!!!!!!!!!! !!!!!!!!!!!!

The total number of choices for selecting 6 representatives without any two occupying neighboring seats is 77597520 .

(a) The number of ways to arrange 5 parents, 5 students, and 1 teacher in a circular arrangement around a table such that no student sits next to another student and no parent sits next to another parent, we can use the principle of inclusion-exclusion.

First, let's consider the arrangements without any restrictions. We have a total of 11 people to arrange around the table (5 parents + 5 students + 1 teacher), which can be done in (11 - 1)! = 10! ways.

Now, let's consider the arrangements where at least two students sit next to each other. We can treat the two adjacent students as a single entity, resulting in 10 entities to arrange around the table (4 parents + 5 student pairs + 1 teacher). This can be done in (10 - 1)! = 9! ways. However, within each student pair, the students can be arranged in 2! ways. Therefore, the total number of arrangements with at least two students sitting next to each other is 9! × 2! ways.

Similarly, we consider the arrangements where at least two parents sit next to each other. Again, we treat the two adjacent parents as a single entity, resulting in 10 entities to arrange around the table (4 parent pairs + 5 students + 1 teacher). This can be done in (10 - 1)! = 9! ways. Within each parent pair, the parents can be arranged in 2! ways. Therefore, the total number of arrangements with at least two parents sitting next to each other is 9! × 2! ways.

By the principle of inclusion-exclusion, the number of valid arrangements is given by

Valid arrangements = Total arrangements - Arrangements with at least two students sitting next to each other - Arrangements with at least two parents sitting next to each other

Valid arrangements = 10! - 9! × 2! - 9! × 2!

Valid arrangements = 2177280

(b) The number of choices for selecting 6 representatives out of 20, where no two chosen representatives occupy neighboring seats, we need to use a combination of counting techniques.

First, choose 6 seats out of the 20 seats in which the representatives will be seated. This can be done in C(20, 6) ways.

Now, since no two chosen representatives can occupy neighboring seats, we can think of the remaining 14 seats as dividers between the chosen representatives. We need to place these dividers in such a way that each chosen representative occupies a separate section.

To ensure that no two representatives occupy neighboring seats, we need to place the dividers such that each section contains at least one seat. We have 6 chosen representatives, so we need to place 5 dividers among the 14 remaining seats. This can be done in C(14, 5) ways.

Therefore, the total number of choices for selecting 6 representatives without any two occupying neighboring seats is given by:

Total choices = C(20, 6) × C(14, 5)

Total choices =  38760 × 2002

Total choices = 77597520

To know more about selecting click here :

https://brainly.com/question/28783648

#SPJ4

Answer:

count the unit squares

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Options:

A. 18, 20, 20, 22, 25

B. 20, 20, 20, 25, 25

C. 16, 19, 21, 22, 22

D. 20, 20, 21, 22, 22

Answer:

A. 18, 20, 20, 22, 25

Step-by-step explanation:

Required

Which list has a mean of 21 and median of 20

Each of the list have 5 numbers and they've all been sorted.

The median is the number at the 3rd position (i.e. the middle number)

So, list C and D are out because they do not have a median of 20.

Next, calculate the mean of lists A and B

[tex]\bar x = \frac{\sum x}{n}[/tex]

A. 18, 20, 20, 22, 25

[tex]\bar x = \frac{18 + 20 + 20 + 22 + 25}{5}[/tex]

[tex]\bar x = \frac{105}{5}[/tex]

[tex]\bar x = 21[/tex]

B. 20, 20, 20, 25, 25

 [tex]\bar x = \frac{20 + 20 + 20 + 25 + 25}{5}[/tex]

[tex]\bar x = \frac{110}{5}[/tex]

[tex]\bar x = 22[/tex]

Only list A has a median value of 20 and a mean value of 21

Answer:

8

Step-by-step explanation:

The degree of a polynomial refers to the term with the highest exponent.  Thus the highest exponent in a degree 3 polynomial is x3; for a degree 5 polynomial, it's x5.  When you multiply

x3*x5 = x3+5 = x8.  

So the product of a degree 3 polynomial and a degree 5 polynomial is a degree 8 polynomial.

Your leading term will result from the 3-degree term of the first polynomial, and the 5-degree term of the second.  So you'll have something like ax3 * bx5.  That will result in x3*x5=x8, so your product will have degree 8.

Answer:

Suppose we add up alternate Fibonacci numbers, Fn-1 + Fn+1; that is, what do ... L(1)=1 and L(3)= 4 so their sum is 5 whereas F(2)=1; L(2)=3 and L(4)= 7 so their ... What is the relationship between F(n-2), and F(n+2)? You should be able to find a ... Fib(N); K (an EVEN number!), Lucas(K) and Fib(K) in each expression like ...

Step-by-step explanation:

Answer:

no because it is not factorable

Step-by-step explanation:

Answer:

[tex]A) x+3[/tex]

Step-by-step explanation:

[tex]\frac{2x^{2}+14x+24 }{2x+8}[/tex]

[tex]=\frac{2(x^{2}+7x+12)}{2(x+4)}[/tex]

[tex]=\frac{x^{2} +7x+12}{x+4}[/tex]

[tex]=\frac{(x+4)(x+3)}{x+4}[/tex]

[tex]=x+3[/tex]

Answer:

B) 7x - 3 = 4

Step-by-step explanation:

3x - 12 = -9

3x = 3

x = 1

A) NOPE

x - 5 = -6

x = -1

B) YES

7x - 3 = 4

7x = 7

x = 1

Answer:

17*10^-3 miles

Step-by-step explanation:

Given data

Speed= 8.5×10^−6 miles per second

Time taken=2×10^3 seconds

We know that the expression for the speed is given as

speed= distance/time

distance= speed* time

substitute

distance= 8.5×10^−6* 2×10^3

distance= 8.5*2*(10^-6+3)

distance= 17*10^-3 miles

Answer:

2.8

Step-by-step explanation:

√(4² - 2²) = √12

=> √[(√12)² - 2²] = √8 ≈ 2.8

Answer:

hope this helped

Answer:

7

Step-by-step explanation:

Answer:

7 units north

Step-by-step explanation:

Count from 3,4 to 10,4 and there are seven units

The magnitude of the vertical force applied to the horizontal leg in the equivalent force system.

To determine the magnitude of the vertical force applied to the horizontal leg, we need to find the vertical component of the given force system. Looking at the diagram, we observe that the force system consists of a vertical force at point A and a horizontal force at point B. We can use trigonometry to find the vertical component of the force at point A.

Let's denote the magnitude of the force at point A as F_A and the angle it makes with the horizontal leg as θ. The vertical component of the force can be calculated using the formula: Vertical component = F_A * sin(θ).

Since the vertical component of the force should be equal to the force we are trying to find, we can set up the equation: Vertical component = F_vertical.

Now, we can substitute the given values into the equation and solve for F_vertical. Once we have the value, we can round it off to the nearest whole number, as instructed.

Please note that without specific values or angles provided in the problem statement or accompanying diagram, it is not possible to provide a precise numerical answer.

Learn more about angles here:

https://brainly.com/question/31818999

#SPJ11

Answer:

8

Step-by-step explanation:

it is

Answer:

8

Step-by-step explanation:

1/4 of 32

1/4 = 25%

25% of 32

32 × 25 ÷ 100

= 8

or

32 ÷ 4 =8

Answer:

The answer given is incorrect

The correct answer is Rs. 3640

The total cost of the paper required to cover one-half of the wooden cone is Rs. 3846.5.

The surface area of a cone is given by the formula:

surface area = π x r x s

where r is the radius of the base of the cone and s is the slant height of the cone. The slant height of the cone is the distance from the apex of the cone to the base, measured along the surface of the cone.

In this case, the diameter of the base of the cone is 14 cm, so the radius is half the diameter or 14 cm / 2 = 7 cm.

The vertical length of the cone is 24 cm, so the slant height of the cone is the square root of the vertical length squared plus the radius squared:

s = √(24² + 7²)

s = √(576 + 49)

s = √(625)

Which simplifies to:

s = 25 cm

Now that we have the radius and slant height of the cone, we can use the formula for the surface area of a cone to find the surface area of one-half of the cone:

surface area = π x 7 cm x 25 cm = 175π cm²

To find the total cost of the paper required, we need to multiply the surface area by the cost per square centimeter:

total cost = 175 x 3.14 cm² x  Rs.7/cm² = Rs. 3846.5

Therefore, the cost of the paper needed to cover one-half of the wooden cone is Rs. 3846.5.

Learn more about the cones here:

brainly.com/question/1578538

#SPJ2

The  hypothetical demand curve for tickets to a particular rock concert is given in the image attached.

According to Samuelson: theory, the law of demand states that people buy more at lower prices and less at higher prices when other things remain constant.

Note that by using the image,

Prices of ticket (cent)    Demand by consumer

5                                   35

4                                  30

3                                    70

2                                    80

1                                    95

Therefore, "Demands curves show how much people will buy the ticket at different prices over time." The Curve shows consumer purchases at different prices.

Learn more about Demand Curves from

https://brainly.com/question/16790743

#SPJ1

Answer:

1st: x-120

2nd: 0

3rd: x+12

4th: 120 + x

5th: x+12

im pretty sure that's right...?

I won't get brainliest lol

Answer:

See below

Step-by-step explanation:

[tex] \frac{3}{4} \div \frac{2}{5} \\ \\ = \frac{3}{4} \times \frac{5}{2} \\ \\ = \frac{3 \times 5}{4 \times 2} \\ \\ = \frac{15}{8} [/tex]

An A is a -algebra over X and A ∪ Ag is not a -algebra over X.

In this case, let's analyze the properties of the sets in question:

X = {a, b, c}

A = {4, X, {a}, {b, c}}

Ag = {4, X, {b}, {a, c}}

To determine if An A is a -algebra over X, we need to check if it satisfies the three conditions of a -algebra:

1. X ∈ An A: In this case, X = {a, b, c} ∈ An A, since X is a subset of itself.

2. An A is closed under complementation: For any set E ∈ An A, we need to ensure that its complement, X \ E, is also in An A. Let's check the sets in A:

- {4} ∈ An A: The complement is X \ {4} = {a, b, c}, which is not in An A.

- X ∈ An A: The complement is X \ X = ∅, which is in An A.

- {a} ∈ An A: The complement is X \ {a} = {b, c}, which is in An A.

- {b, c} ∈ An A: The complement is X \ {b, c} = {a}, which is in An A.

Since not all sets in A have complements in An A, An A is not closed under complementation and therefore not a -algebra over X.

Now let's analyze A ∪ Ag to determine if it is a -algebra over X:

1. X ∈ A ∪ Ag: Since X is a subset of itself, X ∈ A ∪ Ag.

2. A ∪ Ag is closed under complementation: For any set E ∈ A ∪ Ag, we need to ensure that its complement, X \ E, is also in A ∪ Ag. Let's check the sets in A and Ag:

- {4} ∈ A ∪ Ag: The complement is X \ {4} = {a, b, c}, which is in A ∪ Ag.

- X ∈ A ∪ Ag: The complement is X \ X = ∅, which is in A ∪ Ag.

- {a} ∈ A ∪ Ag: The complement is X \ {a} = {b, c}, which is in A ∪ Ag.

- {b, c} ∈ A ∪ Ag: The complement is X \ {b, c} = {a}, which is in A ∪ Ag.

Since all sets in A and Ag have complements in A ∪ Ag, A ∪ Ag is closed under complementation and is a -algebra over X.

In conclusion, option b is the correct answer: An A is a -algebra over X, and A ∪ Ag is not a -algebra over X.

To know more about -algebras, refer here:

https://brainly.com/question/32611431#

#SPJ11

Answer:

-31/8. That's the answer to your question

After considering the given data we conclude that the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis[tex](1, x, x^2, x)[/tex]is:
[0 1 0 0]
[0 0 2 0]
[0 0 0 3]
[0 0 0 0]
And the image of the polynomial is [tex]3 + 3x + 10x^2.[/tex]

The first part of the question asks for the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis [tex](1, x, x^2, x)[/tex] To find this matrix, we have to apply the derivative map to each basis vector and express the result as a linear combination of the basis vectors. The coefficients of these linear combinations will form the columns of the matrix representation.
Applying the derivative map to each basis vector, we get:
[tex]d/dx(1) = 0 = 0(1) + 0(x) + 0(x^2) + 0(x^3)[/tex]
[tex]d/dx(x) = 1 = 0(1) + 1(x) + 0(x^2) + 0(x^3)[/tex]
[tex]d/dx(x^2) = 2x = 0(1) + 0(x) + 2(x^2) + 0(x^3)[/tex]
[tex]d/dx(x^3) = 3x^2 = 0(1) + 0(x) + 0(x^2) + 3(x^3)[/tex]
Therefore, the matrix representation of the derivative map [tex]P_3(R) - - - > P_3(R)[/tex]with respect to the basis [tex](1, x, x^2, x)[/tex] is:
[0 1 0 0]
[0 0 2 0]
[0 0 0 3]
[0 0 0 0]
The second part of the question concerns  for the image of the polynomial 2x - 1 under the linear transformation h with matrix representation:
[0 2]
[2 1]
[4 2]
with respect to the bases B = {1+2, x} and D = {(1), (-1)}.
To evaluate the image of 2x - 1, we first need to express it as a linear combination of the basis vectors in B:
[tex]2x - 1 = (-1/2)(1+2) + (2)(x)[/tex]
Next, we need to evaluate the coordinate vector of this linear combination with respect to the basis B. The coordinate vector is:
[-1/2]
Now, we can evaluate the image of 2x - 1 under h by multiplying the matrix representation of h by the coordinate vector:
[0 2]
[2 1]
[4 2]
[-1/2]
Therefore, the image of 2x - 1 under h is [tex]3 + 3x + 10x^2.[/tex]
To learn more about linear combination
https://brainly.com/question/30480973
#SPJ4

Answer : Null Hypothesis (H0) The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is equal to or greater than the national average of 4%.”

Alternative Hypothesis (Ha) The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is significantly lower than the national average of 4%.”

Explanation :

a. Null Hypothesis (H0) is a statement which suggests that there is no significant difference between two populations or samples in the study. In this scenario, the null hypothesis can be stated as follows:“The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is equal to or greater than the national average of 4%.”

b. Alternative Hypothesis (Ha) is a statement that counters the null hypothesis by suggesting that there is a significant difference between two populations or samples in the study. In this scenario, the alternative hypothesis can be stated as follows:“The proportion of people choosing strawberry as their preferred flavor of ice cream in Berryville is significantly lower than the national average of 4%.”

Learn more about null and alternative hypothesis here https://brainly.com/question/30535681

#SPJ11

Answer:

A

Step-by-step explanation:

the total angles can only add up to 180°, therefore 35 + 70 = 105, 180 - 105 = 75°. 75° = A.

The calculated values of the functions are f(2) = 1/4, f(0) = 1 and f(-3) = 1/8

From the question, we have the following parameters that can be used in our computation:

f(x) = (1/2)ˣ

Using the above as a guide, we have the following:

f(2) = (1/2)² = 1/4

Also, we have

f(0) = (1/2)⁰ = 1

Lastly, we have

f(-3) = (1/2)⁻³ = 1/8

The graph of the function is attached

Read more about exponential functions at

https://brainly.com/question/2456547

#SPJ4

Answer:

<WZY = 31°

Step-by-step explanation:

First, we can see that <XZW is equal to <WZY.

Given that, we know we can set the two equations equal to each other to find "x".

8x - 1 = 5x + 11

Now that the two equations are set equal to each other, all we have to do is simplify to find x.

Bring 5x over and subtract it from 8x.

3x - 1 = 11

Bring -1 over and add it to 11.

Since you're subtracting a negative, it becomes positive allowing you to add it to 11.

3x = 12

Now you need to get x by itself. Do do that, you need to divide three by itself, and whatever you do to one side, you must do to the other.

3x/3 = 12/3

Now you have:

x = 4

____________________________________________________

Now that you know the value of x, all you need to do is plug x back into the equation for <WZY

5(4) + 11

20 + 11

31.

And there is your answer - <WZY = 31°

Answer:

not really good at maths. 15.33

Step-by-step explanation:

3(x-5)-7=3×8

3x-15-7=24

3x =24+15+7

3x = 46

Three will divide it's self to give you one and divide 46 to give you 15.333

(correct me if i'm wrong)

Answer:

[tex]65^{o}[/tex]

Step-by-step explanation:

Angles in a triangle add up to 180

An acute angle is any angle smaller than 90

Since it is a right angle triangle, one of the angles is a right angle and therefore 90

So 180 - 90 - 25 = 65