Five girls and two boys are standing in a line randomly. What is the probability that two boys are next to each other?

Answers

Answer 1
Answer: The fraction 2/7

========================================================

Explanation:

Let's say the teacher pulls the two boys out of the line, and stands in their place. So we have 5 girls and 1 teacher making 6 people total.

There are 6! = 6*5*4*3*2*1 = 720 different permutations here. Order matters. This involves the teacher, so let's have him/her step out of the line and have the two boys replace the teacher's position. This guarantees the boys stick together. For any permutation, we have 2 different ways to arrange the boys. So we have 2*720 = 1440 different ways to arrange the students so that the two boys are next to each other.

This is out of 7! = 7*6*5*4*3*2*1 = 5040 different permutations overall (we're arranging 5 girls+2 boys = 7 people).

The probability we're after is going to be 1440/5040 = 2/7

--------

Or you could see it like this

1440 = 2*6!

5040 = 7! = 7*6!

So,

1440/5040 = (2*6!)/(7*6!)

1440/5040 = 2/7


Related Questions

Can anyone help me please?? Thank you.​

Answers

I don’t know but I’ll say 10 m/ph this is because how do you get from 1 to 5 you multiply by 5 so you have to do the same thing to get the answer for minutes or kilometres per hour which in this case is kilometres per hour

Answer:

okay well the total distance is 3 and 1/3 km  and the speed that it was for him to go downstream was 2/3 km per hour

please help measuring !

Answers

180-102=78

78=2x+12
66=2x
33=x

The answer is 33

A health psychologist knew that corporate executives in general have an average score of 2.55 with a standard deviation of 0.5 on a stress inventory and that the scores are normally distributed. In order to learn whether corporate executives who exercise regularly have different stress scores, the psychologist measured the stress of 30 exercising executives and found them to have a mean score of 2.76. a. Using the five steps of hypothesis testing, was the group of 30 exercising executives different from executives in general? (Use the .05 significance level.) Be sure to sketch the distributions involved. Be sure to fully state the five steps and show ALL calculations/work. b. Additionally, explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual. (Be sure your explanation includes a discussion of the distribution of means--what it is, what it is made of, the concept of how it is created, how itʹs characteristics are created, its role in the overall hypothesis testing process.)

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Population mean (μ) = 2.55

Population standard deviation (σ) = 0.5

Sample size (n) = 30

Sample mean (x) = 2.76

α = 0.05

STEP 1:

Stress score in general executive (s1)

Stress score in exercising executive (s2)

Null : s1 = s2

Alternative : s1 < s2

STEP 2:

Shape of distribution = normal

Population mean (μ) = 2.55

Population standard deviation (σ) = 0.5

Sample size (n) = 30

Sample mean (x) = 2.76

α = 0.05

Decision rule :

α = 0.05 which corresponds to a t score (t0) ;

df = n - 1 = 30 - 1= 30 at 0.05 = 1.699

If :

(Test statistic (t) > t0) ; reject the Null

(right tailed test)

Test statistic (t) :

(x - μ) / (σ/√n)

(2.76 - 2.55) / (0.5/√30)

0.21 / 0.0913

= 2.30

t > t0

2.30 > 1.699

t is more extreme than t0

Hence, reject the null at α = 0.05

On field trips there must be 2 chaperones for every 15 students which ratio correctly express the ratio of students

Answers

Answer:

15:2 or 15 to 2

Step-by-step explanation:

They are asking for a ratio based on how many chaperones per student (in this case 15 students) In other words 15 students for every 2 chaperones.

HELPPP PLEASE!!!! SHOW ALL WORK!!!

Answers

Answer:

x=48

Step-by-step explanation:

Since these angles are supplementary, they add up to 180. so, you can set the equation x+23+x+61=81. Simplify the equation and solve for x

Answer:

#1 is x+23°=23

#2 is x+61°=61

Step-by-step explanation:

Because when you are adding it will always be a positive number

But when you are subtracting it will always be a negative number

I MARK BRAINLEIST! WHEN CONVERTING STANDARD FORM TO SCIENTIFIC FORM WITH A POSITIVE EXPONENT
YOU MOVE TO THE
O LEFT
O RIGHT

Answers

Answer:

You move the 0 to the right

Step-by-step explanation:

Ari rents the bike for 4 hours, and Meg rents the scooter for 3 hours. What is the total cost of the rentals?
The Total cost of the bike and scooter
rental is $___

Answers

Answer: it’s 66 I got it right

Step-by-step explanation:

Answer:

The answer will be 66 !!

Step-by-step explanation:

The answer will be 66 because if you look at the chart you can see how much money is cost to rent a bike for each hour. So for Ari, as he rented a bike it costs 9 dollars per hour. So Ari rented the bike for 4 hours, so multiply 4x9=36. Now for Meg, she rented a scooter for 3 hours, each hour means 10$. Now 3x10=30, Then just add 36+30 you get 66!

**Find the component form of the resultant vector.**

Answers

Answer:

[tex]\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)[/tex]

Step-by-step explanation:

Vector Addition

We are given the points A=(1,3), B=(-4,5), C=(-2,10), D=(0,1). Find:

[tex]\overrightarrow{AB}+\overrightarrow{CD}[/tex]

First, find both vectors from the initial and final points:

[tex]\overrightarrow{AB}=(-4-1,5-3)=(-5,2)[/tex]

[tex]\overrightarrow{CD}=(0-(-2),1-10)=(2,-9)[/tex]

Now find the sum of both vector by adding the components separately:

[tex]\overrightarrow{AB}+\overrightarrow{CD}=(-5,2)+(2,-9)=(-3,-7)[/tex]

[tex]\boxed{\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)}[/tex]

An above-ground swimming pool is leaking. After ½ hour the pool has leaked ⅞ of a gallon of water. How many gallons of water per hour is the swimming pool leaking?

Answers

Answer: 14/8 or 1 and 3/4 of a gallon

Step-by-step explanation: Since its leaking 7/8 every half hour, you would multiple 7/8 by two

0.25k + 1.5 - k - 3.5

Answers

Collect the like terms and the answer should be -0.75k -2 .... you may also find the app “Photo math” helpful as well :)

What is 3. 9, 27, 81, 243 can someone plz help

Answers

Answer:

This is an exponent problem. 3 to the power of 4 or maybe 5

Step-by-step explanation:

Each number in this pattern is multiplied by 3

12
Which value of x makes this equation true? *

- 4 (3 – x) + 2x = 8

Answers

Answer:

I believe that the answer is 3.33

Sara buys a sweater at a department store. The sweater costs $15. The store is having a 20% off sale on everything in the store.


With this sale, what is the final cost of the sweater? Do not consider the sales tax.

The sweater will cost $
dollars.

Answers

Answer:

The sweater will cost $12

Step-by-step explanation:

15 x 20% = 3 15 -3 = 12

What is the answer too −2/3(12c−9)+14c=

Answers

-2/3(12c - 9) + 14c

=-8c + 6 + 14c

=6c + 6

=6(c + 1)

Can someone quickly help me solve this ?!

Answers

Answer: 8

Step-by-step explanation: if you count the angels and the sides then you'll get the answer 8..

The answer is 8
Have a good date

−8 3/4÷2 1/6 please show me ur work

Answers

Answer:

- 4 1/26

Step-by-step explanation:

Solving in steps:

- 8 3/4 ÷ 2 1/6 =- 35/4 ÷ 13/6 =- 35/4 × 6/13 = - 35/2 × 3/13 =- 105/26 =- 4 1/26

Your brother is 1/5 your age. Your sister is 9 years older than your brother. Your sister is 11 years old. Write and solve an equation to find your age a.

Answers

Answer:

your age is 10 and your brothers age is 2 the equation is

Step-by-step explanation:

a=5b=b+9

the first part is how old you are the second is how old your brother is and the third is how old your sister

I’m joy gonna write it because you’ll think I copied but ^^ they’re right I got the same thing

PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((

Answers

Answer:

it is point B

Step-by-step explanation:

because im smart

Answer:

Point B

Step-by-step explanation:

√11 is 3.3

And A is about 2. Something and inbetween D and E is 4 which means C will be 3.5

So it leaves it at B

determine if the function f(x)=3^(2x-3) is exponential

Answers

An exponential function gives a variable raised to the power of x, where the variable is a positive real number

Yes, [tex]\underline{f(x) = 3 ^{(2 \cdot x - 3)}}[/tex] is an exponential function

Reason:

An exponential function is a function that can be written in the form;

f(x) = eˣ

Where;

e = Euler's number, which is the number approximately 2.71828

In the general form, an exponential number is a number given in the form;

f(x) = a·bˣ

Where;

b = A positive real number

The given function; [tex]f(x) = 3 ^{(2 \cdot x - 3)} = \dfrac{3^{2\cdot x}}{3^3} = \dfrac{1}{27} \times 9^x[/tex] is an exponential function

Where;

a = [tex]\dfrac{1}{27}[/tex]b = 9

Therefore, the correct response is; Yes, [tex]f(x) = 3 ^{(2 \cdot x - 3)}[/tex] is an exponential function

Learn more here:

https://brainly.com/question/17153778

jake went on a road trip with his family this summer. On Monday, they drove 629 miles. Tuesday, they drove 215 miles. On Wednesday, they drove 111 miles. And, on Thursday, they drove 588 miles. what is the total number of miles that Jake's family traveled​

Answers

Jake’s family traveled a total of 1,543 miles

What is a 20% tip on a $30 meal

Answers

$6 :)

Have an amazing day!

Which of the following equations is equivalent to x + y = 10?


Answers

Answer:

x + y - 10 = 0

Step-by-step explanation:

x + y - 10 = 10 -10

Move the constant to the left by adding its opposite to both sides

x + y - 10 = 0

The sum of two opposites equals 0

x + y - 10 = 0

^

^

Solution

Find the common difference of the arithmetic sequence 10,1,-8,...

Answers

The common indifference is -9 but I’m not 100% sure
Solution :AP : 10 ,1 , - 8

Common difference = Second term - first term

Common difference = 1 - 10

Common difference = - 9

a technician charges 25$ per hour plus 50$ for a house call to repair home computers. make a table and a graph to show the cost for 1,2,3, and 4 hours of home computer repair service. is there a direct variation?

Answers

Answer:

75$

Step-by-step explanation:

because 25+50=75

Answer:

The graph starts at $75 since the price for call is $50 and 1 hour of work costs $25.

Direct variation is only noticeable at the beginning of the graph after that the function is linear.

Step-by-step explanation:

PLS HELP ME I HAVE A FEW MINS TO ANSWER I'LL DO WHAT EVER YOU WANT JUST HELP ME

Answers

Answer:

a. 160-24=g

b. 160-24=g

   -24

   136=g

c. 136

Write the given statement of the following theorem.

If one angle of a triangle is 90° , then the other two add to 90°.

Answers

If the other two add up to 90° you would divide 90° by 2 getting a total off 45°

a conference hall has 33 rows.the last row contains 80 seats each row has two fewer seats than the row behind it.how many seats are there second to the last row?​

Answers

Answer:

there are 84 seats in the  second to the last row

Step-by-step explanation:

Given that

each row has two fewer seats than the row behind it

It means that

if first row has x seats then

no of seat in second row has (x-2) seats.

and similarly

no of seat in third  row =no of seat in second row - 2seats.

no of seat in third  row = (x-2) seat - 2 seats = x - 4 seats

_____________________________________________

Given that

last row has 80 seats

let the number of seat in first to the last row be x

then number of seat in last row = x-2

we know number of seat in last row = 80

thus

x - 2 = 80

x = 82

Thus,

the number of seat in first to the last row is 82

Similarly let the number of seat in second to the last row be y

then number of seat in first to the  last row = y-2

since number of seat in first to the last row is 82

thus

y-2 = 82

y = 82 + 2 = 84

Thus, there are 84 seats in the  second to the last row.

_________________________________________________

Lances goal is to run 16 laps around the track. Each lap is 350 yards. Currently lances ran 2450 yards around the track. How much is his percent did he run so far??

Answers

Answer:

Hi There!

Your answer is :

He ran 43.75% so far.

Step-by-step explanation:

16 laps = GOAL

350* 16 to determine goal yards

16laps = 5,600yrds

1 lap= 350 yrds

xlaps = 2450 yrds

2450/350 to determine x laps.

7 laps = 2450 yards

He is 2450 yards into his 5,600 yard goal.

IF 5,600 = 100%

/5600

1 yard = 1/56th %

* 2450

2450yards = 43.75%

Hope this helps

How to show the value of 11 in two different ways

Answers

Answer:

1 x 11

10 + 1

Step-by-step explanation:

can someone help me it is math

Answers

Its 1/6

Have a good day

Answer:Its 1/6

Step-by-step explanation:

49×38= 4 × 39 × 8= 12/72= 12 ÷ 12/72 ÷ 12= 16

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