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3 years ago

Find two consecutive whole numbers that 90 lies between

1 answer:

6 0

Let
a--------> the first whole number
a+1-----> the second consecutive whole number

we know that
if 90 lies between
then
[a+(a+1)]/2=90-------> 2a+1=180----> a=179/2-------> a=89.5
a=89.5
a+1=90.5
but
89.5 and 90.5 are not whole numbers

therefore
No solutions exist

the answer is
No solutions exist

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What is f(-x), if f(x)=2|x|+3x

a_sh-v [17]

F(-x) = 2/-x/ + 3(-x) = 2/x/ - 3x;

6 0

3 years ago

Explain how counting number of girls in five children family can be treated as a binomial experiment. What assumptions are neces

Juliette [100K]

This is a binomial experiment and you'll use the binomial probability distribution because:

There are two choices for each birth. Either you get a girl or you get a boy. So there are two outcomes to each trial. This is where the "bi" comes from in "binomial" (bi means 2).
Each birth is independent of any other birth. The probability of getting a girl is the same for each trial. In this case, the probability is p = 1/2 = 0.5 = 50%
There are fixed number of trials. In this case, there are 5 births so n = 5 is the number of trials.

Since all of those conditions above are met, this means we have a binomial experiment.

Some textbooks may split up item #2 into two parts, but I chose to place them together since they are similar ideas.

8 0

4 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

4 years ago

Help please! I have choral practice...

Maslowich

This polygon is composed of a right triangle and a parallelogram.

The area of right angle :
$A_\Delta=\frac{1}{2}\cdot15\cdot8=\frac{1}{2}\cdot120=\boxed{60\ (cm^2)}$

The area of the parallelogram:
$A_P=15\cdot(13-8)=15\cdot5=\boxed{75\ (cm^2)}$

The area of the polygon is equal: $A=A_\Delta+A_P$

Therefore, the answer is:
$\boxed{\boxed{A=60\ cm^2+75\ cm^2=135\ cm^2}}$

7 0

3 years ago

Read 2 more answers

David is buying fish for his aquarium. Clown fish cost $12 each and angel fish cost $7 each. If he has $100 to spend, and he wan

Anni [7]

Answer:

6 clown fish and 4 angel fish

Step-by-step explanation:

lets say he bought 8 clown fish.

12*8 = 96

the last 4 dollars wont be used.

lets say he bought 7 clown fish-

12*7 = 84

100 - 84 = 16. 16 is not a multiple of 7.

lets say he bought 6 clown fish,

12*6 = 72

100 - 72 = 28

28/7 = 4

If David has $100 dollars to spend and wants to spend every dollar, he can buy 6 clown fish and 4 angel fish.

3 0

2 years ago