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2 years ago

12

A ball will be drawn from the bag containing 20 balls numbered one through 20 if each ball is equally likely to be drawn what is

the probability that the number on the bar will be drawn even or less than five

1 answer:

son4ous [18]2 years ago

5 0

Answer:

3/5

Step-by-step explanation:

There are 20 balls, numbered 1 through 20.

Of these, 10 are even, 4 are less than five, and 2 are both even and less than 5.

So the probability is:

P(even or <5) = P(even) + P(<5) − P(even and <5)

P(even or <5) = 10/20 + 4/20 − 2/20

P(even or <5) = 12/20

P(even or <5) = 3/5

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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

4 0

2 years ago

a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the

nlexa [21]

Answer:

The standard equation of the parabola is:

$y=-\frac{3}{2}x^2+12x-18$

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

$y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2$

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

$y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}$

Then the equation of the parabola becomes:

$y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18$

7 0

3 years ago

Ea+ec=5.40, ec*2=s,ea/2=s<br><br> What is Ec?

alexandr402 [8]

I have no idea I am only in Middle School

3 0

2 years ago

Write a mixed number and an improper fraction for the model below

Mariulka [41]

Answer:

2 and 3/4

11/4

Step-by-step explanation:

an improper fraction is any fraction with a numerator bigger then the denominator.

a mixed number is the "proper" version of an improper fraction.

the fraction 11/4 as a mixed number is 2 and 3/4.

to make an improper fraction a mixed number, find out how many times the denominator goes into the numerator. whatever you have left that didn't make 1 whole, turns into the fraction .

hope this helped

4 0

2 years ago

What is another what to write 9x 200

Snezhnost [94]

200x 9, nine times two hundred,

3 0

2 years ago

Read 2 more answers