Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
As we know that,
(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.
(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.
Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.
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How do you know if it is a linear exponential or quadratic graph?
Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.
To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.
Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.
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if pam makes 250 dollars from making 15 pots, what is her piece rate?
Pam's piece rate is $16.67 for every pot she produces.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Pam's piece rate is the amount of money she earns for each pot she makes. In this case, she earned $250 for making 15 pots, so her piece rate is:
$250 ÷ 15 pots = $16.67 per pot
Therefore, Pam earns $16.67 for each pot she makes. This is a way of calculating her pay based on the number of units she produces, rather than by the hour.
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What is the volume of the rectangular prism?
^answer:^
~10 cubic feet~
^step by step explanation:^
first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.
What are the three types of dilation?
Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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Solve for x in the equation 2^(2x-1)x[1/8]^(1-x)=4^(3x+1)
Answer: x=-6
Step-by-step explanation:
[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]
Answer:
Step-by-step explanation:
We have:
2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)
2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)
2^(2x-1) x 2^-3+3x = 2^6x+2
2^5x-4 = 2^6x+2
on comparing both sides we get :
5x-4 = 6x +2
x = -6
Please help me with my HW
Answer:
Step-by-step explanation:
(9a⁴b⁷) x (6a³b⁸)
(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)
54 x a⁷ x b¹⁵ = 54a⁷b¹⁵
Answer:
(9a⁴b⁷).(6a³b⁸)
=54a⁷b¹⁵
A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23-foot ramp, to the nearest tenth of a degree, if its fi nal height is 6 feet.
The angle of elevation of the ramp is 28.6 degrees.
If the ramp's final height is 6 feet, calculate the ramp's angle of elevation to the nearest tenth of a degree.The angle of elevation of the ramp is the angle formed by the ramp to the horizontal ground.It is also known as the angle of inclination. To find the angle, the following equation is used:Tan = (Change in Height) / (Length of Ramp)
Therefore, using the given information, the angle of elevation of the 23-foot ramp is:
Tan = (6 feet) / (23 feet)
Tan = 0.26
= 14.5° (to the nearest tenth of a degree)
Therefore, the angle of elevation of the 23-foot ramp is 14.5°.
The angle of elevation of the 23-foot ramp is 15.7 degrees to the nearest tenth of a degree.This can be found using the equation for finding the angle of elevation of an incline, which is tan θ = rise/run.In this case, the rise is 6 feet (the final height of the ramp) and the run is 23 feet (the length of the ramp).Therefore, the equation becomes tan θ = 6/23, and the angle of elevation can be found by solving for θ.Using a calculator, this value turns out to be 15.7 degrees.To learn more about the angle of inclination refer to:
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Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])
Therefore , the solution of the given problem of triangle comes out to be A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).
Explain the triangle.The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.
Here,
The image A'B'C' is formed by our transformation rule, (+3,y-2)
So:
1. Describe the updated coordinates for points A', B', and C'?
In order to locate these new positions, we have:
A' (-23, 2-2) => A'(1, 0) (1, 0)
B' => (-23, 4-2) => B'(1, 2) (1, 2)
C'=> (0+3,0-2) => C'(3,-2) (3,-2)
2. Explain the qualities that would emerge if the respective vertices were linked together by lines.
We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.
The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.
Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.
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find the lcm of a^3 -125 and a^4 +25a^2 +625
pleaseee helpppp
Answer:
625
Step-by-step explanation:
1.25.625
125 = 5³
625 = 5⁴
prime factor 5 , number 125 is 3 number 625 is 4 LCM is 4
LCM = 5⁴
so the LCM is 625
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology. All the students do at least one of the three subjects. 3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only. Find the number of numbers of students that do two subjects only exactly one subject at least two of the subjects Represent the information on a complete Venn diagram.
Number of students that do two subjects are 12.
Number of students that do only exactly one subject are;
For Art;
⇒ 14
For Chemistry;
⇒ 11
For Bio;
⇒ 8
Number of students that do at least two of the subjects are 15.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.
All the students do at least one of the three subjects.
3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.
Here,
Total students = 48
So, Number of students that do two subjects are = 4 + 3 + 5
= 12
And, Number of students that do only exactly one subject are;
For Art;
⇒ 24 - (3 + 4 + 3)
⇒ 14
For Chemistry;
⇒ 22 - (3 + 5 + 3)
⇒ 11
For Bio;
⇒ 20 - (3 + 4 + 5)
⇒ 8
Number of students that do at least two of the subjects are;
⇒ 3 + 3 + 4 + 5
⇒ 15
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SAFF (Students against Fatty Food) is a group of students who are protesting the food in high school cafeterias. At a recent rally, the students covered the first 40 yards by 40 yards of the football field. There were 24 students in each 8 feet by 8 feet square. How many students were present at the rally?
By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Students traverse a total area of 40 yards by 40 yards, or 1600 yards.
24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.
The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.
Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.
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Which expression is the factored form of X^3 2x^2 5x 6?
The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.
Let f(x) = x³ - 2x² - 5x + 6
Substitute x = 1
f(1) = (1)³ - 2(1)² - 5(1) + 6
⇒ f(1) = 1 - 2 - 5 + 6
⇒ f(1) = -1 + 1
⇒ f(1) = 0
As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)
Now use long division method, we get (x² - x - 6) as another factor.
⇒ f(x) = (x - 1)(x² - x - 6)
⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)
⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))
⇒ f(x) = (x - 1)(x - 3)(x + 2)
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The data below represents the number of desks on each floor of Texter Corporate.
\qquad54,60,65,66,67,69,70,72,73,75,7654,60,65,66,67,69,70,72,73,75,7654, comma, 60, comma, 65, comma, 66, comma, 67, comma, 69, comma, 70, comma, 72, comma, 73, comma, 75, comma, 76
Which box plot correctly summarizes the data?
A box plot that correctly summarizes the set of data is: box plot C.
What is a box-and-whisker plot?In Mathematics, a box plot sometimes also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 54First quartile = 65.Median = 69.Third quartile = 73.Maximum = 76.In conclusion, we can logically deduce that the median of the given data set is 69 while the first quartile is 65 and the third quartile is equal to 73.
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What is the best sequence of names to
identify the elements of this set of
numbers?
(0.67,3-√4,√8,0.14)
1) real, rational, irrational, irrational,
irrational
2) rational, real, integer, irrational,
irrational
3) rational, rational, real, real,
irrational
4) rational, rational, integer, irrational,
rational
On solving the provided question, we can say that - sequence (0.67,3-√4,√8,0.14) are the rational, real, integer, irrational, irrational.
what is a sequence?A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.
here,
the given sequence is (0.67,3-√4,√8,0.14)
as we can see that in the sequence we have a rational number, integer, real number and a irrational so,
the answer is rational, real, integer, irrational, irrational.
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Using long division convert 1/4 to a decimal
Using long division convert 1/4 to a decimal
To convert a fraction into a decimal, we'll just divide the numerator by the denominator:
4√1
we'll divide 1 by 4.
1 divided by 4 equals 0
0
4√1
To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top
0.
4√1.0
Now we can divide 10 by 4, 10 divided by 4 equals 2.
0.2
4√1.0
Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.
0.2
4√1.0
-8
______
2
Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.
0.2
4√1.00
-8
________
20
20 divided by 4 equals 5.
0.25
4√1.00
-8
______
20
Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.
0.25
4√1.00
-8
______
20
20
________
0
So 1/4 is equal to 0.25.
need some help with the screenshot
The graph of the function f(x) = 2x² + 2x - 2 is plotted and attached
How to plot the graph of the equationThe graphs of the function is plotted by making a table of value for a number of the x values and the corresponding y values as done below
Using the function the table is created as f(x) = 2x² + 2x - 2
For x = -4, y = 2 * (-4)² + 2 * (-4) - 2 = 22
For x = -2, y = 2 * (--2)² + 2 * (-2) - 2 = 4
For x = 0, y = 2 * (0)² + 2 * (0) - 2 = -2
For x = 2, y = 2 * (2)² + 2 * (2) - 2 = 10
For x = 4, y = 2 * (4)² + 2 * (4) - 2 = 38
The table of values
x y
-4 22
-2 4
0 -2
2 10
4 38
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What are the 3 types of terms in quadratic equation?
The 3 types of terms in quadratic equation:
1) quadratic term,
2) linear term,
3) constant term.
We know that the second degree algebraic equation in x is a quadratic equation.
The standard form of quadrtic equation is ax^2 + bx + c = 0, where a, b, c are integers.
As thise is a quadratic equation, the value of a can not be zero. a ≠ 0
The term ax^2 is called the quadratic term.
From this term, the name given to the equation(quadrtic equation)
The term bx is called the linear term.
And the term c is called the constant term.
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Three line segments have measures of 18 units, 12 units, and 10 units. Will the segments form a triangle?
Does it form a triangle?
No, the segments will not form a triangle based on the line segments provided.
For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.
In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.
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explaination with steps
Answer:
50
Step-by-step explanation:
angleQPR=50
becauseQR=RP
so angleRQP=RPQ
x=50
Answer:
50
Step-by-step explanation:
angle QPR = 50 because QR= rp
Time vs. Position of Battery Operated Car
5
4
Position (m)
2
0
5
10
Time (s)
15
20
What type of relationship is shown in the graph?
a non-linear, negative relationship
a linear, negative relationship
a linear, positive relationship
O a non-linear, positive relationship
A linear, negative relationship is the type of relationship which is shown in graph of Time vs. Position of Battery Operated Car .
what is linear equation ?A linear equation is an algebraic expression such as y=mx+b. The slope is m, and the y-intercept is B. A "linear equation in two variables" is the term used to describe the previous sentence, which has variables named y and x. Two different variables can be found in bivariate linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
The area's 46-16 opposed to 14 is different from the area's 18 and T in a different way. The place is there. It isn't linearly getting farther apart. The lee is actually growing as a result.
Option B, the slanting upwards, is what we're going to go with. Since it will be linear, it isn't option C. It is untrue that the speaking has not been constant over the distance. Because it is a D-option, this increase-decrease is untrue. Option B is the best choice. Absolutely.
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Use the distributive property to simplify the expression
6(8x+5)
Step-by-step explanation:
6(8x+5)
Use the distributive property to multiply 6 by 8x+5.
48x+30
Hope it Helps!
gary has two ladders for a project one reaches 16 3/7 while the other reaches 12 /5/7 how much higher can the longer ladder reach
The longer ladder can reach 3 8/7 feet higher than the shorter one.
The Proportionality Theory.The longer ladder can reach 4 2/7 feet higher than the shorter ladder. To calculate this, we need to subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet).We can represent this calculation with a fraction equation, as follows:[tex]\frac{16 \frac{3}{7}}{12 \frac{5}{7}} - 12 \frac{5}{7} = \frac{4 \frac{2}{7}}{1}[/tex]To solve this equation, we first need to convert the fractions into equivalent fractions with a common denominator. In this case, the denominator is 7. This means that the first fraction becomes 16 3/7, the second fraction becomes 12 5/7, and the third fraction becomes 4 2/7.Once we have the fractions in the same denominator, we can now subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet). This gives us a result of 4 2/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To put this into perspective, if we were to use the ladders to reach a height of 16 3/7 feet, the shorter ladder would only reach 12 5/7 feet, while the longer ladder would reach 16 3/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To learn more about The Proportionality Theory refer to:
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Find the missing length and area of each figure
LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd
Area = 2 × (1/2) × 6 × 8 = 48 yd²
Subject: Angles In a Circle
I need help with finding out how to get 5, d,e and f and getting the points
Step-by-step explanation:
please see the attachment
(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.To learn more about distribution refer to:
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What is the constant term of 2x 3?
The constant term in the expression 2x + 3 is 3.
The term expression in math is called as the algebraic expression consists of unknown variables, numbers and arithmetic operators.
Here we have the expression 2x + 3.
Now, we have to find the constant term in the expression.
As per the definition of expression, we know that the expression has two part one is variable part and the remaining second part is the constant parts.
As the name suggest, the variable part contains the unknown value like x, y etc. that changes value of the expression depending upon the given value.
Another term is constant, where its value can't be changed.
While we looking into the given expression here we have identified that
=> 2x is the variable term because the value of the term is changed based on the value of x.
Therefore, the constant term is 3.
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Determine the vertical distance and the horizontal distance of point P and point Q. (a) P=4m Q=6m.
if you dog like something
In AABC, AB = AC and AP 1 BC. If AB= (2x + 3) cm, AC = (3y-1) cm, BP = (y + 1) cm and PC = (x + 2) cm find the values of x and y.
Answer:
x = 1y = 2Step-by-step explanation:
Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.
Isosceles triangleCorresponding parts of ∆ABP and ∆ACP are congruent, so we have ...
2x +3 = 3y -1
x +2 = y +1
SolutionSubtracting twice the second equation from the first gives ...
(2x +3) -2(x +2) = (3y -1) -2(y +1)
-1 = y -3 . . . . simplify
2 = y . . . . . . add 3
Substituting into the second equation, we have ...
x +2 = 2 +1
x = 1 . . . . . . . .subtract 2
The values of x and y are 1 and 2, respectively.
What is equivalence and example?
Equivalence Relation is a type of Relation that satisfies the property of Reflexive , Symmetric and Transitive , and an example of such relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] .
What is an Equivalence Relation ?
A relation R on a set A is can be called as an equivalence relation if and only if the relation is reflexive, symmetric and transitive.
It is a relationship on the set which is represented by symbol “∼”.
(i) Reflexive: A relation is termed as reflexive, if [tex](a, a) \in R[/tex], for every [tex]a \in A[/tex].
(ii) Symmetric: A relation is termed as symmetric, if [tex](a, b) \in R[/tex] , then [tex](b, a) \in R[/tex] .
(iii) Transitive: A relation is termed as transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex] .
An Example of Equivalence Relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] because ;
(i) [tex][ (1, 1),(2, 2), (3, 3), (4, 4) ] \in R[/tex] , So , R is Reflexive .
(ii) [tex](2,4) \in R[/tex] and [tex](4,2)\in R[/tex] , Thus , relation given by R is Symmetric .
(iii) [tex](3,1) \in R[/tex] and [tex](1,3) \in R[/tex] ⇒ [tex](3,3) \in R[/tex] , So R is Transitive .
Therefore , the Relation given by R is Equivalence Relation .
The given question is incomplete , the complete question is
What is Equivalence Relation and its Example ?
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(100 points)A catering company offers meal pairings that include an appetizer of either salad or soup and an entree of either chicken or fish. At one event, they serve a total of 78 meals. Of the 46 meals that include salads, 21 also include fish. There are 35 meals with fish as the entree. Determine which two-way frequency table represents this situation. Jk
Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. ?. 35
To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.
Frequency of chicken
= 78 - 46 - 35
= 27.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. 27. 35
The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.
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