A relation is?
a.)the output (y) values of the relation

b.)the input (x) values of the relation

c.)a set of points that pair input values with output values

d.)x and y values written in the form (x, y)

To find the probability that no two people will occupy adjacent seats, consider that n people are seated in a random manner in a row containing 2n seats. Using counting rule for combinations the total number of ways to select n seats of 2n seats is N=(2n/n). 

Now consider an event M that all two people occupy adjacent seats. This can be done by occupying all odd seats so that the even seats are left empty. This arrangement leaves the last 2nth seat empty. Even if one occupies that seat the condition of the event will not break. So, we have (n + 1) seats available for the n people to seat so that no two people occupy adjacent seats. N(M) = (n+1). Thus, the probability that no two people will occupy adjacent seats in a row of 2n seats can be computed as shown :

The probability that no two people will occupy adjacent seats is [(2n-1)!!]/[(2n)!].

To find the probability that no two people will occupy adjacent seats, we need to count the total number of possible arrangements where no two people are seated next to each other, and divide it by the total number of possible arrangements.

Let's consider a scenario where we have 2 people and 4 seats. In this case, the possible arrangements where no two people are seated next to each other are:

So, there are 3 possible arrangements where no two people are seated next to each other out of the total 6 possible arrangements.

Generalizing this, for n people seated in a row containing 2n seats, there are (2n-1)!! possible arrangements where no two people are seated next to each other. The double exclamation mark denotes the double factorial.
Hence, the probability is [(2n-1)!!]/[(2n)!].

https://brainly.com/question/32117953

#SPJ3

Final answer:

By calculating slopes of the triangle's sides and identifying that two of them are negative reciprocals of each other, it's confirmed that the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle.

Explanation:

To determine if the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle, we calculate the slopes of all three sides. The slope of the line between points (-4, 4) and (1, 5) is calculated using the slope formula m = (y2 - y1) / (x2 - x1). Using the coordinates, the slope is (5 - 4) / (1 - (-4)) = 1 / 5. Similarly, the slope between points (1, 5) and (2, 0) is (0 - 5) / (2 - 1) = -5. Lastly, the slope of the line between (-4, 4) and (2, 0) is (0 - 4) / (2 - (-4)) = -4 / 6, which simplifies to -2 / 3. A right triangle has one 90-degree angle, and the slopes of perpendicular lines are negative reciprocals of each other. Therefore, if two of these slopes are negative reciprocals, the triangle is a right triangle. In this case, the slopes -5 and 1/5 are negative reciprocals, confirming that the triangle is a right triangle.

Answer

third option

Step-by-step explanation:

Answer:    

The correct option is C. f(x) = |x + 3| + 2

Step-by-step explanation:

The parent function in this case is : mod x = |x|

Let the parent function be f(x) = |x|

Now, The parent function is transformed 3 units to the left

⇒ f (x) = f(x + 3)

⇒ f(x) = |x + 3|

Also, The parent function is transformed up by 2 units

⇒ f(x) = f(x) + 2

⇒ f(x) = |x + 3| + 2

Therefore, The correct option is C. f(x) = |x + 3| + 2

Answer with explanation:

If you will count the faces of this three dimensional geometrical shape , there are 5 faces in which there are 2 triangles and 3 Quadrilaterals.

So,to draw the net of this solid , you need

⇒As there are 3 Quadrilaterals which is in the shape of parallelogram,

   You need three rectangles ,to draw the net of this object.

Option C: 3

Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.

https://brainly.com/question/32745737

#SPJ12

Reflecting a function across the y-axis will not change its domain or range; for an even function, such as one described by y(x) = -y(-x), the function is inherently symmetric about the y-axis, and thus both the domain and range remain unchanged.

The correct option is  A. Both the domain and range change.

When a function is reflected across the y-axis, its domain and range may be impacted. Reflecting a function across the y-axis replaces each point (x, y) with (-x, y). If the original function is y(x) = -y(-x), then we are dealing with an even function, which is symmetric about the y-axis. In the case of even functions, reflecting them across the y-axis does not change the graph because they are already symmetric. Hence, the domain and the range of the function remain the same after the reflection.

The domain of a function is the set of all possible x-values, and the range is the set of all possible y-values. For a function reflected across the y-axis, the x-values are negated, but since the domain typically includes both positive and negative values for x, the overall set of possible x-values (the domain) does not change. Moreover, the y-values stay the same since they are not affected by the reflection across the y-axis, and thus the range remains the same as well.

The correct option is  A. Both the domain and range change.

To compute for combinations, we will use the method nCr = n! / r! * (n - r)!

Where: n signifies the number of items, and r signifies the number of items being selected at a time.

Solution

1.       11C5 = 11!/ 5! * (11-5)! = 462 ways

2.       6C5 = 6!/ 5! * (6-5)! = 6 ways

3.       6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.

The calculation involves using combinations to find the total number of ways to select 5 people from 11, and then to find the probability of selecting 5 men by dividing the number of ways to select 5 men from 6 by the total number of selections.

The student's question deals with the topic of combinatorics, specifically the selection of groups and calculation of probabilities using the hypergeometric distribution. To find how many ways 5 people can be selected from a group of 11 (6 men and 5 women), we use the combination formula [tex]C(n, k) = n! / (k!(n-k)!).[/tex]

For the first part of the question, selecting 5 people out of 11, the calculation is C(11, 5). To calculate the number of ways 5 men can be selected from 6 men, we use C(6,5).

Lastly, to find the probability that the selected group will consist of all men, we divide the number of ways to select 5 men by the total number of ways to select 5 people from the whole group:

https://brainly.com/question/35126689

#SPJ3

To find the zeros of the function f(x) = 4x2 – x – 5, we first set the equation to zero, factor it to find (4x - 5)(x + 1) = ​0, and solve for x, finding the zeros to be 5/4 and -1.

The first step in factoring the quadratic function f(x) = 4x2 – x – 5 is to set the equation to zero.

The factored form of a quadratic equation is generally represented as (ax + b)(cx + d) = 0, where x is the zeros of the function. So, the equation we have is 4x² - x - 5 = 0.

Now, we need to look for two numbers that multiply to (a*c) = -20 (4*-5) and add up to -1 which are -5 and 4. Hence, the middle expression -x can be expressed as -5x + 4x, so the equation becomes:
4x² - 5x + 4x - 5 = 0.

Factoring, we get the following:
x(4x - 5) + 1(4x - 5) = 0.

Or we could write as:
(4x - 5)(x + 1) = ​0.

Now, to find zeros of the function, we set each factor equal to zero and solve for x:

4x - 5 = 0 implies, x = 5/4.

x + 1 = 0 implies, x = -1.

So, the zeros of the function are 5/4 and -1.

https://brainly.com/question/30398551

#SPJ2

The value of b is [tex]\dfrac{38}{5}[/tex].

In this, the power of x is 1. And it consists of the variable and/or constant term only.

Given

f(x)=5x−5

The average of that is 14 for the [0, b]

To find

The value of b.

For the x = 0, the value of f(x) will be

f(0) = -5

For the x = b, the value of f(x) will be

f(b) = 5b - 5

The average of that is 14.

[tex]\begin{aligned} \rm Average &= \dfrac{f(0)+f(b)}{2} \\14 &= \dfrac{(-5)+(5b-5)}{2} \\28 &= 5b -5 -5\\28 +5 + 5 &= 5b\\5b &= 38\\b &= \frac{38}{5} \\\end{aligned}[/tex]

Thus, the value of b is [tex]\dfrac{38}{5}[/tex].

More about the linear equation link is given below.

https://brainly.com/question/11897796

Answer:

This can be written as x/3, in which x is the number of students.

Step-by-step explanation:

The term quotient means to find what happens when you divide the first by the second. Then we need to pick a variable for the unknown number of students.

using the equation for the transformation:

(x+1, 3y)

 add 1 to very X and multiply y by 3

 so (-2,0) becomes (-1,0)

(-2,3) becomes (-1,9)

(-5,1) becomes (-4,3)

new coordinates are (-1,0) (-1,9) (-4,3)

you don't have an image attached, so to see if they are congruent, the sides need to stay the same lengths and the angles need to stay the same, from the coordinates of the new triangle, I would say they are not congruent

to find x divide 16 by the sin of 30

16 / sin(30) = 32

 if you need 2 decimal places it would be 32.00

Answer:

16  sin30 = 32

Step-by-step explanation:

Answer:

AAS Congruence Theorem

Step-by-step explanation:

i dont know bro

Answer: AAS Congruence Theorem

Step-by-step explanation:

In the given picture , we have given two triangles ΔFGJ and ΔHJG with one common edge i.e. GJ

Now, in the given triangles ΔFGJ and ΔHJG we have

∠F=∠H   [given]

and ∠FGJ=∠HJG  [given]

Also, GJ=GJ            [Reflexive property]

Therefore, by AAS Congruence Theorem,

ΔFGJ ≅ ΔHJG

Answer:

C.) Point B is between points A and C.

Step-by-step explanation:

The simplest way to analyze this is as a line.

This line goes from A to C and somewhere in the middle, is B.

But they tell you that AB + BC = AC.

The distance from A to B plus the distance from B to C is the same as the distance from A to C.

Option A about planes is not the correct one because there's no mention of planes.

Option B about angles is not correct because they only talk about some points of a line. You don't know if there's some angle in between.

The same happed with options D and E.

The recipe requires 2.5 pounds of meat.

we have,

To convert ounces to pounds, we use the conversion factor that 16 ounces is equal to 1 pound.

This means that every pound is made up of 16 ounces.

Given that the recipe calls for 40 ounces of meat, we can divide this quantity by the conversion factor of 16 ounces per pound to find the equivalent in pounds.

Dividing 40 by 16 gives us 2.5. So, the recipe requires 2.5 pounds of meat.

This conversion is based on the relationship between ounces and pounds, where each pound consists of 16 ounces.

So,

When converting from ounces to pounds, we divide the number of ounces by 16 to find the equivalent number of pounds.

Therefore,

The recipe requires 2.5 pounds of meat.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6