Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.
what is variables ?A variable is, to put it simply, a quantity that may be altered and is not fixed. The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types. a quantity that could take any of a range of values. a variable's sign; something that is variable; a component of a scientific experiment that is potentially subject to change.
given
Like terms are those terms that share the same factors.
Consequently, phrases that have identical variables raised to the same exponent are considered similar terms.
What are 25, -3x, and 3x called then , Since the variables or exponent raised to these variables are "unlike" or different, these terms are referred to as unlike terms.
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Give an example of how decisions by the supreme court, under chief justice John Marshall, strengthened federal power.
One of the most important decisions handed down by Chief Justice John Marshall and the Supreme Court was Marbury v. Madison, in 1803.
What is power in math?Power in math is the number of times a number is multiplied by itself. For example, when calculating the number 3 to the power of 4, the result is 81 — 3 multiplied by 3 multiplied by 3 multiplied by 3. When written as an equation, it would look like 3^4 = 81. Power can also be used to calculate exponents, which are the number of times a number is multiplied by itself and then added together.
This case established the concept of judicial review, the power of the Supreme Court to declare laws unconstitutional. This was a significant decision because it gave the Supreme Court the power to interpret the constitution and to determine the limits of federal power. This ruling gave the Supreme Court the ability to strike down acts of Congress and state laws that violated the constitution. This ruling effectively strengthened the power of the federal government by allowing it to enforce its laws over those of the states. The ruling in Marbury v. Madison was a major milestone in the development of federal government power and has been cited in numerous court decisions since then.
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Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.2 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
96.93 cubic inches
553.90 cubic inches
581.59 cubic inches
2,326.36 cubic inches
581.59 cubic inches juice can Ramon pour into 6 cups
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that Ramon is filling cups with juice.
The shape of the cup is like cylinder.
The cup has a diameter of 4.2 inches and height of 7 inches.
We need to find the amount of juice can Ramon pour into 6 cups
Volume of one glass=πr²h
=3.14×(2.1)²×7
=3.14×4.41×7
=96.9318
Now for 6 glasses we have to calculate
=6×96.932
=581.59 cubic inches
Hence, 581.59 cubic inches juice can Ramon pour into 6 cups
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Answer:581.59 cubic inches
The first person to answer was correct.
Step-by-step explanation:
I took the quiz so you don't have to!
What equation has many solutions?
An equation has an many solutions or infinite number of solutions if, when attempting to solve it, you receive a variable or number equal to itself.
An equation can have an infinite number of solutions if certain criteria are met. A system of equations has an infinite number of solutions when the lines meet and have the same y-intercept. If the y-intercept and slope of two lines are identical, they are in fact the same line. In other words, when the two lines intersect, the system should have an infinite number of solutions. It indicates that the system is consistent if it has an infinite number of solutions.
Example:
2x + 3 = x + x + 3
If the equation is simplified using a formula or method for infinite solutions, all sides will be equal. Hence, it has an infinite number of solutions.
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The roots of the equation (3x square-5x-2=0) are Alpha and ßeta. Find the values of
a) Alpha + ßeta. b) Alpha x ßeta
c) Alpha squared + ßeta squared
d) 1/Alpha + 1/ßeta
e) 1/Alpha squared + 1/ßeta squared
If [tex]$\alpha$[/tex]and [tex]$\beta$[/tex] are the roots of [tex]$3 x^2-5 x+2=0$[/tex], then the value of [tex]$\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$[/tex] is 13/6
What are mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." two phrases on either side of the sign are connected by a mathematical equation. Usually, it only has one variable and an equal sign. as in 2x - 4 Equals[tex]$\alpha, \beta$[/tex] are roots of[tex]$3 x^2-5 x+2=0$[/tex]
[tex]& \alpha+\beta=-\frac{b}{a}=\frac{5}{3} a=3, b=-5, c=2 \\[/tex]
[tex]& \alpha \beta=\frac{c}{a}=\frac{2}{3} \\[/tex]
[tex]& \frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha \beta} \\[/tex]
[tex]& =\frac{(\alpha+\beta)^2-2 \alpha \beta}{\alpha \beta} \\[/tex]
Simplifying the question
[tex]& =\frac{\left(\frac{5}{3}\right)^2-2\left(\frac{2}{3}\right)}{\frac{2}{3}} \\[/tex]
[tex]& =\frac{\frac{25}{9}-\frac{4}{3}}{\frac{2}{3}}=\frac{25-12}{9} \\[/tex]
We get,
[tex]& =\frac{13}{9} \times \frac{3}{2}=\frac{13}{6}[/tex]
The complete question is,
If [tex]$\alpha$[/tex]and [tex]$\beta$[/tex] are the roots of [tex]$3 x^2-5 x+2=0$[/tex], then find the value of [tex]$\frac{\alpha}{\beta}+\frac{\beta}{\alpha}$[/tex]
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If theta is an angle in standard position and its terminal
side passes through the point (-9,-5), find the exact value
of CSC(theta) in simplest radical form.
The exact value of CSC(theta) in simplest radical form is √106/6√7.
What is angle?Angle is a two-dimensional figure formed by two rays, or line segments, that have a common endpoint. It is usually measured in degrees or radians, and is used to describe the amount of rotation between two line segments. Angles can be acute, right, obtuse, straight, or reflex depending on the measure of the angle. Angles can also be classified as complementary, supplementary, vertical, adjacent, interior, or exterior.
CSC(theta) is the reciprocal of the Sine of theta and can be found by using the Pythagorean Theorem. The distance from the origin to the point (-9,-5) is the hypotenuse of a right triangle, which has sides of length 9 and 5.
The hypotenuse is equal to the Sine of theta, so by using the Pythagorean Theorem we can find the Sine of theta:
Sin(theta) = √(9^2 + 5^2) = √(81 + 25) = √106.
Therefore, CSC(theta) = 1/Sin(theta) = 1/√106 = √106/106 = √106/6√7.
Thus, the exact value of CSC(theta) in simplest radical form is √106/6√7.
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Outfitters creates Delta apparel and sells the
T-shirts for $15 a piece. The plain gray
T-shirt costs the company $3.50 per shirt
and the screen printing expense is $253
total. Write an equation to represent the
number of shirts Outfitters must sell to
break even.
Define the variables:
Equation:
How many shirts must be sold to break
even?
Outfitters must sell at least 0.4 shirts, which is approximately equal to 0 shirts, to break even.
What do you mean by equation?An equation is a mathematical statement that states that two expressions are equal. It usually consists of variables, coefficients, and constants, connected by operations such as addition, subtraction, multiplication, and division. Equations are used to model relationships between different quantities and to solve problems in various fields such as physics, engineering, and economics. For example, the equation y = mx + b represents a straight line in two-dimensional space, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
Let's define the variables:
x = the number of shirts Outfitters must sell to break even
c = the total cost of production (plain gray T-shirt + screen printing) = $3.50 + $2.50 = $6.00
p = the selling price of the T-shirt = $15.00
The equation to represent the number of shirts Outfitters must sell to break even can be written as follows:
x * p = x * c
Solving for x:
x = c / p
x = $6.00 / $15.00
x = 0.4
Outfitters must sell at least 0.4 shirts, which is approximately equal to 0 shirts, to break even. However, since they can't sell fractional shirts, they must sell at least 1 shirt to break even.
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(x-1)^2=1-x
______________________________________________________________[tex]sqrt(x-1)^2=1-x[/tex]
The value of x is 1.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
√(x - 1)² = 1 - x
√(x - 1)² can be written as (x - 1).
Now,
x - 1 = 1 - x
x + x = 1 + 1
2x = 2
x = 1
Thus,
x is 1.
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1. Ms. Lea ate ¾ of a bag of skittles, Ms. Ava ate 65% of her bag of skittles and Mr. Thomas ate 0.85 of his bag. Ms. Cassie ate ⅘ of her bag. Who ate the most? Explain how you know.
the answer is 0.85, Mr. Thomas ate the most.
What is percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100.
here, we have,
given that,
Ms. Lea ate ¾ of a bag of skittles,
i.e. 0,75
Ms. Ava ate 65% of her bag of skittles
i.e. 0.65
and Mr. Thomas ate 0.85 of his bag.
i.e. 0.85
Ms. Cassie ate ⅘ of her bag.
i.e. 0.8
hence, the answer is 0.85, Mr. Thomas ate the most.
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5/4 gallons of water fill 5/6. How many gallons of water fill the entire bucket?
Answer:
purple
Step-by-step explanation:
the bible says so
It takes the Sun about 2.3 x 10 years to orbit the center of the Milky Way. It takes the Moon about 7.5 x 10-2 year to orbit Earth.
About how many times does the Moon orbit Earth while the Sun completes one orbit around the center of the Milky Way? Write your
answer in scientific notation.
The Moon orbits Earth approximately 30 million times while the Sun completes one orbit around the center of the Milky Way.
What does scientific notation consist of?Using scientific notation, one can express extremely big or extremely small values. When an integer in 1 and 10 is multiplied by the a power of 10, the result is represented in scientific notation.
There is no particular hypothesis at play in this query.
The given numbers are simply used in a calculation.
Divide the length of time it takes for the Sun to complete one full orbit around the Milky Way (2.3 x 109 years) by the length of time it takes for the Moon to complete one full orbit around the Earth (7.5 x 10-2 years) to get at the answer.
This results in a response of 307,200,000, indicating that the Moon orbits Earth approximately 307,200,000 times while the Sun completes one circuit around the galactic center.
The Moon orbits Earth approximately 30 million times while the Sun completes one orbit around the center of the Milky Way.
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Margaret has three cats. Sophie weighs 4. 27 lb,tigger weighs 6. 25 lb,and ghost weighs 4. 7 lb. Which cat have the greatest weight
Margaret has three cats. Sophie weighs 4. 27 lb, tigger weighs 6. 25 lb, and ghost weighs 4. 7 lb. Tigger has the greatest weight.
Sophie weighs 4. 27 lb,
tigger weighs 6. 25 lb and
ghost weighs 4. 7 lb.
6.25 > 4.7 > 4.27
here 6.25 is the greatest number. So, Tigger has the greatest weight (6.25).
There are various units in the measuring system that can be used to measure mass or weight. The kilogram is the metric unit of mass measurement, whereas the pound is the imperial unit of mass measurement. Despite having nothing to do with the word pound and being derived from the Roman word Libra, Lb occurs to be the acronym for the pound. Many individuals use the abbreviation lbs to indicate that they are referencing a lot of pounds of weight. As a result, the terms lb and lbs refer to the same unit of mass.
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How do you integrate Xe 7x?
you can also work with a professional services provider to develop a custom integration solution for your specific needs.
Xe 7x can be integrated into a system in a few ways. The first way is to use the Xe 7x SDK (Software Development Kit) to build a custom solution that integrates the Xe 7x platform with existing systems. This SDK provides a set of tools, libraries, and samples which allow developers to create applications that leverage the Xe 7x platform.
The second way is to use the Xe 7x Connector. This is a pre-built solution that allows you to quickly integrate Xe 7x into existing systems. The Connector provides a set of APIs that allow you to access the Xe 7x platform, as well as several libraries and samples to get you started.
The third way is to use the Xe 7x Marketplace. This is an online store where you can find and purchase pre-built solutions that integrate Xe 7x with various other platforms.
Finally, you can also work with a professional services provider to develop a custom integration solution for your specific needs.
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WILL GIVE BRAINLIST!!
Answer:
what is the question exactly?
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
hope i helped
Pls answer quick as possible !
Answer:
(A.) & (D.) are your answers i hope you have a great day
Step-by-step explanation:
360÷6 long division
How do I find my answer?
Answer:There you go
Step-by-step explanation:
Step 1: Take the first digit of the dividend from the left. ...
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend (if present).
What kind of line is x =- 2?
X = -2 is a vertical line, a straight line that goes straight up and down and does not go from side to side.
A vertical line is perpendicular to the x-axis. The equation for a vertical line is x = some constant, where the constant is the x-coordinate of every point on the line. In the equation x = -2, the constant is -2.
This means that every point on this line has an x-coordinate of -2, no matter what the y-coordinate is. Every point on the line (x, y) will have an x-coordinate of -2, while the y-coordinate can be anything.
For example, the point (x, y) = (-2, 7) is on the line x = -2, while the point (x, y) = (-2, -3) is also on the line x = -2. Since the equation x = -2 is a constant equation, the line will never intersect the x-axis; instead, it will always stay at the same x-coordinate of -2.
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Luke and Isabella make scale drawings of a fountain. The scale from the
fountain to Isabella’s drawing is 6 m to 3 cm. The height of the fountain in
Isabella’s drawing is 5 cm. The scale from the fountain to Luke’s drawing is
5 m to 2 cm. What is the width of the fountain in Luke’s drawing?
Using proportions, the width of the fountain in Luke's drawing is 4cm
What is Width of Luke's DrawingTo find the width of the fountain in Luke's drawing, you can use the proportion:
width(Luke's drawing) / width(fountain) = 2 cm / 5 m
We know that the height of the fountain in Isabella's drawing is 5 cm, and the scale of Isabella's drawing is 6 m to 3 cm, so we can use that information to find the width of the fountain:
width(fountain) = height(fountain) * (scale of Isabella's drawing) = 5 cm * (6 m / 3 cm) = 10 m
Now we can substitute that value into the proportion to find the width of the fountain in Luke's drawing:
width(Luke's drawing) = (width(fountain) * 2 cm) / 5 m = (10 m * 2 cm) / 5 m = 4 cm
So the width of the fountain in Luke's drawing is 4 cm.
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An 8-foot-long board is leaning against a building. The angle formed by the ground and the board is 70 ∘ . What is the distance from the building to the base of the board? Round to the nearest tenth.
The distance from the building to the base of the board is 2.7feet ( nearest tenth).
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The angle of elevation from the point of the board is 70°.
The wall of the building is the opposite to the angle and the the distance from the building to the base of the board is adjascent. The height of the board is the hypotenuse.
Therefore,
cos (tetha) = adj/hyp
cos 70° = x/ 8
x= cos 70° × 8
x = 2.7 feet ( nearest tenth)
therefore the The distance from the building to the base of the board is 2.7feet
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The distance from the building to the base of the board is; 2.7 ft
How to use trigonometric ratios?The six trigonometric ratios are expressed as;
sine (sin) = opposite/hypotenuse
cosine (cos) = adjacent/hypotenus
tangent (tan) = opposite/adjacent
cotangent (cot) = 1/tan
cosecant (cosec) = 1/sin
secant (sec) = 1/cos
Now, we are since the board is leaning against the building and the angle formed by the board with the ground is 70°, then we can say that;
x/8 = cos 70
where x is the distance from the building to the base of the board
x = 8 * cos 70
x = 8 * 0.3420
x = 2.736
Approximating to the nearest tenth gives;
x = 2.7 ft
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The function f(x)=5x converts x nickels to pennies. Find a function that converts x pennies to nickels. Then convert 50 pennies to nickels
The function f(x) converts x nickels to pennies and the function g(x) converts x pennies to nickels. Applying g(50) to 50 pennies gives 10 nickels.
The function g(x)=x÷5 converts x pennies to nickels.
Applying g(50) to 50 pennies:
g(50)=50÷5
=10 nickels
The function f(x)=5x converts x nickels to pennies. This means that for every nickel, 5 pennies are produced. To convert pennies to nickels, the inverse of this function is needed. The inverse of f(x)=5x is g(x)=x÷5. This function converts x pennies to nickels. When g(50) is applied to 50 pennies, the result is 10 nickels. In other words, 50 pennies can be converted to 10 nickels. To summarize, the function g(x)=x÷5 effectively converts pennies to nickels, allowing the user to easily convert between the two currencies.
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What does i mean?
O -√1
O √-1
O √1
O √2
O-√-1
In Math's the unit i mean -√1.
What is meant by imaginary unit?The quadratic equation has a solution in the form of the imaginary unit or unit imaginary number I Despite the absence of a real number for this feature, addition and multiplication can be employed to extend real numbers to complex numbers.
An index that appears below the summation sign serves as a representation of the variable of summing. I is a common way to represent the index.
An indefinite integral is what the integral is known as, and it represents a group of functions (the antiderivative) whose derivative is the integrand. The assessment of definite integrals and indefinite integrals are related in calculus' fundamental theorem.
Therefore, the correct answer is option A) -√1.
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What is the complete factored form of X² 9?
After solving, the complete factored form of [tex]X^2-9[/tex] is (X-3)(X+3).
In the given question, we have to find the complete factored form of [tex]X^2-9[/tex].
To find the factored form we have to follow some rule:
(1) Find a GCF for the numbers in the expression, and then take a look at each variable or expression independently to identify the GCF. If the variable or expression appears in every term, factor out the term with the smallest power.
(2) A GCF can be factored out by writing the GCF outside of the parentheses and dividing each term by the GCF that is inside the parentheses.
To solve this expression we can use the formula [tex]a^2-b^2[/tex] = (a+b)(a-b)
[tex]X^2-9[/tex] = [tex](X)^2-(3)^2[/tex]
[tex]X^2-9[/tex] = (X-3)(X+3)
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The complete question is:
What is the complete factored form of [tex]X^2-9[/tex]?
find the value for which the solution of the initial value problem remains finite as t approaches infinity
The solution of the initial value problem remains finite as t approaches infinity if the eigenvalues of the system are negative or have negative real parts.
The eigenvalues of a system determine the stability of the solution. Negative eigenvalues indicate that the solution will approach a steady state as time goes on. Positive eigenvalues indicate that the solution will diverge, or grow without bound, as time goes on. If the real parts of the eigenvalues are negative, the solution will approach a steady state, but if the real parts of the eigenvalues are positive, the solution will diverge as t approaches infinity.
In order to check for finite solution for a given initial value problem, one needs to evaluate the eigenvalues of the system, and check their real parts. If they are negative, the solution will remain finite, otherwise the solution will diverge as t approaches infinity.
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a)x/5=3
b)x/2=8.5
Find the value of x
Answer:
a. x=15
b. x=17
Step-by-step explanation:
Answer:
A) The equation "x/5=3" can be solved by multiplying both sides by 5 to get rid of the fraction. This gives us "x=15". So the value of x that makes the equation true is 15.
B) The equation "x/2=8.5" can be solved by multiplying both sides by 2 to get rid of the fraction. This gives us "x=17". So the value of x that makes the equation true is 17.
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given an alphabet $\sum$ of $m$ symbols, how many palindromes are there of length $n$? prove that your answer is correct.
Given an alphabet of m symbols, the number of possible palindromes with length n is: m^(n/2) is n is even and m^((n+1)/2) if n is odd.
A palindrome is defined as a set of characters that are the same forwards and backwards. Example pqrrqp
Suppose we have m symbols in an alphabet and we want to construct palindromes with length n.
If n is even, there are n/2 free choices, each is picked from m symbols. Hence, the number of possibilities is m^(n/2)If n is odd, there are (n+1)/2 free choices, each is picked from m symbols. Hence, the number of possibilities is m^((n+1)/2)Example:
The alphabet costs of 10 symbols, for example lower case a,...,j, and we want construct palindromes of length 5. To make a palindrome with length of 5, we need 3 symbols form {a,b,..,j} for example hiaih. Hence, the number of possible palindromes is: 10³ = 1000
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What is the multiplicative inverse of 4 /- 7?
The multiplicative opposite of a number, say, N, is act for by 1/N or N-1. It is also called reciprocal, obtain from the Latin word ‘reciprocals ‘. The meaning of inverse is something which is converse.
The reciprocal of a number obtained is like that when it is multiplied by the original number, the value equals identity 1.
In other words, it is a method of dividing a number by its own to produce identity 1, such as N/N = 1.
When any number is multiplied by its particular multiplicative inverse, the resultant value is equal to 1.
multiplicative inverse of a is 1/a
(4/-7) =4/7
i.e., multiplicative inverse of 4/7 is -7/4.
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WILL GIVE BRAINLIEST FOR SOLVING: If you see this number on a calculator, 3.14E5, how can you express it in standard form?
The scientific number 3.14E5 in standard form is 314,000.
What is standard form?
In mathematics, the most typical way to represent a specific element is called standard form. Every mathematical concept, including big numbers, tiny numbers, equations, and lines, has a standard form. It is the simplest form in which lines, numbers and equations can be represented.
The given scientific number is 3.14E5.
Scientific notation is mostly used by scientists to handle very small or very large numbers. Using calculators to convert length, weight or mass units, often results are displayed in scientific notation.
E5 represents the value 10^5.
So, when the scientific number is converted into exponent form, it is -
3.14e5 = 3.14 x 10^5
Then the result is converted into whole number to get the standard form -
3.14 x 10^5 = 314,000
Therefore, the standard form is 314,000.
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A coin collector has a bag of 50
pennies. What is the "percent
abundance" of the pre-1982
pennies?
The percent abundance of the post-1982 pennies is 56%.
What is percent abundance?The proportion of a given element's all-natural isotopes is known as its percent abundance.percentage of abundant post-1982 penniesFollowing are the calculations for the post-1982 penny's percent abundance;Post-1982 coins divided by all pennies multiplied by 100% equals percent abundance.The proportion of atoms with a particular atomic mass that can be found in a naturally occurring sample of an element is known as the relative abundance of an isotope.
percent abundance = (28) / (50) x 100%
percent abundance = 56%
Thus, the percent abundance of the post-1982 pennies is 56%.
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What are the zeros of the polynomial function
ƒ(x) = -x³ + 2x² + x − 2
The zeros of the polynomial function ƒ(x) = -x³ + 2x² + x − 2 are the x-values at which the function equals zero. The solution is x = 1, x = 2, and x = -1.
What is polynomial?A polynomial is a mathematical expression consisting of variables, coefficients, and exponents. Its basic form is a monomial, which is a single term with a coefficient and an exponent. Polynomials may also include higher degree terms of two or more terms connected by addition, subtraction, and multiplication. Polynomials are used to model a variety of situations in mathematics, engineering, economics, and other fields.
This can be determined by solving the equation ƒ(x) = 0. A cubic equation of this form can be solved by factoring, so the solution is x = 1, x = 2, and x = -1. These three values are the zeros of the polynomial function ƒ(x) = -x³ + 2x² + x − 2.
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Which are ways of showing probability? Select 4 options.
50%
557
1 × 104
25%
Probability the right choices are A and D.A is 50% and D is 25%.
How are probabilities calculated?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.
We are aware that a given event's probability is also its likelihood to occur.
Every event has a probability that ranges from 0 to 1.
If the event won't ever happen, the value is zero; if it will definitely happen, the value is 1.
Moreover, the likelihood may be expressed as a ratio or a percentage, with the percent possible to range from 0% to 100%.
hence, of the available options:
B) 557 is false because the probability is larger than 1, hence it cannot be true.
d) Because there is a higher probability than 1, the calculation 1104=104 is wrong.
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Answer
a and d
Step-by-step explanation:
on a certain night, three couples go to see a play, and sit at random in a row with six seats. what is the probability that each person is sitting next to his or her partner?
There are a total of 6! (6 factorial) ways in which the 6 people can be seated in the row of 6 seats.So the probability that each person is sitting next to his or her partner is 1/15.
To find the probability that each person is sitting next to his or her partner, we need to find the number of ways in which this can happen and divide it by the total number of ways in which the 6 people can be seated.
Each couple can sit in 2 different ways (either the man or the woman first) and there are 3 couples so there are 2^3 = 8 ways for the couples to sit.
Now, we have 3 pairs of people sitting together, and 3 individual seats remaining.
The 3 pairs of people can sit in 3! ways, and the 3 individual seats can be occupied by the remaining 3 people in 3! ways as well.
So, the total number of ways in which each person is sitting next to his or her partner is 8 * 3! * 3!
Now we divide this by the total number of ways in which the 6 people can be seated, which is 6!:
(8 * 3! * 3!) / 6! = (8 * 6) / 720 = 48 / 720 = 1/15
So the probability that each person is sitting next to his or her partner is 1/15.
Learn more about probability at : https://brainly.com/question/30034780
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