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xz_007 [3.2K]
3 years ago
7

What is the solution to the system of equations x = y + 4 2x - 3y = -2

Mathematics
1 answer:
quester [9]3 years ago
7 0

Answer: x = 14 and y = 10

Step-by-step explanation: What we have in the question is a pair of simultaneous equations as follows(

x = y + 4 ———(1)

2x - 3y = -2 ——(2)

Looking at both equations, one of the variables has a coefficient of 1, and as a result of that, we shall use the substitution method.

From equation (1), x = y + 4

Substitute for the value of x in equation (2)

2x - 3y = -2

2(y + 4) - 3y = -2

2y + 8 -3y = -2

-y + 8 = -2

Subtract 8 from both sides of the equation

-y +8 -8 = -2 -8

-y = -10

Divide both sides of the equation by -1

y = 10

Having calculated y, substitute for the value of y into equation (1)

x = y + 4

x = 10 + 4

x = 14

Therefore, x = 14 and y = 10

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Step-by-step explanation:

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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%
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