All categories

3 years ago

17. x^2 + 2x + 1

Mathematics

1 answer:

valentina_108 [34]3 years ago

5 0

Answer:

E. This polynomial could be factored by using grouping or the perfect squares methods.

Step-by-step explanation:

x^2 + 2x + 1

There is no greatest common factor

This is a perfect square

a^2 + 2ab+ b^2 = ( x+1)^2

We can factor this by grouping

x^2 + 2x + 1

(x^2 +x) + (x+1)

x( x+1) + x+1

Factor out x+1

( x+1) ( x+1)

This is not the difference of squares since there is no subtraction

You might be interested in

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

Add together 2350mm 3.42cm 11/2m and 1.45m

Artyom0805 [142]

9.3342meters because you convert 2350mm into m which is 2.35m, + and also convert 3.42cm to m which is 0.0342 then + 1.45m +11/2m= 9.3342m

6 0

3 years ago

An ice-cream parlor donated boxes of ice-cream bars for a school event the organizers need to decide how many ice-cram bars are

mylen [45]

Divide the number of ice-cream bars into the number of people. Example: say you have 20 ice cream bars and 10 people you divide 20/10 and get 2 ice cream bars per person. Hope this helped.

6 0

3 years ago

Read 2 more answers

A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 2 bags of chips for $9.00. Another customer buy

stiv31 [10]

Answer: hot dog = $1.75

Step-by-step explanation:

Let h represent hot dogs and c represent bags of chips.

Customer 1: 4h + 2c = 9.00 → 3(4h + 2c = 9.00) → 12h + 6c = 27.00

Customer 2: 5h + 3c = 11.75 → -2(5h + 3c = 11.75) → -10h - 6c = -23.50

2h = 3.50

÷2 ÷2