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Tasya [4]
3 years ago
8

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

re than 5-year old dvd would still work for more than 3 years?
Mathematics
1 answer:
loris [4]3 years ago
3 0
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%
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Write 9,540,000 in expanded form using exponents to show powers of 10
krek1111 [17]

Answer:

9* 10^{6}+ 5* 10^{5}+4* 10^{4}.

Step-by-step explanation:

Given  :  9,540,000

To find : Write 9,540,000 in expanded form using exponents to show powers of 10.

Solution : We have given 9,540,000

Here 9 is at million place 9000000

5 is at hundred thousand place = 500,000.

4 is at tens thousand place = 40,000

We expanded it as

9, 000,000 + 500,000+40,000.

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9* 10^{6}+ 5* 10^{5}+4* 10^{4}.

Therefore,

9* 10^{6}+ 5* 10^{5}+4* 10^{4}.

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2x²-5x-12=0 (simplify solution set)
Arada [10]

Answer:

x = 4 or x = -3/2

Step-by-step explanation:

To simplify and solve this, let's use the quadratic formula.

So the format of a quadratic equation is supposed look like this:

ax^2+bx+c=0

Let's find a, b, c:

  • a is the coefficient of x^2
  • b is the coefficient of x
  • c is the constant term

Now let's solve the equation.

Let's solve your equation step-by-step.

2x^2−5x−12=0

For this equation: a=2, b=-5, c=-12

2x^2+−5x+−12=0

Step 1: Use quadratic formula with a=2, b=-5, c=-12.

x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}

x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-12)} }{2(2)}

x=\frac{5\pm\sqrt{121} }{4}

x=4 or x=\frac{-3}{2}

<u />

<u>Answer:</u>

x = 4 or x = -3/2

7 0
2 years ago
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