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Brilliant_brown [7]
3 years ago
11

The most popular mathematician in the world is throwing aparty for all of his friends. As a way to kick things off, they decidet

hat everyone should shake hands. Assuming all 10 people atthe party each shake hands with every other person (but notthemselves, obviously) exactly once, how many handshakes takeplace?
Mathematics
1 answer:
ratelena [41]3 years ago
4 0

Answer:

The no. of possible handshakes takes place are 45.

Step-by-step explanation:

Given : There are 10 people in the party .

To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Solution:

We are given that there are 10 people in the party

No. of people involved in one handshake = 2

To find the no. of possible handshakes between 10 people we will use combination over here

Formula : ^nC_r=\frac{n!}{r!(n-r)!}

n = 10

r= 2

Substitute the values in the formula

^{10}C_{2}=\frac{10!}{2!(10-2)!}

^{10}C_{2}=\frac{10!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 \times 8!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 }{2 \times 1}

^{10}C_{2}=45

No. of possible handshakes are 45

Hence The no. of possible handshakes takes place are 45.

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6 0
3 years ago
7.RP.A.1 3. If 1 1/2 cups of something fills 2/3 of a container, how many cups fill the container? ​
Andreas93 [3]

Answer:

Hi there!

Your answer is:

2 & 1/4 <u>OR</u> 2.25 cups fills the container!

Step-by-step explanation:

If 1 & 1/2 (aka 3/2) fills 2/3 of the container, then:

we know that <em>half</em> of 3/2s fills 1/3 of the container

To find half of 3/2, we multiply 3/2 by the <em><u>inverse</u></em> of 2, which is 1/2.

3/2÷2

3/2×1/2 = 3/4 ths

Now that we know 3/4ths fills 1/3 of the container, we add that to 1& 1/2.

3/4+ 1&1/2 = 2 & 1/4

Check your work!

3/4 × 3 should equal 2&1/4 if we are correct

3/4 × 3/1 = 9/4.

Simplify!

9/4 = 2&1/4

That tells us that <u>we</u><u> </u><u>are</u><u> </u><u>correct</u><u>!</u>

Hope this helps!

3 0
3 years ago
Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a
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6 0
3 years ago
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Since 1972 the US. inflation rate has averaged 4.8 % per year . Use the approximate doubling time formula to estimate the doubli
Artemon [7]

Answer:

14  3/4 years

Step-by-step explanation:

Let's assume compound inflation.  The appropriate formula for that is:

A = P(1 + r)^t.

If we represent current prices by P, then double that would be 2P:

2P = P(1 + 0.048)^t    Find t, the time required for prices to double.

Then:

2   =  1.048^t

Taking the natural log of both sides, we get:

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At 4.8 inflation, with annual compounding, prices will double in approx. 14 3/4 years.

3 0
3 years ago
Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number?
azamat

Alright, lets get started.

Jim was thinking of a number.

Suppose the number Jim was thinking, is x.

Jim adds 20 to it means number will be = x+20

And Jim doubles it, means 2*(x+20)

Jim gets 99.2 and as per us, he gets 2*(x+20)

So, making them equal

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2x+40=99.2

Subtracting 40 in both sides

2x+40-40=99.2-40

2x=59.2

x=29.6

It means the original number is 29.6.   :   Answer

Hope it will help :)



6 0
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