How can you show that two objects are proportional with a graph?

1 answer:

6 0

So this is our table:

-----------------
x-values | a b c d e f |
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y-values | g h i j k l |
-----------------

You can know that the values in the table are proportional if:

$\frac{a}{g}=\frac{b}{h} =\frac{c}{i}=\frac{d}{j}=\frac{e}{k}=\frac{f}{l}$

Hope that helps :)

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"the life length x (in years) of a dvd player" is exponentially distributed with mean 5 years. what is the probability that a mo

loris [4]

The exponential distribution is:
$\lambda e^{- \lambda x}$
where $\lambda = \frac{1}{mean}=\frac{1}{5}$

The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.
$P(A|B) = \frac{P(A and B)}{P(B)}$
where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:
$P(x \ \textgreater \ N) = \int_N^{\infty} \frac{1}{5} e^{-x/5} dx = e^{-N/5}$

Sub into conditional probability formula:

$P(x \ \textgreater \ 8 | x\ \textgreater \ 5) = \frac{P(x\ \textgreater \ 8)}{P(x\ \textgreater \ 5)} = \frac{e^{-8/5}}{e^{-5/5}} = e^{-3/5} = 0.549$

Final Answer: Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%

3 0

3 years ago

How do I solve this equation?

Gnom [1K]

$2x(4-x)^{-1/2}-3(4-x)^{1/2}=(4-x)^{-1/2}\bigg(2x-3(4-x)\bigg)$