Franny wants to spend an equal amount of money

Find the geometric sequence.<br> 4, 12, 36, 108, ...

yulyashka [42]

The geometric sequence would be multiplying by 3

3 0

3 years ago

rick earns $8.50 per hour at his mother office. He plans on working 12.5 hours this week. How much money will rick earn?

marusya05 [52]

That would be 8.50 times 12.5 which is $106.25

7 0

3 years ago

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The vertex form of the function <br> y=x^2+8x+29

stira [4]

Answer:

y = (x+4)^2 +13

Step-by-step explanation:

y=x^2+8x+29

To complete the square take the coefficient of the x term

8

Divide by 2

8/2 =4

Then square it

4^2 =16

y=x^2+8x+16+13

= (x^2+8x+16) +13

= (x+4)^2 +13

5 0

3 years ago

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:

$P(X$

8 0

3 years ago

Which of the following expressions has a coefficient of 6 and a constant of 9?

Tcecarenko [31]

It would be C because a coefficient is always with a variable and 6 is with a variable which makes it a coefficient

Hope this helps

Have a great day/night

6 0

3 years ago

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