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3 years ago

-2(5 + 6n) < 6(8 - 2n) solve for n

Mathematics

1 answer:

alexandr402 [8]3 years ago

8 0

Answer:

All real numbers Interval Notation: (-∞,∞)

Step-by-step explanation:

Any value of n makes the inequality true.

Hope this helps.

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Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours is a

Ivan

Answer:

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

$P(X$

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 cumulative distribution for this function is given by:

$F(X) = 1- e^{-\lambda x}, x\ geq 0$

We know the value for the mean on this case we have that :

$mean = \frac{1}{\lambda}$

$\lambda = \frac{1}{Mean}= \frac{1}{2.725}=0.367$

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by: $Var(X) =\frac{1}{\lambda^2}$

And the deviation would be:

$Sd(X) = \frac{1}{\lambda}= \frac{1}{0.367}= 2.725$

And the mean is given by $Mean = 2.725$

Two deviations correspond to 5.540, so we want this probability:

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity:

$P(X$

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3 years ago

Bailey is comparing two squares. The first square has an area of 144 cm2, and the second square has an area of 81 cm2. What is t

Nadusha1986 [10]

Answer:

They are both 63 Inches/ Lengths apart.

Step-by-step explanation:

You see when it comes to cm2 inches and lengths You must always Analyze your work and figure out if you can seperate the two among themselves equally. 81 Goes into 144. 63 plus equation.

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3 years ago

3) The sum of three consecutive numbers is 72. What are the smallest of these numbers?

Oksi-84 [34.3K]

Answer:

Step-by-step explanation:

x+x+1=x+2=72

3x+3=72

3x=69

x=23

23+24+25=72

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3 years ago

5,000 people visited a bookfair in the first week. The numbers increased by 10% in the second week. how many people visited the

lorasvet [3.4K]

Answer:

5500

Step-by-step explanation:

5000 + (10 / 100) x 5000 = 5000 + (1/10) x 5000 = 5000 +500= 5500 people visted the book fair in the second week

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3 years ago

Emily bought some ice cream cones which cost $24. she paid $m and got back $6 of change. Find m

maria [59]

Answer:

m = 30

Step-by-step explanation:

total = 24

m = amount paid

change = 6

m - 6 = 24

+6 +6

m = 30

Hope this helped! Have a nice rest of ur day! Plz mark as brainliest!!!

-Lil G

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3 years ago