prove the following statement:
Let n be an odd positive integer then the sum of n consecutive
integers is divisible by n.

The total number of ways to line up the 11 people such that the bride is next to the maid of honor and the groom is next to the best man is:

9! * 2! * 2! = 40,320.

If we consider the bride and the maid of honor as a single entity, there would be 10 entities in total to be arranged in a row.

Similarly, if we consider the groom and the best man as a single entity, there would be 10 entities in total to be arranged in a row.

Now, we need to consider that the bride and the maid of honor are together, and the groom and the best man are together.

This means that we have two entities (bride and maid of honor, groom and best man) that must be kept together in the arrangement.

We can treat these two entities as single units, which gives us a total of 9 units to arrange.

We can arrange these units in 9! ways.

However, within each of the two units, the bride and the maid of honor can be arranged in 2! ways, and the groom and the best man can be arranged in 2! ways.

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Answer:

The answers for this question are 1 and 0

Answer:

the correct answers are 1 and 0

B. The probability of an outcome is between 0 and 1. C. The sum of the probabilities of all possible outcomes is 1.

Option B is correct because probability values must be between 0 and 1.

Option C is correct because the sum of the probabilities of all possible outcomes must equal 1.

Option A is incorrect because it is not necessary for half of the possible outcomes to have probabilities greater than 0.5.

Option D is incorrect because the distribution does not have to be symmetrical.

Option E is incorrect because the outcomes can have common events and can be dependent.

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The Interstate 90 freeway in the US is (D) 123.9 miles.

Therefore, the Interstate 90 freeway in the US is (D) 123.9 miles.

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Correct question:

i-90 is the longest freeway in the us, stretching from Seattle to Boston. how many miles is it?

a. 248.1

b. 302.1

c. 437.1

d. 123.9

Answer:

I think its false

Step-by-step explanation:

the car went 8 second faster

Answer: 16

If 5/8 of a number, let's call it x, is 40, we can set up the following equation:

5/8 * x = 40

Dividing both sides by 5/8, we get x = 64

Now that we know that the number is 64, we can find a quarter of it by multiplying by 1/4 as follows:

64 * (1/4) = 16

Answer: 1+17r is your answer

Step-by-step explanation: Combine like terms

Answer:

1+17r

Step-by-step explanation:

All values of x in the interval [0, 2] that satisfy the equation are \(\frac{\pi }{2} ,3\frac{\pi }{2}\).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.

The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the values of the unknowns that satisfy the equality are referred to as the equation's solutions.

Calculations:

16cos(x +8sin(2x)=0

Divide by 8

2cos(x)+sin(2x)=0

Identity:

sin(2x)=2sin(x)cos(x)

2cos(x)+2sin(x)cos(x)=0

Factor:

2cos(x)(1+sin(x))=0

2cos(x)=0

cos(x)=0=x=\(\frac{\pi }{2}\),3\(\frac{\pi }{2}\)

(1+sin(x))=0

sin(x)=−1=x=3\(\frac{\pi }{2}\)

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The measure of the length of the dotted line is 3.75 inches. Then the correct option is B.

The hexagon is a two-dimensional geometry with six sides. And the polygon's sides are all straight lines that are joined side by side.

The perimeter of the hexagon is 7.5 inches.

Then the length of the hexagon will be

\(\rm 7.5 = 6x\\\\x \ \ = 1.25\)

The length of the hexagon is 1.25 inches.

Then the diagonal length of the hexagon will be

y = 2 × 1.25

y = 2.5

The diagonal length of the hexagon is 2.5 inches.

Then the length of the dotted line is 3.75 inches.

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Answer: The third option, O 2x²+7x-4

Step-by-step explanation:

     We can use the "FOIL" method. We take the following four sets, multiply them together, then add them for our final answer.

-> first

-> last

-> inner

-> outer

     What does this look like mathematically?

-> first = (2x - 1)(x + 4) = 2x * x = 2x²

-> last = (2x - 1)(x + 4) = -1 * 4 = -4

-> inner = (2x - 1)(x + 4) = -1 * x = -x

-> outer = (2x - 1)(x + 4) = 2x * 4 = 8x

-

2x² - 4 - x + 8x

2x² + 7x - 4

           O 2x²+7x-4

Answer:

\(C. 2x^2+7x-4\)

Step-by-step explanation:

1) Distribute.

\((2x-1)(x+4)\\2x(x+4)-1(x+4)\)

2) Distribute.

\(2x(x+4)-1(x+4)\\2x^2+8x-1(x+4)\)

3) Distribute.

\(2x^2+8x-(x+4)\\2x^2+8x-x-4\)

4) Combine like terms.

\(2x^2+8x-x-4\\2x^2 + 7x - 4\)

Answer:

(D) 1+0.06m

Step-by-step explanation:

Let's say that m=$120

(A)= $127.2

(B)= $127.2

(C)= $127.2

(D)= $8.2

As you can see after I substituted in 120 for (m) and solved, D is the only equation that did not represent her current balance.

I hope this helps!

Answer:

D

Step-by-step explanation:

edge

Este es un problema clásico de álgebra lineal que se puede resolver mediante un sistema de ecuaciones lineales.

Si definimos "a" como el número de aves y "b" como el número de bestias, entonces podemos plantear las siguientes ecuaciones:

a + b = 60 (porque el número total de animales es de 60)

2a + 4b = 200 (porque el número total de patas es de 200)

Podemos resolver este sistema de ecuaciones de varias maneras, pero aquí hay un ejemplo de cómo hacerlo por el método de sustitución:

Despejar "a" en la primera ecuación:

a = 60 - b

Sustituir "a" en la segunda ecuación:

2(60 - b) + 4b = 200

Resolver para "b":

120 - 2b + 4b = 200

2b = 80

b = 40

Sustituir "b" en la primera ecuación para encontrar "a":

a + 40 = 60

a = 20

Por lo tanto, hay 20 aves y 40 bestias en el zoológico.

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Answer:

b+2.673

Step-by-step explanation:

substitute the value of the variable into the equation and simpilfy

Answer:

8.807

Step-by-step explanation:

1. 6.134 + (5.68 - 3.007)

   6.134 + 2.673

   = 8.807 or \((\frac{8807}{1000}, 8\frac{807}{1000} )\)

Answer:20 divided by 300

Step-by-step explanation:

i dont have a calculator

Answer:

x=(22*300)/100

Step-by-step explanation:

When given a percentage in your comparison, there is a standard formula to follow. This is (Is over Of = Percent Over 100). Let me express this mathematically.

Is/Of= %/100

In these questions, there will be one missing value in this expression. In this one, we are given the percent and the value to replace "Of". This makes our expression look like

x/300=22/100

To get x by itself, you multiply 300 to the other side of the equal sign, making it

Answer:

im pretty sure it would be 9 bc there are 3 dif colours and 3 dif finishes and u j count the table

Step-by-step explanation:

In mathematics, every integer is a rational number, hence a whole number 8 can be written as 8/1. 1/3 x 8 = 8/3 in fraction form. 1/3 x 8 = 2.6667 in decimal form.

The simplest form is given as 3/8.

A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.

The number a is called as the numerator and b is the denominator.

Two fractions can be multiplied by taking the product of their numerators and denominators respectively.

The given expression is 1/3 x 8.

It can be simplified as follows,

1/3 x 8

Write 8 in the fraction form as 8 = 8/1

= 1/3  x 8/1`

Multiply the numerators and denominators to obtain,

(1 x 8)/(3 x 1)

= 8/3

The given expression can be simplified as 8/3.

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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The formula to calculate the expected loss is given by the following formula: Expected Loss = Σ (Loss Amount * Probability of Loss)To calculate the expected loss, we need to first multiply the loss amount with the probability of loss, and then add the products.

a. $0 .30Loss amount, X = $0Probability of loss, P(X) = 0.30Expected loss = 0 * 0.3 = $0b. $120 .50Loss amount, X = $120Probability of loss, P(X) = 0.50Expected loss = 120 * 0.5 = $60c. $200 .20Loss amount, X = $200Probability of loss, P(X) = 0.20Expected loss = 200 * 0.2 = $40, the expected loss for the given probabilities of various losses is $0 for a), $60 for b) and $40 for c). The total expected loss would be the sum of all expected losses i.e. $100.

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Answer:

x2 + 9x – 3x – 27 = (x + 9)(x – 3)

Step-by-step explanation:

The four-term polynomial and factored form of x2 + 6x – 27 is x^2 + 9x - 3x - 27 = (x - 3)(x + 9)

Factorization involves splitting a function into several factors

The polynomial is given as:

x^2 + 6x - 27

Expand the expression

x^2 + 9x - 3x - 27

Factorize the expression

x(x + 9) - 3(x + 9)

Factor out x + 9

(x - 3)(x + 9)

So, we have:

x^2 + 9x - 3x - 27 = (x - 3)(x + 9)

Hence, the four-term polynomial and factored form of x2 + 6x – 27 is x^2 + 9x - 3x - 27 = (x - 3)(x + 9)

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The two values on the number line are of opposite values, and have a distance of three halves units to zero. Thus option B.

A number line is a system in which the position of a directed number is located. It extends from negative infinity to positive infinity, thus all numbers can be located on a number line.

A directed number is any type of number which has either a negative or positive sign i.e its direction.

Considering the values given in the question, it can be deduced that;

i. Both values are opposite of each other because of the negative and positive signs (i.e their directions)

ii. The two values are at a distance of one and a halve to the zero point. So that;

one and a halve = 1 1/2

                           = 3/2

Thus both values are at a distance of three halves to zero.

Therefore, the correct option is B. The values are opposites of each other, and their distance to zero is three halves units.

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Answer:

Because she found it improves division.

Step-by-step explanation:

The circle centered at C(-5,4) intersects the line y = 3x + 2 at the point Q, with coordinates (-1/10, 17/10). This point Q serves as the tangent point between the line and the circle.

To find the coordinates of the point Q where the line y = 3x + 2 is tangent to the circle with center C(-5,4), we can use the concept of the slope of a tangent line.

First, we need to find the slope of the tangent line. The slope of the line y = 3x + 2 is 3. For a tangent line to a circle, the radius drawn from the center of the circle to the point of tangency is perpendicular to the tangent line. Since the slope of the radius is the negative reciprocal of the tangent line's slope, the slope of the radius is -1/3.

Next, we find the equation of the radius line passing through the center C(-5,4) with a slope of -1/3. Using the point-slope form, we have:

y - 4 = (-1/3)(x + 5)

To find the point of tangency, we solve the system of equations formed by the line y = 3x + 2 and the radius line:

y = 3x + 2

y - 4 = (-1/3)(x + 5)

Substituting the value of y from the first equation into the second equation:

3x + 2 - 4 = (-1/3)(x + 5)

3x - 2 = (-1/3)x - 5/3

3x + (1/3)x = 5/3 - 2

(10/3)x = -1/3

x = -1/10

Substituting this value of x back into the first equation:

y = 3(-1/10) + 2

y = -3/10 + 20/10

y = 17/10

Therefore, the coordinates of the point Q, where the line y = 3x + 2 is tangent to the circle with center C(-5,4), are (-1/10, 17/10)

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Answer:

12 :D

Step-by-step explanation:

First we substitute all x's for -2 :)

f(-2)=−-2^3−3(-2)^2+8

Now we solve :)

f(-2)=−-2^3−3(-2)^2+8

f(-2)=− -8 −3(-2)^2 + 8

f(-2) = -8 - 3(-4) + 8

f(-2) = - 8 + 12 + 8

f(-2) = 4 + 8

f(-2) = 12 :)

f will equal 12 :)

Have an amazing day!!

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The ratio of the coordinate point on the line is  2 to 7.

The ratio of the coordinate point on the line is calculated as follows;

Let the coordinate points = (xp, yp)

Let the ratio of the line = a:b

xp = x₁  +  (a/(a+b) (x₂ - x₁)

yp = y₁  + (a/a+b) (y₂ - y₁)

-3 = -7 + ( a/a+b)(11 - - 7)

-3 = -7 + (a/a+b)(18)

-3(a + b)  = -7(a+b) + 18a

7(a + b ) - 3(a+b) = 18a

7a + 7b - 3a - 3b = 18a

4b = 14a

4/14 = a/b

2/7 = a/b

2 : 7 = a : b

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In this scenario, the shape of the sampling distribution of X-bar is approximately normal.

The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.

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The intrinsic value of the PUT option is $0. It means the option has no inherent value based on the given information.

To determine the intrinsic value of a PUT option, we compare the strike price (X) with the current market price (S) of the underlying asset. If the strike price is higher than the market price, the intrinsic value is the difference between the strike price and the market price. However, if the market price is higher than the strike price, the intrinsic value is $0.

In the given information, we have the following data:

- Strike price (X): $90

- Market price (S): $47.78

Since the market price is lower than the strike price (47.78 < 90), the intrinsic value of the PUT option is $0. This means that exercising the option would not result in any profit because it is currently out of the money.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = \(25x^{2}\)

Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= \(\frac{6}{5}\)

Now, two perpendicular sides are then,  \(\frac{18 }{5} , \frac{24}{5}\)

\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5