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saveliy_v [14]
3 years ago
11

cindy,jamal,and monique are dividing a piece of land using the lone divider method.after flipping coins monique has been selecte

d to be the divider and divides the land into three pieces.the values of the three pieces of land in the yes of the other players are shown below

Mathematics
1 answer:
lukranit [14]3 years ago
7 0

9514 1404 393

Answer:

The (piece, perceived values) are ...

  • Cindy, (3, 48%)
  • Jamal, (1, 39%)
  • Monique, (2, 33%)

Step-by-step explanation:

We assume the values and questions are as shown in the attachment.

1. After the division, Cindy bids only on piece 3, and Jamal bids only on piece 1. Hence the appropriate final division is ...

  Cindy: piece 3

  Jamal: piece 1

  Monique: piece 2

__

2. Monique divides the land so that the value of each piece to her is 33 1/3%. That is her perceived value for the piece she gets.

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:
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a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}

S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525

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