9 friends are lining up. Joe, Susan, John, and Meredith must be beside each other. How many ways can they line up?

Answers

Answer 1
Answer:  17,280

This is one single number slightly over 17 thousand.

You may need to erase the comma when typing the answer in.

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

Explanation:

Let's say that another person steps in for Joe, Susan, John, and Meredith. I'll refer to this person as the teacher (perhaps these 9 friends are students on a field trip).

The 9 friends drops to 9-4 = 5 people when those four named people leave the group temporarily. Then it bumps up to 5+1 = 6 people when the teacher steps in. Wherever the teacher is located, the four friends that left will replace the teacher. This guarantees that those four friends stick together.

There are 6! = 6*5*4*3*2*1 = 720 ways to arrange those 6 people. The exclamation mark is a factorial symbol.

Within any of those 720 permutations, we have 4! = 4*3*2*1 = 24 ways to arrange those group of named people when they come back to replace the teacher.

So overall the answer is 4!*6! = 24*720 = 17,280

You may need to erase the comma when typing the answer in.

-------------

Side note: There are 9! = 362,880 ways to arrange all nine friends regardless if those four mentioned people stick together or not. We see that they stick together roughly (17,280)/(362,880) = 0.0476 = 4.76% of the time.


Related Questions

Elise's math exam had 50 problems on it. She was able
to do 36 of them in 1 hour. What percent of the math problems did
she complete?

Answers

Answer:

72%

Step-by-step explanation:

Elise did 36 out of 50 problems in 1 hour. Another way to write 36 out of 50 is 36/50.

To find the percent from a fraction, one thing we can do is make the denominator 100 but still make the fraction the same, and then take the numerator.

We have 36/50, but want to make the denominator 100, not 50. We know that 100/50 = 2, so we have to multiply 50 by 2 to get 100.

Keeping the fraction equal, we can multiply 36/50 by 2/2 to get 72/100. We can do this because 2/2=1, so we are keeping the fraction the same -- just changing the numbers a little bit.

A fraction of form x/100 is equal to x%, so 72/100 = 72% as our answer

Help. I will be guessing on this, but I want to make sure this is on here so no one has to guess like I am. Help a brother out

Answers

Answer:

Line 3

Step-by-step explanation:

→ Calculate gradient

[tex]\frac{6-3}{4-2} =1.5[/tex]

Answer:

Line 3

Step-by-step explanation:

(0,0) & ( 4 , 6)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

Negate the conditional statement.
(~ a V ~ b) ►c

Please show your work and give an explanation.

Answers

(not a or not b) implies c   <==>   not (not a or not b) or c

so negating gives

not [(not a or not b) implies c]   <==>   not[ not (not a or not b) or c]

which we can simplify somewhat to

not (not (not a or not b)) and not c

(not a or not b) and not c

(not a and not c) or (not b and not c)

not (a or c) or not (b or c)

not ((a or c) and (b or c))

not ((a and b) or c)

Which complex number does not lie on the line segment plotted on the graph?

Answers

Answer:

Notice that for 3 out of the 4 numbers, there is a relationship between the x and the y coordinate of the number; for 3+i, -2i, -2-4i we have that the real part is larger by 2 from the imaginary part. Thus, the points are on the same line in the imaginary plane; they satisfy x=y+2 or Re{z}=Im{z}+2. However, 2-4i does not satisfy this equation since 2 is not equal to -4+2. Hence, this point does not belong to the line that the other 3 points define.

Step-by-step explanation:

Round 948070 to the nearest hundred? Hurry please

Answers

Answer:

9.48

Step-by-step explanation:

arrange the following in descending order - 5, 0, -15, 2.5, 2.05​

Answers

Answer:

2.5, 2.05, 0, -5, -15

Step-by-step explanation:

for negative numbers the bigger is worth less

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5. A
random sample of 551 children aged 6-10 showed that 48% of them play a sport.
For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t="
before your answers. Round each of your answers to 3 places after the decimal point.
(a) Calculate the value of the test statistic used in this test.
Test statistic's value
(b) Use your calculator to find the P-value of this test.
P-value =
(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level. If
there are two critical values, then list them both with a comma between them.
Critical value(s) -

Answers

Answer:

a) -0.94

b) 0.3472

c) -2.327, 2.327

Step-by-step explanation:

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion is different from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]

A random sample of 551 children aged 6-10 showed that 48% of them play a sport.

This means that [tex]n = 551, X = 0.48[/tex]

(a) Calculate the value of the test statistic used in this test.

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{551}}}[/tex]

[tex]z = -0.94[/tex]

So the answer is -0.94.

(b) Use your calculator to find the P-value of this test.

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least 0.02, which is P(|z| > 0.94), which is 2 multiplied by the p-value of Z = -0.94.

Looking at the z-table, z = -0.94 has a p-value of 0.1736.

2*0.1736 = 0.3472, so 0.3472 is the answer to option b.

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level.

Two-tailed test(test if the mean differs from a value), Z with a p-value of 0.02/2 = 0.01 or 1 - 0.01 = 0.99.

Looking at the z-table, this is z = -2.327 or z = 2.327.

Find the value of y.
Please help :(

Answers

The value of y is 4 √ 3.

Find the equivalent expression using the
same bases.
(98.41)

Answers

9684.5281 I think that’s the answer

The formula for velocity of an object is the equals d over t where he is a velocity of the object t is the distance traveled and t is a time in class well that distance is terrible if you had only this formula to work with what would your first step be to determine how long it takes for the light to return fitness center one additional information do you need to calculate this and solve the variable you're looking for

Answers

Answer:

[tex](a)\ t =\frac{d}{v}[/tex]

[tex](b)\ d = vt[/tex]

Step-by-step explanation:

The question is mixed up with details of another question. See comment for original question

Given

[tex]v = \frac{d}{t}[/tex]

[tex]v \to velocity[/tex]

[tex]d \to distance[/tex]

[tex]t \to time[/tex]

Solving (a): Solve for time

We have:

[tex]v = \frac{d}{t}[/tex]

Cross multiply

[tex]t * v = d[/tex]

Make t the subject

[tex]t =\frac{d}{v}[/tex]

Solving (b): Solve for distance

We have:

[tex]v = \frac{d}{t}[/tex]

Cross multiply

[tex]d = v * t[/tex]

[tex]d = vt[/tex]

Applying for a loan. What separates me from other applicants applying for this money?

Answers

Answer:

Step-by-step explanation:

You could have a good credit score and good credit history.

when 5 is added to 2 times a number , the results is 45. find the number

Answers

Answer:i think its 20

Step-by-step explanation: 20 x 2 is 40 plus 5 is 45

Answer:

✓ x - the number 5 + 2x = 45 2x = 45 - 5 2x = 40 x = 20 5 + 2(20) = 45 5 + 40 = 45 45 = 45 Hope this helps. :-) the answer is 20

Step-by-step explanation: Algebra.com

PLEASE HELP THX<3

Solve for w.

Answers

Answer:

- [tex]\frac{26}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] = -  [tex]\frac{1}{2}[/tex]w - [tex]\frac{2}{3}[/tex]

multiply equation by a common denominator. Let's use 30.  

you get :

6 = -15w - 20

26 = -15w

w = -  [tex]\frac{26}{15}[/tex]

Using the simple spinner below what is the probability of landing on either 2, 4, or 7?

Answers

Answer:

3/10

Step-by-step explanation:

Total possibilities = 10

favourable possibilities = 3

Answer:

A

Step-by-step explanation:

There is a 1 out of 10 chance that it will land on 2.

There is a 1 out of 10 chance that it will land on 4.

There is a 1 out of 10 chance that it will land on 7.

[tex]\frac{1}{10}\cdot3=\frac{3}{10}[/tex] so the anwser is A.

What are the lower, middle, and upper quartiles of this data?
122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Answers

Answer:

71, 71, 75, 85, 98, 98, 104, 111, 114, 122, 164

The middle quartile is 98.

The lower quartile is 80

The upper quartile is 112.5

give me answer please don't skip

If a^2+b^2 = 58 and a-b = 4 then what is the value of ab

Answers

Answer:

ab = 21

Step-by-step explanation:

[tex](a - b)^2 = (a^2 + b^2 ) - 2ab\\\\4^2 = 58 - 2ab\\\\16 - 58 = - 2ab\\\\- 42 = - 2ab\\\\ab = \frac{-42}{-2} = 21[/tex]

Step-by-step explanation:

Th value of ab is 21

Explanation is in the attachment

hope it is helpful to you ☺️

thank you for giving me a chance to answer your question

What is the area of a parallelogram if the length is 4+ x and it's height is x+3

Answers

Answer:

[tex]x^{2}[/tex] + 7x + 12

Step-by-step explanation:

The area of a parallelogram is A = bh, where the base is the length.

To solve this, you have to multiply 4 + x and x + 3.

(4 + x)(x + 3)

If you factor this more, it should be equal to:

[tex]x^{2}[/tex] + 3x + 4x + 12.

This simplified is equal to:

[tex]x^{2}[/tex] + 7x + 12.

Which of the following best represents the linear regression equation for the X values and log Y values of the data shown below

Answers

Answer:

y=103.13x - 183.98

Step-by-step explanation:

Given the data :

To obtain the linear equation which best fits the data ; we could perform a linear regression analysis using a technology to obtain a best fit line.

The linear regression Equation obtained by using technology is :

y=103.13x - 183.98

Where ;

Slope = 103.13

Intercept = - 183.98

y = response variable

x = predictor variable

Answer:

A

Step-by-step explanation:

the answer is A just completed it

Can someone please help me with this?!!!

Answers

Step-by-step explanation:

A.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7.7

Someone pls answer ? It’s 8,9,1,2

Answers

Answer:

Step-by-step explanation:

8.

any number ×0=0

so b

9.

additive identity

any number+0=same number

c

1.

[tex]\frac{(3+u)^2}{8} =\frac{(3+5)^2}{8} =\frac{8^2}{8} =\frac{64}{8} =8\\where ~u=5[/tex]

2.

-2(a-7)=-2×a-2×(-7)=-2a+14

Algebraically show that each of the given combinations are equivalent to the given functions.
h(x) • j(x) is equivalent to k(2) given:
h(x) = - 3x – 1;j(x) = – 7x + 11 ; k(x) = 21.22 – 262 – 11
h(x).j(x) = (
Is h(x).j(x) equivalent to k(x)? yes

Answers

Answer:

Yes they ate Equivalent

Step-by-step explanation:

Given the expression

h(x) = - 3x – 1;j(x) = – 7x + 11 ; k(x) = 21.22 – 262 – 11

H(x)•j(x) = (-3x-1)(-7x+11)

H(x)•j(x) = (-3x)(-7x)-3x(11)-1(-7x)(-1)(11)

H(x)•j(x) = 21x²-33x+7x-11

H(x)•j(x) = 21x²-26x-11

This shows that H(x)•j(x) = k(x)

2(-x-4)+3=-7x+5+5x

Pls help!!!!!!!!

Answers

4 I hope this helps you

1 Simplify

7
x
+
5
+
5
x
−7x+5+5x to

2
x
+
5
−2x+5.
2
(

x

4
)
+
3
=

2
x
+
5
2(−x−4)+3=−2x+5

2 Expand.

2
x

8
+
3
=

2
x
+
5
−2x−8+3=−2x+5

3 Simplify

2
x

8
+
3
−2x−8+3 to

2
x

5
−2x−5.

2
x

5
=

2
x
+
5
−2x−5=−2x+5

4 Cancel

2
x
−2x on both sides.

5
=
5
−5=5

5 Since

5
=
5
−5=5 is false, there is no solution.
No Solution

I WILL GIVE BRAINLIEST FAST
TRUE OR FALSE?
The triangles shown below must be congruent

Answers

B is the answer.

The triangles doesnt creates a SSS,SAS,SAA, scenario.

This triangle isn't ASA because the triangles share the same side but it have different angles that include the side.

in a standard deck of 52 cards what is the probability of drawing 2 jacks

Answers

Answer:

1/169

Step-by-step explanation:

There are 4 jacks in a deck of cards.

So 4/52 is the probability of drawing 1 card

The probability of drawing 2 jacks is 4/52*4/52

Solve, and that is 1/169

I hope this helps!

Change 84cm into millimetres

Answers

Answer:

840 mm

Step-by-step explanation:

multiply by 10

Answer:

840 millimetres

Step-by-step explanation:

To convert cm to mm, multiply the value in cm by 10

84cm x 10 = 840 mm

Hope this helps! <3

​Lisa, an experienced shipping​ clerk, can fill a certain order in 9 hours. Felipe​, a new​ clerk, needs 10 hours to do the same job. Working​ together, how long will it take them to fill the​ order?

Answers

Answer:

9.5hrs

Step-by-step explanation:

since they are working together you have to take the average time since is the same order

In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.

Answers

Answer:

The expected number of winning balls that Heather draws is 0.3.

Step-by-step explanation:

The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Expected value of the hypergeometric distribution:

The expected value is given by:

[tex]E(X) = \frac{nk}{N}[/tex]

Expected number of blue and green balls:

40 balls, which means that [tex]N = 40[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

25 are blue, which means that [tex]k = 25[/tex]

So

[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]

1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.

Of the blue balls, 12% are winning.

Of the green balls, 20% are winning.

Calculate the expected number of winning balls that Heather draws.

[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]

The expected number of winning balls that Heather draws is 0.3.

What is the domain of the function f(x) = (-5/6)(3/5)superscript x

Answers

Answer:

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

[tex]-\infty < x < \infty[/tex]

URGENT PLS HELP

Given f(y)=2y^2 - 4y, and h(x)= x^2 - 1, determine f(h(x))

Answers

Answer:

f(h(x)) = 2•(x²-1)² -4•(x²-1)

help me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me

Answers

Volume of the 3d composite figure is,

(7×6×5)+(7×6×5)/3

= 210+70

= 280 cm³

Relationship between the two volumes,

Volume of the rectangular prism is 3 times the volume of the pyramid.

Answered by GAUTHMATH

Answer:

I was gonna anwer it but somone already did.

Step-by-step explanation:

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