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3 years ago

Expand and simplify these

1 answer:

6 0

$(x+6)(x+9)=x^2+9x+6x+54=x^2+15x+54 \\\\(x-5)(x+2)=x^2+2x-5x-10=x^2-3x-10\\\\(x-1)(x-7)=x^2-7x-x+7=x^2-6x+7\\\\(4x+9)(3x+8)=12x^2+32x+27x+72=12x^2+59x+72\\\\(3x-8)(2x-1)=6x^2-3x-16x+8=6x^2-19x+8\\\\(x+9) ^2=x^2+2\cdot x\cdot9+9^2=x^2+18x+81 \\\\(3x+2)^2=(3x)^2+2\cdot3x\cdot2+2^2=9x^2+12x+4$

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An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

olchik [2.2K]

Answer:

a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire

b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that $p = 0.7$

10 sprinklers.

This means that $n = 10$

a. What is the probability that all of the sprinklers will operate correctly in a fire?

This is $P(X = 10)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282$

0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.

b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?

This is:

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668$

$P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335$

$P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211$

$P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282$

Then

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496$

0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

7 0

3 years ago

I’m having troubles with this one.

nikklg [1K]

Answer:

239 degrees.

Arc is circumference so length = r * 4.17133691221

Step-by-step explanation:

We eliminate RSQ in degrees = 90 + 31 = 121

So that;

RPQ = 360 -121 = 239 degrees

2pi radius (239/360) = r6.28318530718 (0.66388888888)

= r * 4.17133691221

7 0

4 years ago

Help me I don’t get this

natali 33 [55]

Answer:

Step-by-step explanation:

An object on the moon weighs 1/6th of its weight on earth. If the object weighs 12 lbs then it weighs 1/6(12) = 12/6 = 2 lbs. This can be applied to any object's weight using m = e/6.

4 0

3 years ago

Part B

tankabanditka [31]

same needs to climb at a 12 rate

7 0

3 years ago

Nth term (math) asap please.

SOVA2 [1]

Answer:

Just do minus two, and you will get 27-100=-73

Step-by-step explanation:

7 0

3 years ago