All categories

2 years ago

Simple math equation but in not very bright in the head, help would be appreciated :)

Mathematics

1 answer:

algol [13]2 years ago

4 0

Answer:

AA similarity

Step-by-step explanation:

Using angle sum theorem, you can clearly find out the missing angles on the left and right triangles are 40° and 50° respectively.

Therefore, by using any two angles in the triangles, you can prove they are similar by AA similarity.

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

4 years ago

Jim thinks that the value of a baseball card can be modeled by a decay formula and that the value will decrease at a rate of 0.2

Sindrei [870]

Answer: $244.55

A = $250 ; r=0.002 t= 11 [From 2007 to 2018 , t=2018-2007]

6 0

1 year ago

I need help.....plz help...thanks

kvv77 [185]

Answer:

Step-by-step explanation:

X is equal to One so that is why slope 1 and -3

6 0

3 years ago

Can someone help me with this question

Molodets [167]

16 nickles
10 dimes

1.00$ + 0.80$

5 0

3 years ago

josh is 6 years older than 4 times Kim's age. The sum of their ages is less than 31. what is the oldest Kim could be? show all y

Mice21 [21]

Answer:

4 years old.

Step-by-step explanation:

Lets say that Josh's age is j and Kim's age is k. As Josh is 6 years older than 4 times Kim's age, we can write this as an equation:

j = 4k + 6

This is, John's age is equal to four times Kim's plus 6 years.

We then know that, when summed their ages is less than 31, so:

k + j < 31

Replace John's age by our first equation:

k + 4k + 6 < 31

5k + 6 < 31

Subtract 6 in both sides:

5k + 6 - 6 < 31 - 6

5k < 25

Dividing both sides by 5:

5k/5 < 25/5

k < 5

So, Kim's age MUST be less than 5.

If we talk about discrete values, this is 1, 2, 3, 4, 5, 6...., we will say than the oldest Kim could be is 4. If Kim is 5 years old, the sum of ages is 31 and we need it ti be LESS than 31. (we are not considering fractional numbers as 4.5 years old).

So, Kim can be, at maximum, 4 years old.

7 0

3 years ago