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Artyom0805 [142]
3 years ago
9

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

Mathematics
1 answer:
diamong [38]3 years ago
6 0

Answer:

x=19

Step-by-step explanation:

2(x+6)=3(x-4)+5

2x+2*6=3x-3*4+5

2x+12=3x-12+5

12+12-5=3x-2x

19=x

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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 <em>X</em> = temperature increase.

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

The probability density function of <em>X</em> 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 <em>X</em> 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.

<u>We know that:</u>

     \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.

<u>Therefore,</u>

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

7 0
2 years ago
Why is 3.3 &gt; 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
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