In a triangle ABC,AB=9 and BC =12 which of the following Cannot be the length of AC.

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

(a1) The probability that temperature increase will be less than 20°C is 0.667.

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable X as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

7 0

2 years ago

An old rectangular tank with length 0.3 m could hold 154 L of water. A new similar tank has a length of 1.5 m. What is the capac

dimaraw [331]

The length of the new tank is 5 times bigger than the old one, so 154×5=770. As a result, the capacity of the new tank is 770L. Hope it help!

6 0

2 years ago

Read 2 more answers

"The Highest Common Factor (HCF) of my two numbers is 3 The Lowest Common Multiple (LCM) of my two numbers is 45" (b) Write down

Mila [183]

Answer:

Step-by-step explanation:

15 and 3

6 0

2 years ago

It takes one week for a crew of workers to pave 3/5 kilometer of a road. At that rate, how long will it take to pave 1 kilometer

kondaur [170]

1 kilometer =5/3 week

Step-by-step explanation:

Given that the crew paves 3/5 kilometer of a road in 1 week then this can be written as;

3/5 k = 1 week

For 1 kilometer of a road,

3/5k = 1 week

1k=?

perform cross product as;/multiplication equation

1*1 / 3/5

1*5/3

5/3, 1 2/3 weeks

A division equation will be'

3/5 kilometers = 1 week

Divide both sides by 3/5

1 kilometer =5/3 week

Learn More

Multiplication /Division :brainly.com/question/11892889

Keywords: kilometers, equation, multiplication.division

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4 0

2 years ago

What is the final amount if 784 is decreased by 1% followed by a 4% increase?

Iteru [2.4K]

Answer:

The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

A way to solve this problem is as follows:

The general formula for this is taking into account that:

$\\ percent\;change = \frac{change}{starting\;point}$

The starting point is number 784.

The most important key is the solution for this answer is that:

$\\ change = starting\;point - x$

Where x is a number that we need to find. Then

$\\ percent\;change = \frac{starting\;point - x}{starting\;point}$ [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

$\\ 3\% = \frac{784 - x}{784}$