Solve 23h2+h=−13 by using the quadratic formula

Factor the expression f^2+10f+16

denis-greek [22]

Answer: (f + 2) (f + 8)

It's hard to explain, but I suggest you use the AC method. Hope this helps!

4 0

3 years ago

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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

Rewrite the following quadratic functions in intercept or factored form. Show your work.

Dmitry [639]

Answer:

f(x) = 3(x+2)(x-2)

Step-by-step explanation:

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

$f(x) = 3x^2 - 12$

We can factorize the given function so taking the common factors out of it to get:

$f(x)=3x^2 - 12$

$f(x) = 3 (x^2 - 4)$

The term $(x^2-4)$ is in the form $a^2-b^2$ so it can further be factorized to give:

$f(x) = 3 (x+2)(x-2)$

Therefore, the factored form of the given quadratic function is f(x) = 3(x+2)(x-2).

7 0

3 years ago

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What is a geometric sequence and arithmetic sequence? ~MUST EXPLAIN~

Vadim26 [7]

A geometric sequence is one that involves addition or subtraction. One example would be "In an auditorium, the 1st row has 25 seats. The 2nd has 30. The 3rd has 35. How many does the 4th have? Take the formula, x + 5. All you do is simply add 5.

An arithmetic sequence is one that involves multiplication or division. For example, "Jon receives 5 dollars each week. If he waits for 5 months, how much money will he have? Honestly, all you have to do is think about the formula. x * 5. x would be the number of weeks.

I know my answer is not as good as the verified one, but it is simpler and easier to understand. I apologize if it isn't good enough.

6 0

3 years ago

PLEASE ANSWER ASASP!!!!!! 4x + 10 = 30 what is x?

sveticcg [70]

Answer:

x=5

Step-by-step explanation:

4x+10=30

-10 -10 on both sides

4x=20

Divide 4 on both sides

20/4=5

✨Hope this helps!!✨

4 0

3 years ago