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stich3 [128]
1 year ago
10

at a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. people who know each oth

er hug, and people who do not know each other shake hands. how many handshakes occur within the group?
Mathematics
1 answer:
Nitella [24]1 year ago
8 0

Since there are 10 persons in the group who do not know one another, the real number of handshakes will be 45.

<h3>What is combination?</h3>

In probability theory and other branches of mathematics, the term "combination" refers to a succession of results where the order is irrelevant. A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen. Combinations and permutations may appear to be synonyms. However, they are defined differently in probability theory. Combinations: The sequence of results is irrelevant. Permutations: The sequence of events matters.

Here,

Total number of handshakes = 10C2 = (10 × 9)/2 = 45 handshakes.

When 10 people are shaking hands, each one will shake hands with 9 others.

The total number of handshakes in actual = 90/2 = 45 handshakes.

The total number of handshakes in actual will be 45 handshakes as there are 10 people in the group who do not know each other.

To know more about combination,

brainly.com/question/20211959

#SPJ4

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6x-5y=13

Solve for y

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This is in slope intercept form y = mx+b where m is the slope and b is the y intercept

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If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra
bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be l units.

Using pythagoras theorem, we can find out the value of l.

As per theorem:

Hypotenuse^{2} = Base^{2} + Height^{2}\\

\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 =  100\\\Rightarrow l = 10\ units

Lateral surface area of square prism = 4 \times Area of triangular surface

\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units

Surface Area of 5 surfaces of the square prism =

4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units

So, total surface area of composite figure:

240 + 480 = 720 sq units.

7 0
3 years ago
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