It possible for a triangle to have measures in an extended ratio of 1:4:7?

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

Why does a logarithmic equation sometimes have an extraneous solution?

jonny [76]

The main reason behind this is using properties of logarithm .

like

when solving

log_2(x+2)+log_2(x-3)=3

There you use multiplication property and make addition to multiplication then you get extraneous solution because in plenty of cases they occur

like

(-2)²=(2)²

But

-2≠2

Same happens in case of logarithm

6 0

1 year ago

Read 2 more answers

The ratio of yellow blue and red balloons is 2:3:2 respectively. If the total number is 28 is many yellow balloons are there

Phoenix [80]

Answer:

8

Step-by-step explanation:

The ratio of yellow balloons to the total is ...

... 2:(2+3+2) = 2/7

This fraction of 28 balloons is ...

... (2/7)·28 = 56/7 = 8 . . . . yellow balloons

8 0

2 years ago

Can someone please help me find the measure of the exterior angle.

dimulka [17.4K]

Answer:

k = 140°

Step-by-step explanation:

The sum of the interior angles of any triangle = 180°.

64° + 76° + x = 180°

x = 40°

40° + k = 180° because they are supplementary angles

k = 140°

8 0

2 years ago

Read 2 more answers

How would I solve n^2=2n

lidiya [134]

Answer: n=0 or n=2

Step-by-step explanation: Step 1: Subtract 2n from both sides.

n²−2n=2n−2n

n²−2n=0

Step 2: Factor left side of equation.

n(n−2)=0

Step 3: Set factors equal to 0.

n=0 or n−2=0

n=0 or n=2

5 0

2 years ago