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2 years ago

Given f(a) = - 3Va + 9. Find each function value.

Mathematics

1 answer:

mario62 [17]2 years ago

7 0

The function value of f(12) is 27.

<h3>How to illustrate the function?</h3>

It should be noted that a function is simply used to show the relationship that exists between the variables.

Therefore, based on the information, the function f(12) will be:

3x - 9

f(12) = 3(12) - 9

= 36 - 9

= 27

The function value is 27

Learn more about functions on:

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Complete question:

If f(x) = 3x - 9. Find the function value of f(12).

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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:

$P(X$

8 0

4 years ago

Find the equation for the circle with a diameter whose endpoints are (3,-1) and (-2,-1)

cricket20 [7]

Answer:

The equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Step-by-step explanation:

Here, let us assume the two end points of the diameter are:

P (3,-1) and Q (-2,-1)

Now, as we knew diameter is the chord that passer through the center of the circle.

⇒ Mid point of DIAMETER = Center coordinates of the Circle

Let us assume O(x,y) is the center of the line segment PQ.

So, by MID POINT FORMULA:

$(x,y)= (\frac{3 -2}{2} , \frac{-1-1}{2} ) =( \frac{1}{2},\frac{-2}{2}) \\\implies (x,y) =( 0.5 , -1)$

⇒ The center coordinates of the circle = O(0.5,-1) ...... (1)

Now, RADIUS = Half of DIAMETER

Using DISTANCE FORMULA:

$PQ = \sqrt{(3-(-2))^2 + (-1 - (-1))^2} = \sqrt{(5)^2 + 0} = 5$

So, Radius = 5/2 = 2.5 units

Now, the equation of circle with radius r and center coordinate ( h,k) is given as: $(x-h)^2 + (y-k)^2 = r^2$

Substitute r = 2.5 and (h,k) = (0.5,0) we get:

$(x-0.5)^2 + (y-0)^2 = (2.5)^2\\\implies (x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

Hence the equation for the circle is: $(x-\frac{1}{2} )^2 + y^2 = (\frac{5}{2} )^2$

5 0

4 years ago

A tree is three times the height of the school.

natima [27]

Answer:

Can you be a litte more specific

Step-by-step explanation:

6 0

3 years ago

Rewrite the equation in Slope-Intercept Form. y+4=−12(x−2)

eimsori [14]

Answer: y = -12x +20

Step-by-step explanation: 1. distribute the -12 into the (x-2), that equals -12+24

2. subtract the 4 from the left side to move it to the right side of the equation

3. add like terms, so 24 + (-4) or 24-4 which equals 20.

4. Answer: y=-12x+20

8 0

3 years ago

How does understanding place value help you to subtract across zeros?

zysi [14]

When you subtract by zeros the same number comes out

4 0

3 years ago