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RoseWind [281]
2 years ago
4

There are 40 people at Drake's sweet sixteen party. Drake's only rule is that everyone in the party must meet and shake each oth

ers hand. If all 40 guest shake each other's hand once and only once. (1) How many handshakes are there altogether? (50 pts) (2) How did you get your solution? No verbiage should be the same for this. There are multiple ways to think about this. (30 pts) (3) What's the quickest way to figure this out if Drake invited 1000 people? (20 pts)Can someone please answer this with an explanation?
Mathematics
2 answers:
s2008m [1.1K]2 years ago
7 0
1) It's a combination of 2 chosen from 40:
 
⁴⁰C₂ = (40!)/[(2!).(40-2)!] = 780

2) Another way to think about this problem is as follows:

1st shakes hand with 39 (he can't shake his own hand)

2nd shakes hand with 38 (his hand was already shaken by the 1st, so no duplication)

3rd shakes hand with 37 (his hand was already shaken by the 1st, and 2nd, so no duplication)
And so on and so forth...until 1:

Number of hands shaken : 39 + 38 + 37 + 36 + ...+1
The sum = [(1+39).39]/2 = 40x39/2 = 780 
Remember the above is an Arithmetic progression, with first term 1. the last term 39 and the number of terms 39 
S=(a₁+a₃₉)(39/2)

faust18 [17]2 years ago
7 0

Answer:

there are multiple ways to do this

Step-by-step explanation:

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A certain company's main source is a mobile app. The function h models the company's annual profit (in million of dollars) as a
cricket20 [7]

Answer:

At price 3 and 11, the profit will be $0

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

<em> A certain companies main source of income is a mobile app. The companies annual profit (in millions of dollars) as a function of the app’s price (in dollars) is modeled by P(x)=-2(x-3)(x-11) which app prices will result in $0 annual profit?</em>

My answer:

Given:

  • x is the app price
  • P(x) is the profit earned

If we want to find out the app price that will result in $0 annual profit? It means we need to set the function:

P(x)=-2(x-3)(x-11) = 0

<=> (x-3)(x-11)= 0

<=> x - 3 = 0 or x - 11=0

<=> x = 3 or x = 11

So at price 3 and 11, the profit will be $0

Hope it will find you well.

5 0
2 years ago
Read 2 more answers
Marissa bought 60 horns for her New Year’s Eve party for $83.40.
katovenus [111]

Answer:

We don't have the statements but I can tell you the following info:

Step-by-step explanation:

83.4/60= $1.39 for each horn

18*1.39= $25.02 for the 18 additional horns.

$83.40+25.02= $108.42 for the total 78 horns

3 0
2 years ago
Agustina made a scaled copy of the following quadrilateral. She used a scale factor less than 1. What could be the length of the
Leya [2.2K]

Answer:

A

Step-by-step explanation:

8 0
2 years ago
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Mr. Bartley is taking the theater club on a field trip to see the musical wicked. The school treasurer asked Mr. Bartley for the
Darya [45]

Answer: Tickets cost $25 and each person must contribute $2 for the bus. There are 52 people going on the trip.


Step-by-step explanation:

Given: Mr. Bartley is taking the theater club on a field trip [which must include bus or other vehicle] to see the musical wicked. The school treasurer asked Mr. Bartley for the group's total ticket cost.

He wrote the following cost function for the school treasurer.

Total Cost =52(25+2)

Since cost function is a function based on number of people and per head cost.

So, the statement which best describe the cost function is "Tickets cost $25 and each person must contribute $2 for the bus. There are 52 people going on the trip."


5 0
2 years ago
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A student walks 1/4 Mile from her home to the store on her way to a friend's house if the store is 1/3 of the way to a friend's
exis [7]

the store is 1/3 the way to her friend's house, not 1/3 mile.

this explains solution:

1/3x = 1/4

x = 1/4 * 1/3

x = 3/4

Notes:

X: is the total distance.

1/3 is the one portion of total distance.

1/4 mile is the distance store.

3 0
2 years ago
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