Ascientist wants to research the potential spread of germs by contact. she knows that the number of possible handshakes within a group of n people is given by the equation nequalsone half left parenthesis n squared minus n right parenthesis . everyone at a party shook hands. there were 171 handshakes in all. how many people attended the? party?

19

Step-by-step explanation:

Here we have to find out number of people attended the party. we are given with the number of the handshakes in the party .

We are going to use the following formula to determine the number of guests

Nos. of handshakes

Here we have H = 171

Hence our equation becomes

now we solve it by splitting the middle term method

Now we have to find the factors of 342 whose difference to 1. The factors are 19 and 18 in this case. hence we slit our middle term like this

Hence

either

(x+18)=0 or (x-19) =0 Thus

x=-18 which is not possible as no of people can not be less than 0

x=19 which will our answer

We can draw a graph where the x-axis represents the years, and the y-axis represents the sales.

So the points are  (2002, 19550) and (2010, 35145), where the second coordinate represents the sales made in the year written in the first coordinate.

and the line drawn through these 2 points represents the sales in the other years.

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Given any 2 point P(m,n) and Q(k,l),

the coordinates of the midpoint of the line segment PQ are given by the formula:

, 

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Thus, the midpoint of points (2002, 19550) and (2010, 35145) is given by



Thus, the sales in 2006 are approximately $ 27,347.5