Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?

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

3 years ago

Simplify (23)^–2 genuinely confused

statuscvo [17]

Answer:

1/529

Step-by-step explanation:

$23^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\23^{-2}=\frac{1}{23^2}\\\\23^2=529\\\\=\frac{1}{529}$

7 0

3 years ago

Find the coordinates of the point where the line <img src="https://tex.z-dn.net/?f=y%3D5x%2B7%5C%5C" id="TexFormula1" title="y=5

Anvisha [2.4K]

Answer:

(0, 7)

Step-by-step explanation:

The point that crosses the y-axis is called the y-intercept of the line.

We are given an equation of the line and we need to determine the y-intercept. This can be done by determining the constant in the equation.

What are constants?

Constants are such terms that include only numbers. There should be no variables in constants.

We know that:

$\bullet \ \text{Given equation of line: y = 5x + 7}$

The constant we can see in the equation is "7". Therefore, the y-intercept is 7.

Note: The y-intercept of the line must have an x-coordinate of 0.

Therefore,

⇒ Coordinates of y-intercept: (x, y) ==> (0, 7).

7 0

2 years ago

Why is 3.3 > 3.2999 please can any explain

photoshop1234 [79]

Answer:

Step-by-step explanation: its cuz 3.3 is a equal to 3.30000 so 3.2999 would be less than it as it is just becoming smaller and smaller but whilst still staying the same number so 3.3000000=3.3 just like 3.29999999=3.29 all it is, is the repeating function in decimals.

5 0

2 years ago

Which two properties characterize an air mass?

Lapatulllka [165]

Answer:

Step-by-step explanation: Air masses are given a two-part name that describes the humidity and temperature characteristics of the region where they form

5 0

3 years ago

Read 2 more answers