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2 years ago

The sum of four consecutive odd integers is 328. What are the integers? show your work please

Mathematics

2 answers:

valina [46]2 years ago

8 0

Answer:1,3,5,7,

Step-by-step explanation:

lisabon 2012 [21]2 years ago

5 0

Step-by-step explanation:

For a formal algebraic solution, you might do something like this....

x = 1st integer

x+2 = 2nd

x+4 = 3rd

x+6 = 4th

The sum is 328:

Then solve that equation to find x and thus find the solution to the problem.

Or, if formal algebra is not required (and you want to get the answer as fast as possible)....

The average of the four integers is 328/4 = 82; the four integers are the two odd integers either side of 82 and closest to 82 -- 79, 81, 83, and 85.

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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

Step2247 [10]

Answer:

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.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

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:

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

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

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

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

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

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

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

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

3 towers, so $n = 3$

We have to find:

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

In which

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

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

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

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

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

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3 years ago

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elena55 [62]

Step-by-step explanation:

By binomial theorem,

T(r+1) = nCr * a^(r+1) * b^r

Term 4 = 7C3 * (2x)^4 * (-5y)^3 = 35 * (16x^4) * (-125y^3) = -70000x^4y^3.

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*Independent events *not mutually exclusive events

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Not mutually exclusive event means that both can happen at the same time.

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