a group of seven people are attending the movies together. (a) two of the seven insist on sitting side-by-side. in how many ways can the seven be seated together in a row? (b) two of the people do not like each other and do not want to sit side-by-side. now how many ways can the seven be seated together in a row?

It was first called "pi" in 1706 by William Jones, because pi is the first letter in the Greek word perimitros, which means "perimeter."

The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let us find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 399

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 399

3X + 3 = 399

3X + 3 - 3 = 399 - 3

3X = 396

3X/3 = 396/3

X = 132

Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.

Hence , The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

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The system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics.

Here,

Given data:

Time taken by Latanya to solve a problem = 1.5 minute.

Time to read one page = 2 minutes.

Number of problems completed = x problems.

Total time used for reading = y  minutes.

Using the data to consider:

Let x be the the number of math problems that Latanya solved.

Let y be the number of pages that Latanya read.

thus,

1.5x +2 y = 48

and

x = 4 + y

Thus, we can conclude the the system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

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The cost of each pen would be 5 dollars.

What is a unit value?

When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. Context: The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities

The shopkeeper has 56 pens. and he sold them for 280 dollars

Cost of each pen = total amount/ number of pens

                            = 280/56

                            =10/2

                            = 5

Hence, the cost of each pen would be 5 dollars.

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The sum of the integers from 1 to 100 is 5050. You can find this sum by adding all of the integers together or by using the formula for the sum of an arithmetic series.

In this case, there are 100 terms, and the average of the first and last term is (1 + 100) / 2 = 50.5, so the sum is 100 * 50.5 = 5050.

Another way to find the sum is To find the sum of the integers from 1 to 100, we can add all of the integers together. This can be done by starting with 1 and repeatedly adding 1 to get the next integer, or by using a calculator or computer program to do the calculations for us.

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The answer to the expression -( 7 4x )= 9 is -7, since subtracting 7 from both sides of the equation leaves us with 4x = 2, and then dividing both sides of the equation by 4 gives us x = -7.

The expression -( 7 4x ) = 9 can be solved by using basic algebraic operations. First, we subtract 7 from both sides of the equation to obtain -4x = 2. This is because when subtracting a number from both sides of an equation, we are essentially adding the opposite of that number to both sides. Then, we divide both sides of the equation by 4 to obtain x = -7. This is because when dividing both sides of the equation by a number, we are essentially multiplying both sides by the inverse of that number. Therefore, the answer to the expression is -7.

-(7 4x ) = 9

-7 - 4x = 9

-4x = 2

x = -7

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Answer: I am bad at math, but I'd say _> is the sign...

Step-by-step explanation:

elloooo

Answer: I don't know

Step-by-step explanation:

Answer:

Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased

Step-by-step explanation:

Answer:

320 teenagers

Step-by-step explanation:

10% = 0.1

Take 3200 times 0.1 = 320

So, there are 320 teenagers attended the football game.

Answer: x= 4/k

Step-by-step explanation:

Answer:

B.) [tex]\frac{4}{k}[/tex]

Step-by-step explanation:

[tex]3kx+24=9kx\\3(kx+8)=9kx\\\frac{3(kx+8)}{3}=\frac{9kx}{3}\\kx+8=3kx\\(kx+8)-kx=(3kx)-kx\\8=2kx\\\frac{8}{2k}=\frac{2kx}{2k}\\\frac{4}{k}=x[/tex]

The three types of set based on the number of elements is empty set, finite set and infinite set.

In mathematics, a set is a collection of unique objects. The number of elements in a set can be finite or infinite.

An empty set is a set with no elements. It is also called a null set. For example, a set of natural numbers less than 0.

Finite set is a set containing finite number of elements, that is the number of elements in the set is countable. For example, a set of natural numbers less than 100.

Whereas infinite set is a set with infinite number of elements, that is the number of elements in the set is not countable. For example, a set of natural numbers.

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Answer:

Step-by-step explanation:

The phase of the systems life cycle during which users are trained to use the new system is called the implementation phase. In this phase, the new system is installed and made operational, and users are trained on how to use it effectively. This phase typically follows the design and development phases and precedes the maintenance phase.

What is the main focus of the implementation phase in the systems life cycle?

The main focus of the implementation phase is training users to use the new system effectively. This includes installing the system and making it operational, as well as providing necessary support and training to ensure users are able to utilize the system efficiently.

The phase of the systems life cycle during which users are trained to use the new system is the implementation phase. This is the phase where the new system is actually implemented and made available for use by the users. It is important to provide training to users during this phase so that they are able to effectively use the new system and understand its functionality.

Therefore, users are trained to use the new system during the implementation phase.

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The implementation phase of the systems life cycle is the time when users are taught how to utilize the new system.

The new system is installed, made operational, and users are instructed on how to utilize it efficiently during the implementation phase. In most cases, this phase comes after the design and development phases and comes before the maintenance period.

Why is user training important during the implementation phase of the systems life cycle?

User training is important during the implementation phase of the systems life cycle because it ensures that users are able to effectively use the new system and understand how it works. This is essential for the successful adoption and utilization of the system by the organization. Without proper training, users may struggle to use the system effectively, leading to reduced productivity and potentially even causing issues with data accuracy and integrity. By providing thorough user training, organizations can ensure that their employees are able to use the new system efficiently and effectively, leading to a successful implementation.

The implementation phase of the systems life cycle is the time when users are taught how to utilise the new system. In this stage, the new system is really put into use and made accessible to users. During this stage, it's crucial to give users training so they can utilize the new system correctly and comprehend its functions.

Therefore, during the implementation phase, users are instructed on how to utilize the new system.

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Answer:

( x + 6, y + 4)

Step-by-step explanation:

Let's pick point S at ( -9, -4); it changes to point S' at ( -3, 0)

The x increase by 6, and the y increase by so the answer is

( x + 6, y + 4)

An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

Given that,

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The pipe is located 9 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 9 inches from the vertex (0,0)

9 inches is the focus of the mirror

The distance between the vertex and the focus = 9

Since parabola is upwards and vertex is (0,0) we use formula,

[tex]4py = x^{2}[/tex]  

Where,

p is the distance between the vertex and focus p = 9

Now,

[tex]4*9*y = x^{2}[/tex]    

[tex]36y =x^{2}[/tex]

Now isolate y by dividing 36 on both sides, we get

y = [tex]\frac{x^{2} }{36}[/tex]

Therefore,

An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

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The initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours  of flight.

The linear model that can be used to predict the amount of jet fuel present on the Boeing 747-8 Intercontinental jet after 18 hours of flight without refueling is given by the equation

F = 63,500 - (800 x 18),

where F is the amount of jet fuel in gallons and 18 is the number of hours of flight. This equation indicates that after 18 hours of flight, the jet would have an estimated amount of jet fuel of 42,400 gallons remaining. This amount is significantly lower than the initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.

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The Nature of roots of the quadratic equation "5x² -3x +2 = 0" is  imaginary and conjugate   .

To find the Nature Of Roots of the Quadratic Equation ax² + bx + c = 0 , we find the discriminant(D) by the formula ; D = b² - 4ac .

the quadratic equation is given as 5x² -3x +2 = 0 ;

On comparing , we get , a = 5  , b = -3 and c = 2 .

Substituting the values in the Discriminant formula mentioned above , we get

D = (-3)² - 4×5×2

= 9 - 40

= -36 .

Since the value of the discriminant is less than 0 ,

Therefore  , the roots will be imaginary and conjugate .

The given question is incomplete , the complete question is

What is the nature of the roots of the equation 5x² -3x +2 = 0  ?

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The perimeter of the new TV will be 179.77 inches.

From the information, the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches and the new TV is 66 inches across the diagonal.

It should be noted that the perimeter simply means the total length of the boundary of the object. This will be calculated thus:

= (66 × 87.16) / 32

= 5752.56 / 32

= 179.77 inches.

In conclusion, the perimeter is 179.77 inches.

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Answer:

Three and four  and five  and zero.

Step-by-step explanation:

Answer:

3 and 4

Step-by-step explanation:

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

First we define a reference system.

Let's assume the horizontal axis as positive towards the right.

Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.

The equilibrium equation is given by:

-20-25+F=0

Where,

F: force with which Gunther pulls the rope.

Clearing F we have:

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

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Number of combinations = 56 combinations can be created from the letters in the word "friendly"

Points to remember

nCₐ = n!/(r!(n - r)!)

The given word is "FRIENDLY"

F R I E N D L Y is a 8 letter word.

To find the number of combinations

5 letters can be selected from 8 letter = 8C₅

8C₅ = 8!/(8 - 5)!5!

= 8!/3!5!

= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)

= 8 * 7

=  56

5 letter combinations can be created from the letters in the world “friendly = 56

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The value of polynomial 5x - 4x² + 3 at x=0 is equal to 3

Given that,

The polynomial is 5x - 4x² + 3

To find : The value of polynomial 5x - 4x² + 3 at x=0

A combination of more than two algebraic expressions, particularly when they each contain a distinct power of the same variable (s).Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Given : x = 0

→ 5x - 4x² + 3

→ 5 ( 0 ) - 4 ( 0) ² + 3

→ 0 - 0 + 3   ( ∵ here + 0 - 0 cancels )

→ 3

Therefore, The value of polynomial 5x - 4x² + 3 at x=0 is 3.

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The amount of fabric used on the headband and wristband for each player is 27.64 inches.

The operations that we use in particular actions like adding and taking away things or adding multiple times, diving things, etc.

The four basic Mathematical operations are addition, subtraction, multiplication, and division.

Here in this problem, we use divisions to solve the problem,

Given that,

Nancy uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. 378.83 inches of fabric used on wristbands for the players only.

Number of headbands made with 866.18 inches

= 43 (player's) + 3 (coach's)  

= 46 headbands

The amount of fabric used for 1 head band = (866.18)/46 = 18.83 in

378.83 inches of fabric used on wristbands for the players only.  

The amount of fabric used for each wristband = 378.83/43 = 8.81 in

Amount of fabric used on headband and wristband = 18.83 + 8.81

= 27.64 inches

Therefore,

The amount of fabric used on the headband and wristband for each player is 27.64 inches.

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Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].

Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex] .

Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].

Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].

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The probability that the sample proportion is more than 40% is approximately .0001.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To find the probability that the sample proportion is more than 40%, we need to use the normal distribution and the central limit theorem.

The central limit theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To find the probability that the sample proportion is more than 40%, we need to first calculate the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion (38%), and the standard deviation of the sample proportion is equal to:

  [tex]standard\ deviation = sqrt((population\ proportion * (1 - population\ proportion)) / sample\ size)\\\\= \sqrt{((.38 * .62) / 400)}\\\\= .048[/tex]

Next, we need to standardize the sample proportion of 40% by subtracting the mean and dividing by the standard deviation:

z = (40% - 38%) / .048 = 4.17

The probability that it is less than or equal to 40% is approximately .9999.

The probability that the sample proportion is more than 40% is then equal to 1 - .9999 = .0001.

So, The probability that the sample proportion is more than 40% is approximately .0001.

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On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)

The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.

The answer to the question is that all real numbers or (−∞,∞)

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The  polynomial function that could be represented by the graph is; f(x) = x³ + x² - 6x

Let us find the zeros of the polynomial from the graph. The zeros of the polynomial will be the points where the graph crosses the x-axis.

Thus, we see that the graph crosses the x-axis at x = -3, 0 and 2. Thus, the factors of the polynomial are;

(x - 0), (x + 3) and (x - 2)

Therefore, the equation of the polynomial is;

f(x) = x(x - 2)(x + 3)

Expanding this gives us;

f(x) = x(x² + x - 6)

f(x) = x³ + x² - 6x

We conclude that is the equation of the polynomial represented by the graph.

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Figure P is the result transformation figure O by the rule (x + 1, y-4). In other words, figure O shifted 1 unit left and 4 units downward direction.

What is meaning transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

The coordinate of vertices of figure O are (2,4), (3,5), and (4,2).

The coordinate of vertices of figure P are (3, 0), (4,1), and (5, -2).

The difference between x-coordinates is (3 - 2) = (4 - 3) = (5 - 4) = 1.

The difference between y-coordinates is (0 - 4) = (1 - 5) = ( -2 - 2) = -4.

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2 is a  prime number because it has only two factors (1 x 2).

A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.

Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.

Given why 2 is prime,

The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.

so 2 has only two multiple

1 and 2,

Hence 2 is a prime number.

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