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slavikrds [6]
3 years ago
5

Compute the standard deviation of the data set. Round to the nearest hundredth, if needed.

Mathematics
2 answers:
Nookie1986 [14]3 years ago
7 0

Answer:

\sigma =3.74

Step-by-step explanation:

Given : 4.9, 4.9, 9.9, 9.9, 14.9

To Find: Standard deviation

Solution:

Total number of observations = 5

Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}

Mean = \frac{4.9+4.9+9.9+9.9+14.9}{5}

Mean = 8.9

Thus \bar{x}=8.9

Now, Formula of standard deviation =\sigma = \sqrt{\frac{\sum(x_i-{x})^2}{n}}

So, \sigma = \sqrt{\frac{(4.9-8.9)^2+(4.9-8.9)^2+(9.9-8.9)^2+(9.9-8.9)^2+(14.9-8.9)^2}{5}}

\sigma =3.74

Thus Option A is correct.

Hence the standard deviation of the data set is 3.74.

Mkey [24]3 years ago
3 0
Standard deviation is calculated by the square root of the variance. Now, how do we solve the variance? The variance is the <span>average of the </span>squared differences from the Mean. Calculating the variance, we can obtain a standard deviation of <span>3.74. Therefore, the correct answer is option A.</span>
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The top and bottom margins of a poster 66 cm each, and the side margins are 44 cm each. If the area of the printed material on t
jasenka [17]

Answer:

  • width: 24 cm
  • height: 36 cm

Step-by-step explanation:

When margins are involved, the smallest area will be the one that has its dimensions in the same proportion as the margins. If x is the "multiplier", the dimensions of the printed area are ...

  (4x)(6x) = 384 cm^2

  x^2 = 16 cm^2 . . . . . divide by 24

  x = 4 cm

The printed area is 4x by 6x, so is 16 cm by 24 cm. With the margins added, the smallest poster will be ...

  24 cm by 36 cm

_____

<em>Comment on margins</em>

It should be obvious that if both side margins are 4 cm, then the width of the poster is 8 cm more than the printed width. Similarly, the 6 cm top and bottom margins make the height of the poster 12 cm more than the height of the printed area.

_____

<em>Alternate solution</em>

Let w represent the width of the printed area. Then the printed height is 384/w, and the total poster area is ...

  A = (w+8)(384/w +12) = 384 +12w +3072/w +96

Differentiating with respect to w gives ...

  A' = 12 -3072/w^2

Setting this to zero and solving for w gives ...

  w = √(3072/12) = 16 . . . . matches above solution.

__

<em>Generic solution</em>

If we let s and t represent the side and top margins, and we use "a" for the printed area, then the above equation becomes the symbolic equation ...

  A = (w +s)(a/w +t)

  A' = t - sa/w^2

For A' = 0, ...

  w = √(sa/t)

and the height is ...

  a/w = a/√(sa/t) = √(ta/s)

Then the ratio of width to height is ...

  w/(a/w) = w^2/a = (sa/t)/a

  width/height = s/t . . . . . . the premise we started with, above

6 0
3 years ago
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Lena [83]

Answer:

2

Step-by-step explanation:

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8 0
3 years ago
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H=(√3)*a/2 = 41.2

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Answer:

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Step-by-step explanation:

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176 is the brothers weight.
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3 years ago
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