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3 years ago

Please help find the value of x for this equation

Mathematics

1 answer:

jonny [76]3 years ago

4 0

Answer:

Step-by-step explanation:

We would like to find the value of x.

Since the triangle is isosceles, the drawn altitude bisects the base of length 8. This means that the big triangle is split into two congruent triangles with base 4 and height 5.

Notice that by definition, as well, the altitude of 5 is perpendicular to the base of length 8. So, we have two right triangles, each with legs of 4 and 5 and hypotenuse x.

We apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, we have:

4² + 5² = x²

16 + 25 = x²

41 = x²

x = √41

The answer is thus A.

~ an aesthetics lover

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

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Assuming the incident of fires for individual reactors can be described by a Poisson distribution, what is the probability that

Maksim231197 [3]

Complete Question

The Brown's Ferry incident of 1975 focused national attention on the ever-present danger of fires breaking out in nuclear power plants. The Nuclear Regulatory Commission has estimated that with present technology there will be on average, one fire for every 10 years for a reactor. Suppose that a certain state has two reactors on line in 2020 and they behave independently of one another. Assuming the incident of fires for individual reactors can be described by a Poisson distribution, what is the probability that by 2030 at least two fires will have occurred at these reactors?

Answer:

The value is $P(x_1 + x_2 \ge 2 )= 0.5940$

Step-by-step explanation:

From the question we are told that

The rate at which fire breaks out every 10 years is $\lambda = 1$

Generally the probability distribution function for Poisson distribution is mathematically represented as

$P(x) = \frac{\lambda^x}{ k! } * e^{-\lambda}$

Here x represent the number of state which is 2 i.e $x_1 \ \ and \ \ x_2$

Generally the probability that by 2030 at least two fires will have occurred at these reactors is mathematically represented as

$P(x_1 + x_2 \ge 2 ) = 1 - P(x_1 + x_2 \le 1 )$

=> $P(x_1 + x_2 \ge 2 ) = 1 - [P(x_1 + x_2 = 0 ) + P( x_1 + x_2 = 1 )]$

=> $P(x_1 + x_2 \ge 2 ) = 1 - [ P(x_1 = 0 , x_2 = 0 ) + P( x_1 = 0 , x_2 = 1 ) + P(x_1 , x_2 = 0)]$

=> $P(x_1 + x_2 \ge 2 ) = 1 - P(x_1 = 0)P(x_2 = 0 ) + P( x_1 = 0 ) P( x_2 = 1 )+ P(x_1 = 1 )P(x_2 = 0)$

=> $P(x_1 + x_2 \ge 2 ) = 1 - \{ [ \frac{1^0}{ 0! } * e^{-1}] * [[ \frac{1^0}{ 0! } * e^{-1}]] )+ ( [ \frac{1^1}{1! } * e^{-1}] * [[ \frac{1^1}{ 1! } * e^{-1}]] ) + ( [ \frac{1^1}{ 1! } * e^{-1}] * [[ \frac{1^0}{ 0! } * e^{-1}]]) \}$

=> $P(x_1 + x_2 \ge 2 )= 1- [[0.3678 * 0.3679] + [0.3678 * 0.3679] + [0.3678 * 0.3679] ]$

$P(x_1 + x_2 \ge 2 )= 0.5940$

3 0

3 years ago

On Saturday Stella worked for two hours helping her mother in the house. she spent 1/3 of her time doing laundry, 1/4 of a time

raketka [301]

$\bf \stackrel{\textit{total hours time}}{2}-\cfrac{1}{3}-\cfrac{1}{4}\impliedby \textit{we'll use an LCD of \underline{12}}
\\\\\\
2-\cfrac{1}{3}-\cfrac{1}{4}\implies \cfrac{(12\cdot 2)~-~(4\cdot 1)~-~(3\cdot 1)}{12}\implies \cfrac{24-4-3}{12}\implies \cfrac{17}{12}
\\\\\\
\textit{12 goes into 17 \underline{1 time} and it has a \underline{remainder} of 5 }\implies 1\frac{5}{12}$

which is one hour and 25 minutes.

7 0

4 years ago