If 92x = \(\frac{1}{3}\)(27x), find x
2
1
-1
-2
Correct answer is C
92x = \(\frac{1}{3}\)(27x)
(22)2x = \(\frac{(3^{3x})}{3}\)
(34x) = 33x - 1
4x = 3x - 1
4x - 3x = -1
x = -1
Express 2.7864 x 10-3 to 2 significant figures
0.28
0.27
0.0028
0.0027
Correct answer is C
2.7864 x 10-3 = 0.0027864
= 0.0028(approx. 2 s.f)
What is the median of the following scores: 22 35 41 63 74 82
82
52
49
22
Correct answer is B
22 35 41 63 74 82
Median = \(\frac{41 + 63}{2} = \frac{104}{2}\)
= 52
40
45
55
60
Correct answer is B
\(\frac{x + 50 + 70}{3} = 55\)
x + 120 = 3(55)
x + 120 = 165
= 165 - 120
x = 45%
\(\frac{2 + \sqrt{3}}{3}\)
\(\frac{1 - \sqrt{3}}{3}\)
\(\frac{1 + \sqrt{3}}{3}\)
\(\frac{2 - \sqrt{3}}{3}\)
Correct answer is D
Sin 60 = \(\frac{\sqrt{3}}{2}\); cos 60o = \(\frac{1}{2}\)
= \(\frac{1 - \sin 60}{1 + \cos 60} = \frac{1 - \frac{\sqrt{3}}{2}}{1 + \frac{1}{2}}\)
= \(\frac{2 - \sqrt{3}}{3}{2}\div \frac{2 + 1}{2}\)
= \(\frac{2 - \sqrt{3}}{2} \times \frac{2}{3}\)
= \(\frac{2 - \sqrt{3}}{3}\)