three couples have reserved seats in a row for a concert. in how many different ways can they be seated when

Answers

Answer 1

a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.

b) If each couple sits together, there are 48 different arrangements for three couples to be seated.

What is Fundamental counting principle?

If an event can happen in m different ways and another event can happen in n different ways, then the sum of the occurrences of the two events is m x n.

Given:

Three couples have reserved seats in a row for a concert.

(a) There are 3 couples, so 6 people must be seated in seats in row.

It is permutation of 6 elements, therefore, there are

6!=720 ways three couples can be seated when there is no seating restriction.

(b) We want that each couple sits together.

First we will find the number of permutations of 3 couples:

There are 3!=6 permutations of couple. (they can be ordered in 6 different ways).

Now we will find the number of permutations of each couple:

There are 2!=2 permutations of 2 people that makes a couple.

Therefore, by Fundamental Counting Principle, there are

3! ⋅ 2! ⋅ 2! ⋅ 2! = 6 ⋅ 2 ⋅ 2 ⋅ 2 = 48

ways three couples can be seated when each couple sits together.

Hence,

a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.

b) If each couple sits together, there are 48 different arrangements for three couples to be seated.

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Complete question:

Three couples have reserved seats in a row for a concert. In how many different ways can they be seated when (a) there are no seating restrictions? (b) each couple sits together?


Related Questions

Solve 3x² - x = 10

A.X=2 and X=-15
B. X=-5 and X= 2/3
C. X=-5/3 and X=2
D. X=-3 and X=10

Answers

Answer:

C. x = -5/3 and x = 2

Step-by-step explanation:

Bring the 10 over to the other side of the equation.

3x² - x - 10 = 0

Factorise.

(3x + 5)(x - 2) = 0

3x + 5 = 0 or x - 2 = 0

3x = -5 or x = 2

x = -5/3 or x = 2

use the product rule to find the derivative of the given function. b. find the derivative by expanding the product first.

Answers

The derivative of the given function using product rule is 6x+1 .

What is Product Rule?

This rule is used when we want to differentiate a function that may be regarded as the product of one or more functions.

Let u(x) and v(x) be differentiable functions.Then the product of the functions u(x)v(x) is also differentiable and: (uv)′=u′v+uv′

Main Body:

We add the derivative of the first times the second to the first times the

derivative of the second.

Power Rule:

If f(x)=xn

where n is any real number, then:

(xⁿ)′=nxⁿ⁻¹

. We have,

f(x) = (x-1) (3x+4)

Differentiate with respect to z by using product rule

(uv)′=u′v+uv′

h' (x) = (x-1)' (3x+4) +(x-1)(3x+4)'

h'(X) = 1(3x+4) + (x-1) (3)

On simplifying:

h'(x) = 3x+4 +3x-3

h'(x) = 6x +1

Hence the derivative of function is 6x+1.

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let m be the number of five-element subsets that can be chosen from the set of the first 14 natural numbers so that at least two of the five numbers are consecutive. find the remainder when m is divided by 1000.

Answers

There are 123 different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

Probability: The branch of mathematics known as probability deals with numerical expressions of the probability that an event will occur, or the probability that a statement will be true.

The probability of an event is a number between 0 and 1, with approximately 0 meaning improbability and 1 meaning certainty.

The probability of an event occurring increases with its probability. A simple example is tossing a fair (fair) coin.

Both outcomes (heads and tails) have equal probability, the coin is fair, heads are more likely than tails, there are no other possible outcomes, and either outcome has half the probability.

According to our question:

Let n be the maximum number of subsets of 5 elements that can be chosen from the first 14 natural numbers,

where at least 2 of the 5 digits are consecutive.

We created a block of two consecutive numbers ((1,2), (2,3), (13,14), etc.).

Now you can select this block in 13 different ways. You have to choose 3 numbers from the remaining 12 numbers.

So, from the multiplication principle, we know that we have 13 × (123).

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Can someone please help me

Answers

Answer:

6

Step-by-step explanation:

Perimeter = 2l + 2w

48 = 2(18) + 2(w)

48 = 36 + 2w

12 = 2w

w = 6

Could you please give me brainliest for this? Thank you!

question: 14. which of the following shapes replaces the question mark to complete the series? ? 8 oo aa

Answers

Pattern Recognition is defined as the pattern is a number, shape, or something repeated in a particular way. Analysis of patterns should consider on different basis. The correct option is option (d).

The main basis of Pattern Recognition are the following:

1. Color change

2. Shape change

3. Rotation change

4. Size change

we have given three shapes pattern and we have to find out the perfect shape for forth place and the required shape follow the order like others.

After examine the pattern, we can see that the first figure is a filled triangle and the second figure is a hollow circle. This pattern is maintained alternately. The last figure(3rd place) is an open circle, so the next figure is a filled triangle.

So, the correct option is d.

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9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.

Answers

The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.

A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.

Initial Pass: 2 9 8 7 6 5 1 4 3

The array's first two members are initially compared using an insertion sort.

Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.

Therefore, 2 is currently kept in a sorted sub-array.

Second Pass: Continue with the next two elements and compare them.

2 8 9 7 6 5 1 4 3

Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.

Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.

Moving on to the following two components, which are 9 & 7,

2 7 8 9 6 5 1 4 3

Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.

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Helppppppppppppppppppppppppp

Answers

First, evaluate (-4/7)^2 to get 16/49

Then multiply by the negative for -16/49

Answer:

-[tex]\frac{16}{49}[/tex]

Step-by-step explanation:

First do: (-[tex]\frac{4}{7}) ^{2}[/tex], which is -[tex]\frac{4}{7}[/tex]*-[tex]\frac{4}{7}[/tex] which is [tex]\frac{16}{49}[/tex] and then add in the other negative:   -[tex]\frac{16}{49}[/tex]

What is the distance between (-3, 4) and (-3, 10)? on a graph

Answers

Answer:

6 units away

Step-by-step explanation:

Since they already have the same x-axis I just need to find the difference in the y-axis

the base of the first booth is the shape of a triangle. write a polynomial that represents the area of the booth. write your answer in descending order. please use the palette below to enter your answer.

Answers

The polynomial that represents the area of the booth is 3[tex]t^3[/tex]-12t.

How to calculate polynomial for triangle area?

Polynomial is a expression of variable, coefficients, and constants with mathematics operation of subtraction, addition, multiplication, and powers (only positive integers) of variable.

So, basically to calculate polynomials is the same as normal calculations except that the numbers are changed to variables.

Base length = 2[tex]t^2[/tex]-8

Height length = 3t

Calculate the area of triangle. So,

Area of triangle = (1/2) × base × height

= (1/2) × 2[tex]t^2[/tex]-8 × 3t

= (1/2) × 6[tex]t^3[/tex]-24t

= 3[tex]t^3[/tex]-12t

Thus, the area of the booth can be written by this polynomial 3[tex]t^3[/tex]-12t.

Your question is incomplete, but most probably your full question was (image attached).

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In two or more complete sentences, describe how to determine if the function f(x)=2cos(x) is even by looking at a graph.

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The given function f(x) = 2 cos (x) is an even function because the result of the cosine of negative angles are the same with those of positive angles.

How to determine an Even Function?

To check if a function is odd or even, we have to calculate f(−x).

The function is even if f(-x) = f(x)

The function is odd if f(-x) = -f(x)

We are given the function as; f(x) = 2 cos (x)

f(-x) = 2 cos (-x)

Now, we know that the cosine of a negative angle always gives the same value as the cosine of the positive angle and as such, we can say that;

2 cos (-x) = 2cos (x)

The same result as f(x) which tells us that it is an even function

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if a set of exam scores forms a normal, symmetrical distribution with all measures of central tendency in the center of the distribution, what can you conclude about the students' scores?

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If a set of exam scores forms a normal, symmetrical distribution with all measures of central tendency in the center of the distribution we can say about student's score that, about an equal number of students had relatively high and relatively low score.

A symmetrical distribution entails that the scores have the same number at a given distance above or below the average. Therefore an equal number of people had relatively high and relatively low scores. This contradicts most having relatively high or low scores, or not drawing any conclusions about scores.

Symmetrical distribution is evident when values of variables occur at a regular interval. In addition, the mean, median and mode occur at the same point.

Three of the many ways to measure central tendency are the mean, median and mode.

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Which is the best estimate of the
solution for the system of linear
equations graphed below?
A.(0.5,2)
B. (1.5, 2)
C. (2,1.5)
D. (2.5, 1.5)

Answers

Answer:

B. (1.5, 2)

Step-by-step explanation:

Hope it helps!

Answer:

B

Step-by-step explanation:

The intersection of the two lines looks to be about (1.5 , 2)

3x + 4x +5x = 4(x + 2) Please write as the actual answer and a decimal

Answers

Answer: 1

Step-by-step explanation:

We can rewrite the equation as

12x = 4x +8

8x= 8

x=1

Find the missing value. Round your answer to the nearest tenth of a percent. Principal=$1300, Rate=?, Time=18 months, Simple Interest=$90

Answers

The missing value in the simple interests formula is rate and it is solved to be 4.62%

How to find the rate

The formula for simple interest is

= P * T * R / 100

P = principal= $1300

T = time = 18 months = 1.5 years

R = rate = ?

simple interest = $90

substituting the values

90 = 1300 * 1.5 * R / 100

90 * 100 = 1300 * 1.5 * R

9000 = 1950R

R = 9000 / 1950

R = 4.615385

R = 4.62

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33, 25, 42, 25, 31, 37, 46, 29, 38 what is the interquartile range of the data?

Answers

The interquartile range of the data will be 13

When arranged from lowest to highest, the IQR reflects the median 50% of values. To calculate the interquartile range (IQR), firstly compute the median (middle value) of the data's lower and upper halves. All those are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The interquartile range is the difference between quarters three and then one.

first, let us sort the data from lowest to highest

25,25,29,31,33,37,38,42,46

Q1- median of the lower half of the data=(29+25)/2=27

Q3-median of the upper half of the data=(38+42)/2=40

the interquartile range of the data will be Q3-Q1

40-27= 13

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Five bands in a tour agree to determine the order of performance based on random selection. The names are placed on cards and the cards are pulled randomly.

What is the probability of Ultraviolet performing fourth and Abacus performing last?
A: 3/5
B: 7/120
C: 7/32
D: 1/20

Answers

The probability of Ultraviolet performing fourth and Abacus performing last is 1/20.

What is probability ?

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

In a tour, five bands agree to determine the order of performance on the basis of random selection.

Since, the name of 5 bands are pulled randomly.

The probability of Ultraviolet performing fourth = 1/5

And the probability of Abacus performing last = 1/4, since 1 place is fixed for Ultraviolet.

Probability of Ultraviolet performing fourth and Abacus performing last

= 1/5 x 1/4 = 1/20

The required probability is 1/20.

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What is the difference in total degrees between a regular hexagon and a regular pentagon?.

Answers

Answer:

180

Step-by-step explanation:

Pentagon has a total interior angle of 540 degrees.

Hexagon has a total interior angle of 720 degrees.

720-540 = 180

in regression analysis, measures the proportion of the variation in the dependent variable that is explained by the independent variable(s).

Answers

The coefficient of determination (R² or r-squared) is a statistical measure in a regression model that determines the proportion of variance in the dependent variable that can be explained by the independent variable.

What is variance?

Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.

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if i don't get this right i fail

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The value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

Applying intersecting secants theorem:

4(4 + x) = 3(3 + 5)

16 + 4x = 24

4x = 8

x = 2

In the second circle:

9(4x) = 8(4x+2)

After solving we get:

x = 4

Thus, the value of x in the first circle is 2, and in the second circle is 4 after applying the intersecting secants theorem.

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If x4xy= x16, what is the value of y?

Answers

Answer:

4/x

Step-by-step explanation:

Simplify: 8x62x4
A.6x2
B.4x2
C.8x10
D.10x10

Answers

You Would Multiply 8x62x4 and then Multiply all of the other options a, b, c, and d and see which one matches, but none of them matches

Please Help what is x

Answers

Answer:  x=[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

There are special right triangles in this! First, you need to find out what I am saying.

45-45-90 triangle

The bottom triangle has angles measures of 45, 45, and 90 degrees. There is a theorem that states that the two legs are equal, and the hypotenuse is leg×[tex]\sqrt{2}[/tex].

Plugging it in will give you leg lengths of  [tex]4\sqrt{2}[/tex].

Plug in that number into the side that connects with our next very special triangle:

30-60-90 triangle

Another theorem states that the hypotenuse is shorter leg times 2, the longer leg is shorter leg times [tex]\sqrt{3}[/tex].

Great! We have the shorter leg. Now we need to find the hypotenuse. Multiply [tex]4\sqrt{2}[/tex] by 2, and you get [tex]8\sqrt{2}[/tex]. That is x!

The final answer to this problem is: x=[tex]8\sqrt{2}[/tex]

Hope this helped a lot!

My answer would be x is equal to 8 check 2

i need help ASAP please.​

Answers

Answer:

altitude=8mm

Step-by-step explanation:

so a^2+b^2=c^2

substitute and you get

a^2+6^2=10^2

a^2+36=100

a^2=100-36=64

a^2=64

a=8

Answer: 8 mm

Step-by-step explanation:

      The altitude of the triangle can also be known as the "height" from the highest point as a straight line perpendicular to the opposite side (the "bottom" which is also known as the "base" of the triangle).

      This altitude makes two right triangles, so we will use the Pythagorean theorem to help us solve.

      a² + b² = c²

      a² + (6)² = (10)²

      a² + 36 = 100

      a² = 64

      a = 8

 

           The altitude of this triangle is 8 mm.

Triangle PQR has the following measures: p= 16.2 m, q = 35.0 m, and m/R = 75°.
What is the area of triangle PQR?

Answers

After solving the area of the triangle PQR obtained will be equal to 273.6 m²

What is a triangle?

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given information given in the question,

p= 16.2

q = 35.0 m and,

m ∠R = 75°

Find x by cosine rule,

cos 75° = (16.2² + 35² - x²)/(2 × 16.5 × 35)

x = 34.5 m

The value of r is 34.5 mm then the third side of the triangle pqr will be,

Use heron's formula,

s = (16.2 + 35 + 34.5)/2

s = 42.85

Area = [tex]\sqrt{s(s-p)(s-q)(s-r)}[/tex]

A = √42.85(42.85 - 16.2)(42.85 - 35)(42.85 - 34.5)

A = 273.6 m²

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a binomial distribution has a 60% rate of success. there are 18 trials. what is the probablility that there will be at least 12 successes

Answers

The probability that there will be at least 12 successes in the total 18 trials with 60% rate of success is ¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

Binomial Probability distribution, In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments.

We have given that :

Rate of sucess (p) = 60% = 0.6

Rate of failure (q) = 1 - 0.6 = 0.4

Number of trials (n) = 18

We want to find P(there will be at least 12 sucess)

Use binomial distribution to find given mentioned probability.

X ~ Bin( 18, 0.6)

P (X= x ) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

Let, X= Number of success among 18

So that it suitable for binomial distribution with parameters are n and p.

P(there will be atleast 12 success)

= P(X>= 12)

18

= ∑ ⁿCₓ (p)ˣ(q)⁽ⁿ⁻ˣ⁾ =

x = 12

¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰

= say x

Hence, the required probability is x

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Find the area of the composite figure. I got 78 but my teacher said that it is incorrect. WILL MARK BRAINLIEST! Thanks!

Answers

Answer:

44

Step-by-step explanation:

Essentially there are 3 triangles

The top left has a base of 5 and a height of 4

Its area is 1/2 x b x h = 1/2 x 5 x 4 = 10

Then there are two triangles with the same base of 2.5 + 6 = 8.5 and same height of 4 feet. So each of the triangles has the same area as the other.

Total area of both triangles = 2 (1/2 x b x h) = bh = 8.5 x 4 = 34

Total area = 10 + 34 = 44

Answer:

44 ft²

Step-by-step explanation:

Here's how I divided the parts of the composite figure:

1. There is a triangle at the left with the vertex pointing down and base above. The base is 5 ft. The height is 4 ft.

2. There are 4 triangles left. I divided them into two triangles like this:

An upper triangle which has a base of 2.5 ft + 6 ft, and a height of 4 ft with a horizontal base on the bottom and a vertex on the upper side.

A lower triangle that is a mirror image of the triangle just above. The dimensions are the same.

Triangle on upper left:

base = 5 ft

height = 4 ft

Triangles at right (2 triangles with the same dimensions)

base = 2.5 ft + 6 ft = 8.5 ft

height = 4 ft

area of triangle = base × height / 2

Total Area = (5 ft)(4 ft)/2 + 2 × (8.5 ft)(4 ft)/2

Total Area = 10 ft² + 34 ft²

Total Area = 44 ft²

Given that (-2,3) is on the graph of y=f(x), find a point that must be on the graph of y=f(2x+1)+3. Express your answer as an ordered pair (a,b) where a and b are real numbers.

Answer for 100 points.

Answers

The ordered pair that is on the function y=f(2x+1)+3 is (-3/2, 6)

Which ordered pair is on the function y=f(2x+1)+3?

Here we know that for the function:

y = f(x)

And we know that the point (-2, 3) belongs to the function, this means that:

f(-2)= 3

Now we want to find a point on the function:

f(2x + 1) + 3

If we find x such that:

2x + 1 = -2

2x = -3

x = -3/2

Now we can evaluate the function in that value of x to get:

y = f(2*-3/2 + 1) + 3

y = f(-2) + 3

y = 3 + 3

y = 6

Then we have the point (-3/2, 6) on the function.

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explain why we need to define the vector space p n as the set of all polynomials with degree up to and including n instead of the more obvious set of all polynomials of degree exactly n .

Answers

Any n-dimensional vector should be able to be represented in space

What is standard form of a polynomial?

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on.

To find the degree of the polynomial, add up the exponents of each term and select the highest sum ( if there are more than 1 variable in single term) or highest power of variable

Any n-dimensional vector should be able to be represented in space.

If it only has terms of degree n, it can only express polynomials of degree n.

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Two towns have accumulated different amount of snow. IN town 1, the snow depth is increasing by 3 1/2 inches every hour, and currently has 5 inches of snow. IN town 2, the snow depth is increasing by 2 1/4 inches every hour, and currently has 6 inches of snow. In how many hours will the snowfall of both towns by equal.

Answers

The snowfall of both towns by equal in 4/5 hours or 48 minutes.

What is a linear equation?

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Assuming the no. of hours to be x, therefore the expression for town 1 is

y = (7/2)x + 5 and the expression for town 2 is y = (9/4)x + 6.

The snowfall of both towns by equal when,

(7/2)x + 5 = (9/4)x + 6.

(7/2)x - (9/4)x = 6 - 5.

[(14 - 9)x]/4 = 1.

(5/4)x = 1.

x = 4/5 hours Or (4/5)×60 = 48 minutes the snowfall of both towns by equal.

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Someone answer this please thank you

Answers

Answer:

The answer is 1/2

Step-by-step explanation:

x1 y1. x2. y2

(5, 8) (2, 2)

So you suppose to subtract xl by x2 then subtract y1 by y2

5-2.

------=

8-2.

which equal 3/6. Which 3/6 is equal to 1/2

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