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3 years ago

7-9: Practice Buddy: Independent Practice; Problem Solving please help!

Mathematics

2 answers:

Thepotemich [5.8K]3 years ago

7 0

4/3/8 is the answer

strojnjashka [21]3 years ago

3 0

Answer:

4/3/8

Step-by-step explanation:

12/1/2-8/8/1

=25/2-65/8

=100-65/8

=35/8

=4/3/8

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Find the value of x

valina [46]

Answer:

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Step-by-step explanation:

7 0

4 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

PLEASE HELP !!!!!!!!Solve the system of equations using the linear combination method.

vfiekz [6]

Answer:

The solution would be (5, -2)

Step-by-step explanation:

To use this method, start by multiplying the second equation by -1. Then add the two equations together.

9x + 5y = 35

-2x - 5y = 0

------------------

7x = 35

x = 5

Now that we have the value of x, use it to solve either equation for y.

2x + 5y = 0

2(5) + 5y = 0

10 + 5y = 0

5y = -10

y = -2

6 0

4 years ago

How many triangles can be made with the angle 70°, 70°, and 70°

seraphim [82]

Hey there!
Your answer is 0.
All the angles of a triangle must add up to 180 degrees.
However, the sum of these angles is not equal to 180 degrees.
70 + 70 + 70 = 210
210 is not equal to 180.
Hence, no triangles can be made using the angles 70, 70, and 70.
Hope this helps!

7 0

3 years ago

Write the equation of a line passing through -1,4 and perpendicular to x+2y=11

Sophie [7]

Y=2x+6
gradient is found from the formula,
$\frac{ - 1}{ - \frac{1}{2} } = 2$
y intercept is found by subbing the values of (-1,4) into the equation y=2x+c

8 0

4 years ago