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Dmitry [639]
3 years ago
9

Anlatarak cevaplarsanız sevinirim

Mathematics
1 answer:
IgorLugansk [536]3 years ago
5 0

Answer:

A)26

Step-by-step explanation:

12 nin dogal sayi bolenleri 1,2,3,4,6 ve 12 dir yani ucgen 6 dir

20 nin en kucuk kati 20 yani kendisidir(20 kendisinin 1 katidir)

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Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible c
lutik1710 [3]

Answer:

Tamara should expect the sum of the two cubes to be equal to 5 20 times.

Step-by-step explanation:

The sample space of rolling a number cube are:

S = {1, 2, 3, 4, 5, 6}

If two such cubes are rolled together, then the sum of the two cubes will be 5 for the combinations below:

S₁ = {(1, 4), (2, 3), (3, 2) and (4, 1)}

The total number of outcomes will be, <em>N</em> = 36.

Compute the probability that the sum of rolling two numbered cubes as follows:

P(\text{Sum}=5)=\frac{4}{36}=\frac{1}{9}

Let <em>X</em> = number of time the sum of the two numbers on two cubes is 5.

Two numbered cubes are rolled <em>n</em> = 180 times.

The event of getting a sum of 5 in independent of the other results.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 180 and <em>p</em> = \frac{1}{9}.

The expected value of <em>X</em> is:

E(X)=np

Compute the expected number of times Tamara expects the sum of the two cubes to be equal to 5 as follow:

E(X)=np\\=180\times \frac{1}{9}\\=20

Thus, Tamara should expect the sum of the two cubes to be equal to 5 20 times.

8 0
3 years ago
Which of the following ordered pair could represent the x-intercept of a function?
loris [4]

Answer:

(15,0)

Step-by-step explanation:

when we talk about x intercept, then you must remember that y will be zero

if you wanna find y intercept, the x will be zero

8 0
3 years ago
Given that 6x – 5y = 14<br>Find x when y = 2​
Sloan [31]

Answer:

x = 4

Step-by-step explanation:

Given

6x - 5y = 14 ← substitute y = 2 into the equation

6x - 5(2) = 14

6x - 10 = 14 ( add 10 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

4 0
2 years ago
Read 2 more answers
Samantha is making a quilt and she has determined she needs 450 square inches of yellow fabric and 478
asambeis [7]

Conversions:

1 yard = 36 inches

The store only sells fabric by the by the quarter yard.

<h2><u><em>The yellow fabric: 450/36 = 12.5 square yards</em></u></h2><h2><u><em>The blue fabric: 478/36 is around 13.3 square yards</em></u></h2>

Total Amount: 12.5+13.3=

<h2><u><em>25.8 square yards</em></u></h2>

7 0
2 years ago
An article suggests that a poisson process can be used to represent the occurrence of structural loads over time. suppose the me
kirill115 [55]

Answer:

a) \lambda_1 = 2*2 = 4

And let X our random variable who represent the "occurrence of structural loads over time" we know that:

X(2) \sim Poi (4)

And the expected value is E(X) = \lambda =4

So we expect 4 number of loads in the 2 year period.

b) P(X(2) >6) = 1-P(X(2)\leq 6)= 1-[P(X(2) =0)+P(X(2) =1)+P(X(2) =2)+...+P(X(2) =6)]

P(X(2) >6) = 1- [e^{-4}+ \frac{e^{-4}4^1}{1!}+ \frac{e^{-4}4^2}{2!} +\frac{e^{-4}4^3}{3!} +\frac{e^{-4}4^4}{4!}+\frac{e^{-4}4^5}{5!}+\frac{e^{-4}4^6}{6!}]

And we got: P(X(2) >6) =1-0.889=0.111

c)  e^{-2t} \leq 2

We can apply natural log in both sides and we got:

-2t \leq ln(0.2)

If we multiply by -1 both sides of the inequality we have:

2t \geq -ln(0.2)

And if we divide both sides by 2 we got:

t \geq \frac{-ln(0.2)}{2}

t \geq 0.8047

And then we can conclude that the time period with any load would be 0.8047 years.

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

P(X=x)=\lambda e^{-\lambda x}

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution"

Solution to the problem

Let X our random variable who represent the "occurrence of structural loads over time"

For this case we have the value for the mean given \mu = 0.5 and we can solve for the parameter \lambda like this:

\frac{1}{\lambda} = 0.5

\lambda =2

So then X(t) \sim Poi (\lambda t)

X follows a Poisson process

Part a

For this case since we are interested in the number of loads in a 2 year period the new rate would be given by:

\lambda_1 = 2*2 = 4

And let X our random variable who represent the "occurrence of structural loads over time" we know that:

X(2) \sim Poi (4)

And the expected value is E(X) = \lambda =4

So we expect 4 number of loads in the 2 year period.

Part b

For this case we want the following probability:

P(X(2) >6)

And we can use the complement rule like this

P(X(2) >6) = 1-P(X(2)\leq 6)= 1-[P(X(2) =0)+P(X(2) =1)+P(X(2) =2)+...+P(X(2) =6)]

And we can solve this like this using the masss function:

P(X(2) >6) = 1- [e^{-4}+ \frac{e^{-4}4^1}{1!}+ \frac{e^{-4}4^2}{2!} +\frac{e^{-4}4^3}{3!} +\frac{e^{-4}4^4}{4!}+\frac{e^{-4}4^5}{5!}+\frac{e^{-4}4^6}{6!}]

And we got: P(X(2) >6) =1-0.889=0.111

Part c

For this case we know that the arrival time follows an exponential distribution and let T the random variable:

T \sim Exp(\lambda=2)

The probability of no arrival during a period of duration t is given by:

f(T) = e^{-\lambda t}

And we want to find a value of t who satisfy this:

e^{-2t} \leq 2

We can apply natural log in both sides and we got:

-2t \leq ln(0.2)

If we multiply by -1 both sides of the inequality we have:

2t \geq -ln(0.2)

And if we divide both sides by 2 we got:

t \geq \frac{-ln(0.2)}{2}

t \geq 0.8047

And then we can conclude that the time period with any load would be 0.8047 years.

3 0
3 years ago
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