Answers
Answer: x = 25
Step-by-step explanation:
2x-10 = x+15
x = 15+10
x=25
The required value of x in the given triangle is 25, evaluated by following the definition of angle bisectors.
Given that, MNO is a triangle, where OP is the angle bisector, in the given scenario we have to determine the value of the x.
Following the definition of an angle bisector, the angle bisector for any angle bisects the angle into two equal halves, So,
Angle PNO = Angle PMO
2x-10=x+15
Simplify the above expression to evaluate x.
2x-10=x+15
2x-x=15+10
x=25
Thus, the required value of x in the given triangle is 25, by following the definition of angle bisectors.
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Related Questions
1.3) (7²-√81) + √125 a) 5 b) 8 c) 10 d) 4
Answers
The value of (7²-√81) + √125) is 45
What are square root and square?Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.Similarly, the square of 4 is 16 and the square root of 16 is 4.
A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system. Therefore 4, 16, 25 are examples of perfect squares
7²-√81) + √125 is calculated as
49- 9+ 5 = 45
Therefore the value of 7²-√81) + √125 = 45
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simple and easy please
Answers
The exponential function that models the data is f(x) = 8(1/2)ˣ
How to write an exponential function that models the data?The general form of exponential function is given by:
f(x) = abˣ
Where a is the initial value of output variable, b is the growth or decay factor and x is the value of input variable
From the table:
when x = 0, f(x) = 8:
f(x) = abˣ
8 = ab⁰ (remember: b⁰ = 1)
8 = a
a = 8
when x = 1, f(x) = 4:
f(x) = abˣ
4 = 8 × b¹
4 = 8b
b = 4/8
b = 1/2
Thus, substituting a and b into f(x) = abˣ will give the exponential function that models the data:
f(x) = 8(1/2)ˣ
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What is the additive inverse of [(- 3 )+ (- 6 )]?
Answers
The additive inverse of (-3) + (-6) is (3 + 6) which is 9
The additive inverse of a number is its opposite, or the number that when added to the original number results in zero. In other words, it is the number that can "cancel out" the original number and make it disappear.
For example, the additive inverse of 3 is -3, because 3 + (-3) = 0. Similarly, the additive inverse of -6 is 6, because -6 + 6 = 0.
Now, for the given expression, the additive inverse of (-3) + (-6) is the number that can "cancel out" the expression and make it disappear. By adding the additive inverse of each term of the given expression we would get 0. Therefore the additive inverse of (-3) + (-6) is (3 + 6) which is 9.
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Help find the perimeter
Answers
Answer:
Step-by-step explanation:
As 9: 16.2
Then 6: EF Lets take EF as side x
9:16.2 as
6:x CROSS MULTIPLY ( 9×x and 16.2×6)
Cross multiplying gives you: 9x and 97.2
Then divide both answers by 9 ( 97.2÷9 and 9x÷9)
This gives you x=10.8 which is side EF
To find side AB ADD 9 and 6 to get 15 and subtract this from 36 and you get 21.
Using the same method to find EF find DE and you will get 37.8
Therefore, perimeter becomes:
16.2 + 37.8 + 10.8 = 64.8
HOPE THIS HELPS
Answer:
P△DEF=64,8
Step-by-step explanation:
P△ABC=36, AC=9, BC=6 → AB=21
AB/DE=BC/EF=AC/DF
AC/DF=9/16,2; AB/DE=21/DE ⇒ DE=(21*16,2)/9=37,8
AC/DF=9/16,2; BC/EF=6/EF ⇒ EF=(6*16,2)/9=10,8
P△DEF=16,2+37,8+10,8=64,8
A high school student has deposited $850 in a savings account that earns interest at a rate of 2.9% compounded monthly. What will the account balance be in seven years? Round the answer to the nearest hundredths place.
$864.48
$1,041.06
$6,317.60
$9,382.32
Answers
The account balance in seven years will be $9,382.32.
What is balance?Balance in math is the idea of equal parts on either side of a given equation. The concept of balance is used in algebraic equations and inequalities where the two sides of the equation must be equal in order for the equation to be true. Balance is an important concept to learn in math, as it is used to solve many problems. Balance can also be used in geometry to understand symmetry and shapes, as well as in calculus to understand derivatives and integrals. Balance is a fundamental concept in math that can be used in a variety of ways.
This can be calculated by multiplying the initial deposit of $850 by (1 + 0.029/12)^84, which is equal to 9,382.3198.
After rounding to the nearest hundredths place, the answer is $9,382.32.
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Answer:
$1,041.06
Step-by-step explanation:
Got it right.
How do you calculate pixel size with FOV and matrix size?
Answers
By dividing the field of view by the matrix size, one can get the pixel size.
A single dot on the user's screen is measured in pixels. The image will be displayed on any screen by the combination of numerous spots. Pixel dimensions are the length and width of a picture expressed in pixels. to determine the field of view (FOV), matrix size, and pixel size which is generally in millimetres per pixel).
The number of pixels in the image is known as the matrix size, and FOV is commonly expressed in degrees. Using this formula, you may get the size of each pixel in millimetres by converting the FOV from degrees to millimetres and dividing it by the number of pixels.
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The measures of two angles of a triangle are 25° and 87°. Is the triangle acute, right, or obtuse? Explain.
A.
Acute; the measure of the third angle is 68°. So all three angles are acute.
B.
Acute; the measure of the third angle is 78°. So all three angles are acute.
C.
Obtuse; 25° + 87° = 112° and 112° is an obtuse angle.
D.
Right; 25° + 87° = 112° and 202°
−
-
112° = 90°.
Answers
Obtuse; 25° + 87° = 112° and 112° is an obtuse angle is the correct answer.
What is triangle?Triangle is a three-sided polygon with three angles. All the sides of a triangle are connected, forming a closed shape. Triangles come in many different shapes and sizes. The most common type of triangle is an equilateral triangle, which has three equal sides and three equal angles. Other types of triangles include isosceles, scalene, obtuse, and right triangles. Triangles are used in many different fields, including architecture, engineering, and mathematics.
The triangle is obtuse because 25° + 87° = 112° and 112° is an obtuse angle. An obtuse triangle is one in which one angle has a measure greater than 90°.
The remaining two angles are acute, meaning they measure less than 90°.
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Find the volume of a pyramid with a square base, where the area of the base is 4. 6\text{ cm}^24. 6 cm 2 and the height of the pyramid is 2. 3\text{ cm}2. 3 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answers
The volume of the pyramid is 3.5 cubic centimeters.
The volume of a pyramid can be calculated using the formula:
V = (1/3) * Base area * Height
Where Base area is the area of the base of the pyramid, and Height is the distance from the base to the apex of the pyramid.
Given that the area of the base of the pyramid is 4.6 cm^2 and the height of the pyramid is 2.3 cm, we can substitute these values into the formula and solve for the volume:
V = (1/3) * 4.6 cm^2 * 2.3 cm = 3.53 cm^3
So the volume of the pyramid is 3.53 cubic centimeters. Rounded to the nearest tenth of a cubic centimeter, the volume is 3.5 cm^3.
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Dakota and Cody sold a total of 16 items during their winter fundraising event. Cody sold four more than twice the number of items Dakota sold.
Formulate a system of equations that can be used to determine number of items Dakota sold, x, and Cody sold, y, then solve the system using substitution. Check your work by graphing.
Answers
The system of linear equation is x + y = 16 and y = 2x + 4. Dakota sold 4 items and Cody sold 12 items
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Let x represent the number of items Dakota sold and y represent the number of items Cody sold.
Dakota and Cody sold a total of 16 items, hence:
x + y = 16
y = 16 - x (1)
Also, Cody sold four more than twice the number of items Dakota sold, hence:
y = 2x + 4 (2)
substituting y = 16 - x:
16 - x = 2x + 4
3x = 12
x = 4
y = 16 - x = 16 - 4 = 12
Dakota sold 4 items and Cody sold 12 items
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Keisha had 2/7 of a spool of yarn. She used 4/5 of her yarn for a project. What fraction of the spool was used for the project? Write your answer in simplest form.
Answers
Answer:
8/35
Step-by-step explanation:
2/7 x 4/5 = 8/35 (that is the simplest fraction)
To make it easier to visualize, let's say someone gave you 1/2 a spool, then you use 1/2 of that 1/2. How much did you use? 1/2 x 1/2 = 1/4
1. Antonio sets his remote-controlled car at the start of the racetrack and starts its run on the track. His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line. How long is the racetrack? (a) Let x = the length of the racetrack. Write an equation that fits the story (b) Solve the equation from Part a. (How long is the racetrack?) Show your work. (c) How much farther did Antonio’s car have to go to the finish line? Show your work. Answer:
Answers
a) The equation that fits the story is given as follows:
2x/5 = 28.
b) The length of the racetrack is given as follows: 70 meters.
c) Antonio had to go 42 meters farther to reach the finish line.
How to obtain the length of the race track?The length of the race track is obtained applying the proportions in the context of this problem.
His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line, hence the distance driven during this entire period is of:
38 - 10 - 28 m.
28 m is 2/5 of the track length, which is going to be called x, hence the equation is given as follows:
2x/5 = 28.
The track length is then obtained as follows:
2x = 5 x 28
x = 5 x 14
x = 70 meters.
Thus the remaining distance is of:
70 - 28 = 42 meters.
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Find Dy/Dx By Implicit Differentiation. 5x^2-xy-4y^2=0
Answers
The Implicit Differentiation of 5x^2-xy-4y^2=0 is Dy/Dx= (5x-y)/(-4y)
Using implicit differentiation, Dy/Dx can be found by taking the derivative of both sides with respect to x.
On the left side, the derivative with respect to x of 5x2 is 10x and the derivative with respect to x of -xy is -y.
On the right side, the derivative of 4y2 with respect to x is 0.
Therefore, the equation becomes 10x - y = 0.
Solving for y gives y = 10x.
Substituting this into the original equation, we get 5x2 - 10x2 - 4(10x)2 = 0, which simplifies to -5x2 - 40x2 = 0.
Finally, we can solve for Dy/Dx:
Dy/Dx= (5x-10x)/(-4(10x))
Dy/Dx= (5x-y)/(-4y)
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How do you know if the equation is quadratic or not with example?
Answers
You get a quadratic equation when the square of the expression that comes after b plus b times that same expression not squared plus c equals 0.
Any equation in algebra that can be written in standard form as
ax^2+bx+c=0,
where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.
The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.
Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.
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A computer costs $800. It loses 1/4 of its value every year after it is purchased.
Use your equation to find v when t is 5. Show how you substituted
In context of the problem,what does the above value of v mean when t was 5?
Answers
The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.
what is equation ?A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter.
given
This equation can be used to represent the value of the computer: price of the computer one year ago x (1 - rate of decline)
The computer's current market value 0 = $800
Computer value at time 1 is $800 multiplied by 3/14 by 1 to get $600.
The computer's current market value 2 = $600 x 3/4 = $450
Computer value at time 3: $450 multiplied by 3/4, or $337.50
The computer is worth $800 when it is created, $600 when it is used for the first time, and $450 when it is used for the second time.
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In \triangle GHI,△GHI, \overline{IG}\cong \overline{HI} IG ≅ HI and \text{m}\angle H = 51^{\circ}.m∠H=51 ∘ . Find \text{m}\angle G.m∠G.
Answers
The measure of the angle ∠G of the isosceles triangle will be 51°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The two triangular legs and their opposing angles are congruent in an isosceles triangle.
In triangles △GHI, IG ≅ HI, and the measure of the angle ∠H = 51°. Then the measure of the angle ∠G will be given as,
The two sides of the triangle △GHI will be congruent. Then the triangle is known as an isosceles triangle.
If IG ≅ HI, then the measure of the angle ∠G ≅ ∠H.
The measure of the angle ∠G of the isosceles triangle will be 51°.
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5. A t-shirt is on sale for 20% off the original price (x). Circle the expressions that would help find the sale price of the t-shirt?
x-.20x
x +.20x
(1-.20)x
.80x
80x
.20x
Answers
Therefore , the solution of the given problem of expression comes out to be 0.8x is the required expression.
Expression : what is it?Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.
Here,
Given :
Let x be the original price
To find the expression after 20 % discount :
=> x * 20/100 = 0.2x
So,
New price:
=> x - 0.2x
or
=> 0.8x
Therefore , the solution of the given problem of expression comes out to be 0.8x is the required expression.
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An athlete ran 77 km in 7 days. What is the rate the athlete ran per day?
Answers
Answer:11
Step-by-step explanation:
77 divided by 7 is 11.
Help me please i will make u the brainlyest please help me. I even gave you 50 points.
Answers
The solution to the simplification of each of the fractions are;
1) ³/₄ * ¹¹/₅
2) 1 ³/₅ miles
3) 1¹/₈ yards
How to solve fraction problems?
1) We are told that;
Caleb has 2¹/₅ yards of rope
Quantity of rope used by Caleb = ³/₄
Thus;
³/₄ of 2¹/₅ simply means that we will multiply both.
2¹/₅ can also be expressed as 11/5. Thus, we now have;
³/₄ * ¹¹/₅
2) Number of miles mary hiked = 6²/₅ miles = 32/5 miles
He stopped at 1/4 of the way.
Thus;
Number of miles before stopping = 1/4 * 32/5 = 8/5
= 1 ³/₅ miles
3) The area is gotten by;
A = length * width
A = 1¹/₂ * ³/₄
= 3/2 * 3/4
= 9/8
= 1¹/₈ yards
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what is the equation of a line with a y-intercerpt of a -3 and a slope of 5
Answers
Answer:
Step-by-step explanation:
y = (a-3)x+5
Answer:
y=3x+5
Step-by-step explanation:
i need this like right now.
Answers
Answer:
y = 13
Step-by-step explanation:
given (7, 33 ) is a solution of the top equation, then
x = 7, y = 33 satisfies the equation , that is
33 = 7a + 5 ( subtract 5 from both sides )
28 = 7a ( divide both sides by 4 )
4 = a
then
y = 4x + 5 ← top equation
substitute y = 4x + 5 into the other equation
9x + 2(4x + 5) = 44
9x + 8x + 10 = 44
17x + 10 = 44 ( subtract 10 from both sides )
17x = 34 ( divide both sides by 17 )
x = 2
substitute x = 2 into the top equation for value of y
y = 4x + 5 = 4(2) + 5 = 8 + 5 = 13
Greatest common factor of 18, 30, 54
Answers
Answer: 6
Step-by-step explanation:
Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
30°
0
000
60°
BC=5√2, AC = 10
AB=14, AC = 28
AB= 3, BC = 3√3
AB=
4√3, BC = 4
BC=
19√3, AC = 38√3
BC=16, AC = 32
Answers
1) Ed invests $1,000 into a money market account that earns 8% annual interest compounded quarterly. How much money will
he have earned after 8 years?
Answers
The money market account earns 8/4 = 2% interest per quarter.
In one year, there are 4 quarters.
so, the formula to calculate the balance after 8 years is:
A = P (1 + r/n)^(nt)
where A is the final balance, P is the principal (initial investment), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested for.
Substituting in the given values,
A = 1000 (1 + .02)^(4*8)
A = 1000 (1.02)^32
A = 1000 (1.8587)
A = 1858.7
So after 8 years, Ed will have earned $1858.7.
help me please . i really need help.
Answers
Answer: Congruent figures can slide, flip, or turn.
(Translate, reflect, or rotate)
Corresponding Angles are congruent. (Not always)
Corresponding Sides have a scale factor.
Corresponding Sides are Congruent. (Only if they have the same side and shape)
Corresponding Angles have a scale factor. (I Dont Know about this one)
All transformations (translation, reflection,
rotation, and dilation) result in congruent figures. (It would be similar to the pre-image)
i hope this helps sorry I can't do much but i think it might just be the 3 without the bolded words behind it
solve the systems. 3r=1-s
7s=4-6r
help quick.
Answers
Answer: r= 1/5 and s = 2/5
Step-by-step explanation:
trust me
What is the expression written as a single power?
(−4)8 · (−4) −5. (-4)⁰
O (-4)⁰
O-4
(-4)³
O-43
Answers
The expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the expression as -
(−4)⁸(−4)⁻⁵(-4)⁰
The given expression is -
(−4)⁸(−4)⁻⁵(-4)⁰
(- 4)⁸ ⁻ ⁵ ⁺ ⁰
(- 4)³
Therefore, the expression (−4)⁸(−4)⁻⁵(-4)⁰ written as a single power is given by (- 4)³.
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The price of a TV was $900 on Tuesday. On Wednesday, the manager reduced the price by 5%. What was the price in dollars of the TV after the reduction?
Answers
900 x .05 = 45
900 - 45 = 855
Miriam took a survey, asking each family in her neighborhood how many pets they have. She made a graph showing the results: [asy] size(5.5cm); draw((0,30)--(0,0)--(41,0)); for(int i=1; i<7; i+=1) {draw((0.6,5*i)--(-0.6,5*i)); draw((0.6,5*i)--(41,5*i),black+0.5+dashed); }; path a=(3,0)--(3,30)--(9,30)--(9,0)--cycle; path b=(9,0)--(9,15)--(15,15)--(15,0)--cycle; path c=(15,0)--(15,15)--(21,15)--(21,0)--cycle; path d=(21,0)--(21,30)--(27,30)--(27,0)--cycle; path e=(27,0)--(27,5)--(33,5)--(33,0)--cycle; path f=(33,0)--(33,5)--(39,5)--(39,0)--cycle; fill(a,gray); fill(b,gray); fill(c,gray); fill(d,gray); fill(e,gray); fill(f,gray); draw(a); draw(b); draw(c); draw(d); draw(e); draw(f); label(rotate(-45)*scale(0.8)*"0 pets",(5,-1),SE); label(rotate(-45)*scale(0.8)*"1 pet",(11,-1),SE); label(rotate(-45)*scale(0.8)*"2 pets",(17,-1),SE); label(rotate(-45)*scale(0.8)*"3 pets",(23,-1),SE); label(rotate(-45)*scale(0.8)*"4 pets",(29,-1),SE); label(rotate(-45)*scale(0.8)*"5 pets",(35,-1),SE); label(scale(0.8)*"1",(-0.6,5),W); label(scale(0.8)*"2",(-0.6,10),W); label(scale(0.8)*"3",(-0.6,15),W); label(scale(0.8)*"4",(-0.6,20),W); label(scale(0.8)*"5",(-0.6,25),W); label(scale(0.8)*"6",(-0.6,30),W); label(scale(0.8)*rotate(90)*"Number of families",(-3.5,15),W); [/asy]Determine the median number of pets per family.
Answers
The median number of pets per family is 2.
What is median number?Median number is the middle value of a set of numbers when they are arranged in numerical order. It is also known as the middle number or the 50th percentile. The median number is used to find the middle value when there is an odd number of values in the set, or to find the average of the two middle values when there is an even number of values in the set.
This can be determined by looking at the graph and counting the number of families in each bar.
The bar with 2 pets has the most families, and is the median number.
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Solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for j.
Write your answer as a decimal.
Answers
Answer:
j = 1.5
Step-by-step explanation:
You want to solve the equation 0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 for the value of j.
SimplifyIt usually works well to simplify such an equation as the first step. That means eliminating parentheses and combining like terms.
0.3j-(0.1j-3) + 0.1 = 2 (j+0.1) + 0.2 . . . . . . given
0.3j -0.1j +3 +0.1 = 2j +0.2 +0.2 . . . . . . eliminate parentheses
0.2j +3.1 = 2j +0.4 . . . . . . . . . . . . collect terms
Solution2.7 = 1.8j . . . . . . . . . . . subtract (0.2j +0.4)
1.5 = j . . . . . . . . . divide by 1.8
The solution is j = 1.5.
__
Additional comment
You are often taught to solve this kind of 3-step equation by subtracting the unwanted variable term and the unwanted constant term in two steps. (The third step is dividing by the coefficient of the variable.) Here, we show those subtractions being done both at once.
The variable term we choose to subtract is the one with the smallest coefficient. That way, the result of the subtraction (1.8j) leaves the coefficient of the variable as a positive number.
Sometimes the variable term on the right is subtracted, so you end up with a "j = " equation. In that case, the equation you would be solving as the last step is ...
-1.8j = -2.7
which requires arithmetic with negative numbers. Negative numbers tend to be associated with more mistakes, so we choose not to go there.
How many pizzas in the Venn diagram
have ham as an ingredient?
Has ham
Meat feast
Scorcher
Hawaiian
Capricciosa
Has olives
Napolitana
Veggie
Pepperoni
Margherita
Answers
According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.
what is Venn diagram ?The Venn diagram, a frequent style of diagram showing logical connections between sets, was made popular by John Venn in the 1880s. Diagrams are used to teach fundamental set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. The relationships between two or more groups of elements are shown in a Venn diagram by overlapping circles and other shapes. When arranging information graphically, it is frequently advantageous to emphasize the similarities and differences between components. The intersection of two large circles forms the central empty area of a Venn diagram.
given
From the image,
ham is an ingredient in Meat feast, Scorcher, Hawaiian, and Capricciosa.
According to the venn diagram, the circle surrounds four pizzas. Ham is present in Meat Feast, Scorcher, Hawaiian, and Capricciosa.
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