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DanielleElmas [232]
3 years ago
10

Use geometric series to find the fraction of 0.8967898989

Mathematics
1 answer:
Sliva [168]3 years ago
8 0

I'm guessing the repeating part is 89 at the end, so that

x=0.8967\overline89\implies10^4x=8967.\overline{89}

Then

10^4x=8967+\displaystyle89\sum_{i=1}^\infty\frac1{100^i}

10^4x=8967+89\left(\dfrac1{1-\frac1{100}}-1\right)

10^4x=8967+\dfrac{89}{99}

x=\dfrac{8967}{10^4}+\dfrac{89}{99\cdot10^4}

x=\dfrac{443911}{495000}

###

An arguably quicker way without using geometric series:

10^4x=8967.\overline{89}

10^6x=896789.\overline{89}

10^6x-10^4x=887822

x=\dfrac{887822}{10^6-10^4}=\dfrac{443911}{495000}

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3 years ago
Find the indicated probability by using the complementation rule. A percentage distribution is given below for the size of famil
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Answer:

The correct option is c.

Step-by-step explanation:

The percentage probability distribution is:

Size (X)      Percentage

 2                   39.9

 3                   24.4

 4                   20.1

 5                   10.8

 6                    3.3

 7                     1.5

Total             100.0

Compute the probability that the size of the family is 4 or more as follows:

P (X ≥ 4) = P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7)

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Thus, the probability that the size of the family is 4 or more is 0.357.

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7 0
3 years ago
How in the world do I answer this problem??​
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Answer:

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Step-by-step explanation:

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Note that SU = ST + TU = y + 18

So we have 2y - 4 = y + 18

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So ST is 22.

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