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icang [17]
3 years ago
14

Prove that at a party where some people shake hands, the number of people who shake hands with an odd number of people is an eve

n number.
Mathematics
1 answer:
Kobotan [32]3 years ago
5 0
If there are n people, each person could shake hands with 0 people, 1 person, 2 people,... on up to shaking hands with n − 1
people. Count how many different answers there are to asking the person the question "How many hands did you shake?" How many people are there? If the people are the pigeons, and the possible answers to the question "how many hands did you shake" are the holes, can we conclude anything yet? No? How about now noticing that at least one of the holes "I shook hands with noone" or "I shook hands with everyone" has to be empty... now what?

"Since there are more pigeons than holes there must be a hole with at least two pigeons in the same hole" Now, replace the word "pigeons" and "holes" with the appropriate terms for the context of your specific question, remember we are talking about people and number of handshakes they participated in.
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10. If 1000 cm = 1 l, find the capacity of the following water tank in litre
Lelu [443]
<h2>Given :</h2>

  • length = 200 cm

  • breadth = 150 cm

  • height = 100 cm

<h2>Solution : </h2>

\large \boxed{volume = l \times b \times h}

  • 200 \times 150 \times 100

  • 3000000  \: \: cm {}^{3}

Through the statement above we have,

  • \small\mathrm{1000  \: cm³ = 1  \:  \: }l

  • \small\mathrm{1 \: cm {}^{3}  =  \dfrac{1}{1000} \: }l

  • \small\mathrm{3000000 \: cm {}^{3}  = 3000000 \times  \dfrac{1}{1000}  \: }l

  • \small\mathrm{3000000 \: cm {}^{3}  = 3000000 \times  \dfrac{1}{1000}  \: }l

  • \small\mathrm{ 3000 \:  \: litres}

_____________________________

\mathrm{ \#TeeNForeveR}

3 0
3 years ago
Which expression shows an equivalent form of the expression<br> xpression 97.93?
Korvikt [17]

Answer:

i think this is what you mean:90 + 7.93

Step-by-step explanation:

4 0
3 years ago
julie grows apples. the first year she planted 6 seeds. the second year she planted 18 seeds. the third year she planted 54 seed
luda_lava [24]

Answer:

90-96

Step-by-step explanation:

7 0
3 years ago
A recent study from the University of Virginia looked at the effectiveness of an online sleep therapy program in treating insomn
Ludmilka [50]

Answer:

1. The 99% confidence interval for the difference in average is -6.47377 < μ₁ - μ₂ < -11.34623

2. The possible issues in the calculations includes;

a. The confidence level used in the confidence interval can influence the result of the confidence interval observed

b. The sample size is small

Step-by-step explanation:

1. The number of adults with insomnia in the sample = 45

The number of adults that participated in the therapy, n₁ = 22

The number of candidates that served as control group, n₂ = 23

The average score for the for the 22 participants of the program, \overline x_1 = 6.59

The standard deviation for the 22 participants of the program, s₁ = 4.10

The average score for the for the 23 subjects in the control group, \overline x_2 = 15.50

The standard deviation for the 23 subjects in the control group, s₂ = 5.34

The confidence interval for unknown standard deviation, σ, is given by the following expression;

\left (\bar{x}_{1}- \bar{x}_{2}  \right )\pm t_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}

α = 1 - 0.99 = 0.01

α/2 = 0.005

The degrees of freedom, df = 22 - 1 = 21

t_{\alpha /2} = t_{0.005, \, 21} = 1.721

Therefore, we have;

\left (6.59- 15.5  \right )\pm1.721 \cdot \sqrt{\dfrac{4.10^{2}}{22}+\dfrac{5.34^{2}}{23}}

The 99% confidence interval for the difference in average is therefore given as follows;

-6.47377 < μ₁ - μ₂ < -11.34623

Therefore, there is considerable evidence that the participants in the survey  had lower average score than the subjects in the control group

2. The possible issues in the calculations are;

a. The confidence level used in the confidence interval can influence the result of the confidence interval observed

b. The sample size is small

5 0
2 years ago
5b^2(9b-7)+(-9b^2)(4b-3) in simplest form
Lady bird [3.3K]
The answer is 9<span>b<span><span>​^3</span><span>​​</span></span></span>−8<span>b^<span>​<span>2. Good luck!!!!</span></span></span>
6 0
3 years ago
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