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Black_prince [1.1K]
3 years ago
10

WORTH 30 POINTS PLEASE HELP

Mathematics
2 answers:
Vlad1618 [11]3 years ago
8 0
Group A:
1 dot at 9:     1 x    9 =     9
7 dots at 10: 7 x 10 =   70
8 dots at 15: 8 x 15 = 120
8 dots at 17: 8 x 17 = 136
6 dots at 19: 6 x 19 = 114

Mean: (9+70+120+136+114) / (1+7+8+8+6) = 449/30 = 14.97

Group B:
6 dots at 10: 6 x 10 = 60
5 dots at 14: 5 x 14 = 70
6 dots at 18: 6 x 18 = 108
5 dots at 25: 5 x 25 = 125
4 dots at 28: 4 x 28 = 112
4 dots at 29: 4 x 29 = 116

mean: (60+70+108+125+112+116) / (6+5+6+5+4+4) = 591 / 30 = 19.70

The group that has a lower mean age of painting students is Group A. Its mean is 14.97 or 15 years of age.
const2013 [10]3 years ago
7 0

The answer is B. Group A has less variability in the data.

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How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0
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Answer:

\displaystyle x = \frac{\pi}{3} +k\, \pi or \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi, where k is an integer.

There are three such angles between 0 and 2\pi: \displaystyle \frac{\pi}{3}, \displaystyle \frac{2\, \pi}{3}, and \displaystyle \frac{4\,\pi}{3}.

Step-by-step explanation:

By the double angle identity of sines:

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Rewrite the original equation with this identity:

2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0.

Note, that 2\, (2\, \sin x \cdot \cos x) and (-2\, \sin x) share the common factor (2\, \sin x). On the other hand, 2\sqrt{3}\, \cos x and (-\sqrt{3}) share the common factor \sqrt[3}. Combine these terms pairwise using the two common factors:

(2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0.

Note the new common factor (2\, \cos x - 1). Therefore:

\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0.

This equation holds as long as either \left(2\, \sin x + \sqrt{3}\right) or (2\, \cos x - 1) is zero. Let k be an integer. Accordingly:

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  • \displaystyle \cos x = \frac{1}{2}, which corresponds to \displaystyle x = \frac{\pi}{3} + 2\, k \, \pi and \displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi.

Any x that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

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  • \displaystyle x =- \frac{\pi}{3} +2\,k\, \pi.
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Answer:

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Step-by-step explanation:

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