thus ,incomputable. is another word for undecidable.
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
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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!
A hot air balloon is cruising at an altitude of 120 m above ground when it begins its descent the balloon descends at a rate of 4.5 m per minute explain how you would set up the equation to model when the balloon will reach an altitude of 75 m above ground then solve the equation and check your solution
The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.
The balloon will reach an altitude of 75 meters above the ground.
Now, 120-75 =45 meters
Let t be the time to descends 45 meters
So, 120 - 4.5t= 75
= -4.5 t = 75-120
= -4.5t = -45
= t = -45/(-4.5)
= t = 10 minutes
Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
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The light blue askes for the word form, the green says g= -1, the yellow askes for possible solutions, the purple wants how you shade the number line.
Please help!!!!!!!!!!!!!!!!!!!!!
Answer: get yio colors straightv
Step-by-step explanation:
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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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.
What is a shape called with 1000000000 sides?
Answer:
Regular megagon
Step-by-step explanation:
Regular megagon is a shape called with 1000000000 sides.
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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3. A sample of 10 networking sites for a specific month has a mean number of visits of 26.1 and a sample standard deviation of 4.2. Find a 99% confidence interval of the population mean.
The confidence interval is (22.68,29.52).
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
n = 10
x = 26.1
s = 4.2
Two-sided confidence interval :
CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]
= [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]
= (26.1−3.42,26.1+3.42)
= (22.68,29.52)
Hence, the confidence interval is (22.68,29.52).
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How do you simplify 3 ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 350: 250: 125
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
350/5: 225/5: 125/5
70: 45: 25
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 14: 9: 5.
70/5: 45/5: 25/5
14: 9: 5
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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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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
Sidney would like to buy a winter coat with an original price of $44.60. Which coupon should she use?
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
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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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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In a market urvey, 100 trader ell fruit. 40 ell apple, 46 orange, 50 mangoe, 14 apple and orange, 15 apple and mangoe and 10 ell all three fruit each of the 100 trader ell at leat one of the three fruit. (A) how many trader ell only one fruit. (B) how many trader ell only two fruit
A)There are 88 trader sell only one fruit.
B) There are 46 trader sell only two fruit.
Since there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
B) Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
O∩M = 100 -117
O∩M = 17 traders
Now,
n(A∩O) -n(O∩M) - n(A∩M)
= 14 + 17 + 15
= 46
Therefore, the number of traders that sells two fruits are 46.
A) oranges n(O)
= 46-(4+10+ x)
= 32
Again,
mangoes n(M).
= 50-(5+10+x)
= 35
Now,
apple n(A)
= 40-(4+10+5)
= 21
Now, adding all of them we get:
n(o) + n(M) + n(A) = 32 + 35 + 21
= 88
Therefore, 88 trader sells only two fruit
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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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Please help im not smart
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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What are the factors of a term 5x?
The factors of 5x as calculated from the data given is found to be as 5, x and 1 .
On factorizing 5x we can write it as ,
5 x 1 x x .
Therefore the factors are 5 , 1 and x.
There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.
The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.
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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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two families with four people in each family go to a movie theater. in how many ways can they be seated
According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.
What seating configuration?The direction that each person is facing is crucial when arranging the people.
In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.
Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.
There are two different ways to arrange the groups so they can sit together.
2! = 2 * 1
2! = 2ways
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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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Find the area of the polygon with the given vertices.
W(-1, 1)
-4
Z(-3,-2)
4
Ay
2
-4
2
X(4,1)
4 x
Y(2,-2)
The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.
What is polygon?A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.
The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,
where XW is the vector from W to X and ZY is the vector from Z to Y.
In this example,
XW = (3, -2) and ZY = (-2, -4).
Therefore, the area of triangle
WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.
The area of triangle XYA is calculated similarly,
where XY = (2, 3) and YA = (-2, -4).
Therefore, the area of triangle
XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.
The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.
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How is the number of Electoral College seats per state determined? A. by the number of party delegates assigned to the state B. by the total number of
Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.
What is the makeup of the Electoral College? There are 538 electors in all. The number of electors allotted to each state is equal to the sum of its two Senate seats plus the number of representatives in the House of Representatives.Three electoral votes are granted to the District of Columbia under the 23rd Amendment. According to the amount of each State's population as established by the Census, each State is given a certain number of electors equal to the sum of its U.S. Senators (which are always two) and U.S. Representatives.There are two steps involved in selecting each State's electors. The political parties in each State first select elector candidate slates before the general election. Second, during the general election, each State's voters choose its electors by voting ballots.To learn more about Electoral College refer to :
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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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