0
0.9
1.1
1.2
Correct answer is C
\(\frac{0.021741 \times 1.2047}{0.023789}\) = \(\frac{0.0255 \times 1.2}{0.024}\) (to 216)
= \(\frac{0.0264}{0.024}\) = 1.1
x < 11
x < -1
x > 6
x > 11
Correct answer is D
\(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4) = \(\frac{x + 1}{3} - 1\) > \(\frac{x + 4}{5}\)
\(\frac{x + 1}{3} - \frac{x + 4}{5} -1\) > 0
= \(\frac{5x + 5 - 3x - 12}{15}\)
2x - 7 > 15
2x > 22 = x > 11
Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
131
125
123
120
Correct answer is B
Arrange in ascending order
89, 100, 108, 119, 120,130, 131, 131, 141, 161
Median = \(\frac{120 + 130}{2}\) = 125
Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
(313)\(_3\)
(1000)\(_3\)
(1020)\(_3\)
(1222)\(_3\)
Correct answer is C
Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
(212)\(_3\) + (222)\(_3\) = 1211\(_3\)
→ 1211\(_3\) - 121\(_3\)
= 1020\(_3\)
Evaluate \(\frac{2\sin 30 + 5\tan 60}{\sin 60}\), leaving your answer in surd form.
\(\frac{2\sqrt{3}}{3} + 10\)
\(\frac{3\sqrt{2} - 1}{5}\)
\(\frac{3\sqrt{2} + 1}{5}\)
\(\frac{2\sqrt{3}}{3} - 10\)
Correct answer is A
\(\frac{2\sin 30 + 5\tan 60}{\sin 60}\)
\(\sin 30 = \frac{1}{2}; \tan 60 = \sqrt{3}; \sin 60 = \frac{\sqrt{3}}{2}\)
\(\therefore \frac{2\sin 30 + 5\tan 60}{\sin 60} = \frac{2(\frac{1}{2}) + 5(\sqrt{3})}{\frac{\sqrt{3}}{2}}\)\)
= \(\frac{1 + 5\sqrt{3}}{\frac{\sqrt{3}}{2}}\)
= \(\frac{2(1 + 5\sqrt{3})}{\sqrt{3}}\)
= \(\frac{2 + 10\sqrt{3}}{\sqrt{3}}\)
Rationalizing, we get
= \(\frac{2\sqrt{3} + 30}{3}\)
= \(\frac{2}{3} \sqrt{3} + 10\)