Mathematics Middle School

Nine people come to a party and shake hands with each other. If each person shakes the hand of every other​ person, how many handshakes​ occur?

Answers

Answer 1

Final answer:

There will be 36 handshakes among the nine people at the party, as determined by the combination formula 9C2.

Explanation:

Calculating Handshakes

To determine the number of handshakes that occur when nine people shake hands with each other, we can use the concept of combinations. In a handshake situation, the order in which the handshakes occur does not matter; what matters is which two people are shaking hands. Therefore, we can use the formula for combinations without repetition, which is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose at a time.

In this case, there are 9 people (n=9) and the handshake involves 2 people at a time (k=2). So, the calculation would look like this:

9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 × 8) / (2 × 1) = 36 handshakes

Therefore, there would be a total of 36 handshakes among nine people at the party.

Related Questions

Kevin wanted to know how many minutes are in 2 years.
he set up the conversion below

365 days 24 hours 1 hours
2 years *------------ * ------------ * -----------
1 years 1 day 60 minutes

1. what did Kevin do wrong

2. what can Kevin do to fix it

Answers

Part 1
Kevin did not indicate the conversions between years, days, hours, and minutes.

Part 2
The correct calculation for the number of minutes in 2 years is
[tex]2 \, years \\ = (2 \, years)*(365 \, \frac{days}{year})*(24 \, \frac{hours}{day} )*(60 \, \frac{minutes}{hour} ) \\ = 1,051,200 \, minutes[/tex]

Answer: 1,051,200 minutes

What is .86 divided by 5 minus .3 times .5

Answers

The answer is 2.2 buddy
.86÷5-.3×5= -1.328 the answer is -1.328

Answer 12 plzzzz‼️‼️ asap!

Answers

Create equal fractions to find the number of hours he used the health club for.

2/13=x/29.25

Then, simplify so that x is by itself.

(29.25x2)/13 = x
x= 58.5/13
x=4.5 hours
13/2 = 6.5
They charge $6.50 per hour
29.25/6.50 = 2925/650 = 4.5
He was in the health club for ~ 4.5 hours

hope this helps

What is 4 ÷457 long division

Answers

The answer is 114.25
0.008752735 is the right answer 

Hwong Has 39 Muffins.If each of hos Guest will Eat 2 Muffins, Hwong figures That He Can Serve Muffins To 19 Guest

Answers

That is correct because 2x19=38 which is the closest number without going over

alexander the great became king in 336 BB and died 13 years later. what year did he die?

Answers

323 BC. When working before Christ the more recent the year is, the smaller the number is.
323 B.C.E. because 336- 23=324 B.C.E.

If each square in the grid has a side lengt of 8mm,what is the-width and height of the rectangle

Answers

one of them is 4 and one is 2

What is 239901 rounded to the nearest ten thousand

Answers

The answer is 240,000

What is the value of the underlined digit? 5,678.321. The underlined digit is 1.

Answers

0.001

Hope this helps!
.001     the decimal is important because in the number the 1 is after the decimal, itrepresents the fact that its not a whole number. The two zeros are there to replace the two numbers that come before the 1 and after the decimal. they replace 32

Compare the integers indicated on the graph below.

A. -6 > -12

B. -12 > -6

C. -4 > -8

D. -8 > -4






5)

Answers

The correct answer is A. -6 > -12


Hope that helped! :)

I need the answer to this question ASAP please help.

Answers

(3/5)^3 = (3^3)/(5^3) = 27/125
3^3 = 3x3x3 = 27
5^3 = 5x5x5 = 625
27/625 is the answer and it can’t be simplified

A manufacturing company with 450 employees begins a new product line and must increase their number of employees by 18%. How many total employees does the company now have?

Answers

The answer would 531. You would add 18% more employees to the company so the answer is 531. I really hope this helped you. Have a nice day!

How to solve a=9y+3yx

Answers

Therefore, the equation [tex]y = \frac{a}{9 + 3x}[/tex] represents y as a function of a and x, showing how changes in a and x affect the value of y.

The given equation a = 9y + 3yx is a literal equation, meaning it relates multiple variables (in this case, a and y) with constants. Our goal is to isolate y, which means we want y to be expressed solely in terms of a and x, without any other variables.

To do this, we first factor out the common factor y from the right side of the equation, leaving us with a = y(9 + 3x). This step simplifies the equation and makes it easier to isolate y.

Then, to solve for y, we divide both sides of the equation by (9 + 3x), effectively undoing the multiplication by (9 + 3x) on the right side. This leaves us with [tex]y = \frac{a}{9 + 3x}[/tex].

In this final expression, y is in terms of a and x, indicating that the value of y depends on the values of a and x. As a and x vary, the value of y changes accordingly, following the relationship described by the equation.

Complete Question:

Solve the literal equation for y.

a = 9y + 3yx

y =

−30+(−40)+(−70 equivalent expression

Answers

−30−40−70

=−70−70

=−140


I need help with math.............

Answers

Greetings!

Solve using the properties of equality:
[tex]2(x+2)=4x+1-2x[/tex]
Distribute the Parenthesis.
[tex]2x+4=4x+1-2x[/tex]
Combine like terms.
[tex]2x+4=2x+1[/tex]
There are no possible solutions.

Hope this helps.
-Benjamin

Suppose you used the distributive property to get the expression 12x+3y-9. With what expression could you have started?

Please help.

Answers

the answer could be 3(4x+y-3)
Before using the other methods for factoring, this is the first type of factoring you should try. Basically, you’re reversing the distributive property. What you’re doing is finding the greatest common factor for all of the terms.
Examples:

Factor 2x + 4
Greatest common factor for both of the terms is 2.
2x + 4 = 2(x + 2)

Factor 4x2 + 12
Greatest common factor for both terms is 4.
4x2 + 12 = 4(x2 + 3)

Factor 5x2 + 10x + 25
Greatest common factor for all of the terms is 5.
5x2 + 10x + 25 = 5(x2 + 2x + 5)

Find the greatest common factor for 12, 3 and -9.

After playing with the numbers around, I got 3.

3(4x + y - 3)

So, 3(4x + y - 3) is the answer.

How do you write 2.2 in word form?

Answers

2.2=22/10=2+0.2=2+2/10

so it could be said as 2 and 2 tenths
two and two-tenths
 2      .          2

I need help -3x=x-(6-2x)?

Answers

Answer:

X=1

Step-by-step explanation:

3/4 x+5− 1/2 x=3 Solve For X Need Answer Fast Please!!!!!!!

Answers

3/4x + 5 - 1/2 x=3 = -8

I believe this is the right answer :)

Answer:

8 1/5

Step-by-step explanation:

Solve the equation ax+b=c for x

Answers

ax+b=c
ax=c-b
x=(c-b)/a
The solve of this equation will be X=(C-b)/A

(2*1)+(6*1/1000) write in standard form

Answers



2+1006

=1008

1000+8=1008

Hope this helps

mr. peters buys 3 1/4 pound of grapes for $4.55 what is the unit cost of the grapes

Answers

divide 3 1/4 with 4.55

one type of insect is 0.0052 meter long.what is this length in scientific notation

Answers

Because scientific notation has to be in between 1 and 10, you would need this to be 5.2. Count the spaces and since its getting smaller your exponent is negative. 

Your answer should be 5.2*10^(-3)

In albany it is -4°f in chicago it is -14°f‚ in minneapolis it is -11°f‚ and in toronto it is -13°f. in which city is the coldest?

Answers

Chicago because on the number line, the numbers to the left get smaller, and the numbers to the right get bigger. Negatives on the number line are going right, and getting smaller, even though it seems the numbers are getting bigger.
EX: -14,-13, -12,-11,-10...

the largest negative number would be the coldest, so -14 would be the coldest.

 Chicago is the coldest city

Please help not sure on this

Answers

If I am correct, it would be dropped at -3, side adding to negative numbers make them increase to positive numbers.

Susan currently has an account balance of $1,336.60. Her initial deposit on the account was $820 and it earned 4.5% simple interest. How long has Susan held the account?

Answers

Here we need the time, so
t = I/pr = (1336.6-820)/(820)(.045) = 14 years



7.The mass of a grain of sand is approximately 2.8×10^−11 grams

Select from the drop-down menu to correctly complete the statement.
The mass of a grain of sand is approximately 2.8×10^−8

Answer Choices:
A. Milligram
B.Gram
C.Killogram

Answers

i just took the test.. the answer is A. Have a nice day!

Answer:

a

Step-by-step explanation:

math questions down below

Answers

#1 the correct answer is 6/7
#2 the correct answer is -9

True or false 6,859^1/3 can be written as square root 3 19^3

Answers

[tex]6859^{ \frac{1}{3}} [/tex]

Using the index law [tex]a^{ \frac{m}{n}} = (\sqrt[n]{a} )^m[/tex]

[tex] \sqrt[3]{6859}=19 [/tex], so we can also write this as
[tex]( \sqrt[3]{19^3} )[/tex]

Answer: TRUE

zack watches tv 3 times as much as joel. Joel watches tv 2 hours a day. how many hours a day does Zack watch tv?

Answers

Jole - 2 hours a day
Zach- 3(2) hours a day
The answer is:
6 hours a day
joel- 2 hours
zack- times 3
2x3=6.
Zack watches tv for 6hours a day
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