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3 years ago

The solution to 2X -2+5 = 13 is

Mathematics

2 answers:

Nadya [2.5K]3 years ago

7 0

Isolate the variable by dividing each side by factors that don’t contain the variable

X=5

jonny [76]3 years ago

4 0

Answer:

Step-by-step explanation:

2x -2+5=13

2x +3 =13

2x = 13-3

2x = 10

x = 10/2

x = 5

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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:

$p = 0.383$

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

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

(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 $f(3) = 0.09$

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

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

18 Points! K12 Student struggling with deadline!

Liula [17]

Answer:

Step-by-step explanation:

The easiest way is to substitute 8 for x in the first equation,

5 0

3 years ago

the ratio of goats to sheep at a university research farm is 4: 7. The number of sheep at the arm is 28. what is the number of g

GalinKa [24]

4+7=11 i.e. The whole.
7/11=28

1/11=4
Goats are 4/11 therefore
4 x 4= Ans
All the animals add up to 44 and if you check w/ 7/11 it is correct.

4 0

3 years ago

I need the answer please

devlian [24]

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Answer: x = 37

Explanation:

2x-5 + 3x = 180

5x - 5 = 180

5x = 185

x = 37

I hope this helped!

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5 0

3 years ago

Read 2 more answers

What kind of triangle has three angles of measure 83 degrees, 31 degrees and 66 degrees?

andreyandreev [35.5K]

Hi!

An obtuse angle is one greater than 90 degrees, a right angle one that is 90, and acute less than 90.

An obtuse triangle is one with one obtuse angle, all the rest being acute. A right triangle is one with one right angle, all the rest acute. And finally, an acute triangle is one with three acute angles.

In this case, the angles measure 83 degrees, 31 degrees, and 66 degrees. All of them are acute angles, as they're all less than 90 degrees.

Therefore, the triangle is an acute triangle.

Hope this helped!

5 0

4 years ago

Read 2 more answers