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maksim [4K]
3 years ago
10

What values are needed to make each expression a perfect square trinomial?

Mathematics
2 answers:
ExtremeBDS [4]3 years ago
8 0

Answer:

x^2 + 4x + 4

x^2 - 10x + 25

works on edge

Ivahew [28]3 years ago
3 0

Answer:

4;

25

Step-by-step explanation:

x² + 2(x)(2) + 2²

x² + 4x + 4

x² - 2(x)(5) + 5²

x² - 10x + 25

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At least 96.00​% of the data in any data set lie within how many standard deviations of the​ mean? Explain how you arrived at yo
zheka24 [161]

The answer assumes that the question is about the <em>normal distribution</em>.

Answer:

96% of the data in any data set <em>normally distributed</em> is 2.05 <em>standard deviations</em> <em>above</em> and <em>below</em> the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the <em>standard normal distribution</em> that permits obtaining any probability from any normally distributed data, doing the following transformation:

\\ z = \frac{x-\mu}{\sigma}

That is, in this case, we subtract a given value <em>x</em> from the <em>population mean</em> and then divide the result by the <em>population standard deviation</em>. This is a z-score, and this value is associated with the probability for a <em>standard normal distribution</em>, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the <em>standard normal distribution</em>, there is associated a ubiquitous <em>standard normal table</em> for possible values of <em>z</em> and the corresponding probability. Then, knowing that the data are <em>normally distributed</em> and having both distribution <em>parameters</em>, namely, the <em>population mean</em> and <em>population standard deviation</em>, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that <em>the z-score value tells us how many standard deviations</em> <em>from the mean</em> are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a <em>cumulative standard normal table from the mean</em>.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a <em>cumulative standard normal table from the mean</em>. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 <em>standard deviations</em> <em>above</em> and <em>below</em> the mean.  

 

5 0
3 years ago
Isosceles triangle, perimeter if the perimeter of isosceles triangle abc is 20 and the length of side ac is 8, what is one possi
Hoochie [10]

The perimeter = 20 and AC = 8

Now as it is not mentioned which sides are equal of the isosceles triangle ABC,

We have two possible situations.

1)

If AC is the base

In that case AB = BC

Now AC = 8, AB = x , BC = x

So x + x + 8 = 20

2x + 8 = 20

2x = 12

x = 6

AB = BC = 6

2)

IF AC is not the base,

Then

AC = BC or AC = AB

So BC = 8 or AB = 8

If AB = AC = 8

Then

BC + 8 + 8 = 20

BC = 4

So there are two possible lengths of BC

Either it is BC = 8 or BC = 6 or BC = 4

The figure is attached for your reference.


5 0
3 years ago
Read 2 more answers
How are the triangles similar pleaseee help I’ll give you BRAINLIEST
Bad White [126]

Answer:

SSS

Step-by-step explanation:

Only sides are given, not angles, so you know it's side-side-side

7 0
3 years ago
describe the mathematical order of operations. if you use an acronym for your description, make sure you define what each letter
MrMuchimi
PEMDAS

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
3 0
3 years ago
Read 2 more answers
Find the volume of the given solid: Bounded by the cylinder y^2+z^2=4 and the planes x = 2y, x = 0, z = 0 in the first octant.
rodikova [14]

The solution would be like this for this specific problem:

<span>V = ∫ dV </span><span>
<span>= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr </span>
<span>= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr </span>
<span>= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr </span>
<span>= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr </span>
<span>= ∫0→2 [ 2·r² ] dr </span>
<span>= (2/3)·2³ - (2/3)·0³ </span>
<span>= 16/3 </span></span>

So the volume of the given solid is 16/3. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

3 0
3 years ago
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