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3 years ago

8

If 20 were added to each of the vlaues in a data set that originally had a standard deviation of 8, the standard deviation of th

e resulting data would be 28

1 answer:

Nitella [24]3 years ago

3 0

Answer:

False (I assume it's a true/false question)

Step-by-step explanation:

Standard deviation measures how spread out the data is. If you add 8 to all the data values, the distribution of data moves to the right (on a graph) 8 units. The shifted data are no more and no less spread out than before. The standard deviation does not change.

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3 years ago

The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. Th

Orlov [11]

The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

<h3>How to determine the length</h3>

The cosine rule is given as;

$c = \sqrt{a^2 + b^2 - 2ab cos \alpha }$

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

$c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}$

$c = \sqrt{533 - 308 * 0. 7660}$

$c = \sqrt{533 - 235. 93}$

$c = \sqrt{297. 072}$

$c = 17. 24$ feet

Using sine rule

$\frac{a}{sin A } = \frac{c}{sin C}$

$\frac{a}{sin 70} = \frac{17. 24}{sin 40}$

Cross multiply

$a$ × $sin 60$ = $c$ × $sin 70$

$a$ × $0. 8660$ = $17. 24$ × $0. 9397$

$a = \frac{16. 20}{0. 8660}$

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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2 years ago

strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, formulas for the candle are described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$ (2)

Where:

$r$ - Radius, in centimeters.

$h$ - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

$h = \frac{V}{\pi\cdot r^{2}}$

By substitution in (2) we get the following formula:

$A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)$

$A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}$

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

$4\pi\cdot r -\frac{2\cdot V}{r^{2}} = 0$

$4\pi\cdot r^{3} - 2\cdot V = 0$

$2\pi\cdot r^{3} = V$

$r = \sqrt[3]{\frac{V}{2\pi} }$

There is just one result, since volume is a positive variable.

Second Derivative Test

$A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}$

If $\left(r = \sqrt[3]{\frac{V}{2\pi}}\right)$ :

$A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }$

$A_{s} = 12\pi$ (which means that the critical value leads to a minimum)

If we know that $V = 3217\,cm^{3}$ , then the dimensions for the minimum amount of plastic are:

$r = \sqrt[3]{\frac{V}{2\pi} }$

$r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}$

$r = 8\,cm$

$h = \frac{V}{\pi\cdot r^{2}}$

$h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}$

$h = 16\,cm$

And the amount of plastic needed to cover the outside of the candle for packaging is:

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$

$A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)$

$A_{s} \approx 1206.372\,cm^{2}$

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

3 0

2 years ago