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3 years ago

Solve for xx. Write the smaller solution first, and the larger solution second. X^2 + 12x + 27 = 0x 2 +12x+27=0

Mathematics

2 answers:

sineoko [7]3 years ago

7 0

Answer:

x = -9, -3

Step-by-step explanation:

x^2 + 12x + 27 = 0

We need 2 numbers whose product is + 27 and whose sum is + 12. These are 3 and 9. So the factors are:-

(x + 3)(x + 9) and this = 0

So (x + 3) = 0 or x + 9 = 0

x = -3 , -9

Marta_Voda [28]3 years ago

4 0

Answer:

-5 and 7

Step-by-step explanation:

we need to find numbers a and b such that a+b=-2 and ab=-35.

a=5 and b=-7 satisfy both conditions, so our equation can be re-written:

(x + 5)(x-7) = 0

According to the zero-product property, we know that

x+5=0 or x-7=0, which means

x=-5x or x=7

Please mark brainliest and thank! Thank you!

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Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

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Solution to the problem

Part a

For this case we want this probability:

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And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

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