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3 years ago

Use the multiplication method to solve the following systems of equations. 1. 4q – 2r = 36 and 6q + r = 10

Mathematics

1 answer:

sasho [114]3 years ago

7 0

Answer: r = -11, q =3.5

Step-by-step explanation:

4q – 2r = 36 ....... eqn. 1

6q + r = 10 ..............eqn 2.

from eqn. 2 make r subject formula i.e.

r = 10- 6q (substitute for 'r' in eqn. 1)

we have;

4q - 2(10-6q) = 36 (open bracket)

4q -20 + 12q = 36 (collect like terms)

4q+12q = 36+20

16q = 56

q = 56/16

q = 3.5

substitute for q in eqn. 2.......

6(3.5) + r = 10

21 + r = 10

r = 10-21

r = -11, q =3.5

Please give me brainliest...thanks

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f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

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15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

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$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

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The probability of finding a value higher than x is:

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We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

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Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

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$P(X \geq 2) = P(X = 2) + P(X = 3)$

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$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

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