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2 years ago

Write two numbers that multiply to the value on top and add to the value on bottom. 27 -12

Mathematics

2 answers:

stellarik [79]2 years ago

8 0

Answer:

-3 and -9

Step-by-step explanation:

First, it is helpful to write out what is given by the question, with variables x and y.

x*y = 27

x+y = -12

Now we will isolate a variable from one and plug it into the other:

y = -12 - x

x(-12-x) = 27

-x^2 -12x -27 = 0

x^2 + 12x + 27

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

x must be either -9 or -3

Now we plug those x-values into either equation to get their corresponding y-values:

-9 + y = -12

y = -3

-3 + y = -12

y = -9

We can see that the first x value (-9) corresponds to y = -3, and the second pair is -3 and -9. Either way, the pair is -3 and -9.

Therefore the pair of numbers must be -3 and -9.

mariarad [96]2 years ago

4 0

Multiply 3x9 and it gives u 27
And -3 plus -9 equal -12

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Answer:

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Step-by-step explanation:

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2 years ago

The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitor

nadya68 [22]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: