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stiks02 [169]
3 years ago
12

Factor the following quadratic expression n^2+ 4n-12

Mathematics
1 answer:
nirvana33 [79]3 years ago
3 0

Answer:

(n + 6)(n - 2)

Step-by-step explanation:

Given

n² + 4n - 12

Consider the factors of the constant term (- 12) which sum to give the coefficient of the n- term (+ 4)

The factors are + 6 and - 2 , since

6 × - 2 = - 12 and 6 - 2 = + 4

Then

n² + 4n - 12 = (n + 6)(n - 2) ← in factored form

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A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength
irinina [24]

Answer:

Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.

Step-by-step explanation:

We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.

<u><em>Let </em></u>\bar X<u><em> = sample mean comprehensive strength</em></u>

The z-score probability distribution for sample mean is given by;

                          Z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = population mean comprehensive strength = 5500 psi

            \sigma = standard deviation = 100 psi

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P(\bar X > 4985 psi)

    P(\bar X > 4985 psi) = P( \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{4985-5500}{\frac{100}{\sqrt{9} } } ) = P(Z > -15.45) = P(Z < 15.45)

                                                                  = <u>0.99999</u>

<em>Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.</em>

4 0
3 years ago
The blueprint for a new swimming pool uses the scale 3/4 inch = 2 feet. If the actual dimensions of the pool will be 8 ft wide b
weeeeeb [17]

Answer:

The dimensions of the pool on the blueprint would be 3 in wide by 4.5 in long.

Step-by-step explanation:

First I turned 3/4 into a decimal, which would be 0.75. The I divided the dimensions of the pool by two. This way I could multiply the .75 by how many sets of two feet there were in the dimensions. Finally I multiplied 4 by .75 and I multiplied 6 by .75. That is how I found my answer.

5 0
3 years ago
Can two rectangles with the same side lengths be congruent
sveta [45]

Answer:

the angles in squares and rectangles it's always 90° so two squares or two rectangles with same side lengths are congruent.

8 0
2 years ago
Read 2 more answers
Ax-bx+y=z the formula that could be used to find x
Illusion [34]

ax-bx+y=z the formula that could be used to find x

Answer:

<h2>x=z−y/a−b</h2>

5 0
3 years ago
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0.09859154929 round to nearest tenth
Free_Kalibri [48]

Answer:

0.1

Step-by-step explanation:

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