The sum of four numbers is 1214\(_5\). What is the average expressed in base five?
114
141
401
411
Correct answer is B
Convert to base 10, divide and then re-convert to base 5.
If \(\frac{9^{2x-1}}{27^{x+1}} = 1\), find the value of x.
8
5
3
2
Correct answer is B
\(\frac{9^{2x - 1}}{27^{x + 1}} = 1\)
\(\implies 9^{2x - 1} = 27^{x + 1}\)
\((3^{2})^{2x - 1} = (3^{3})^{x + 1}\)
\(2(2x - 1) = 3(x + 1) \implies 4x - 2 = 3x + 3\)
\(4x - 3x = 3 + 2 \implies x = 5\)
63
84
113
133
Correct answer is D
45/2% + 95/2% = 70%
100% - 70% = 30% (i.e women)
=> 30% = 84
1% = 84/30
95/2% = (84/30 x 95/2) = 133.
3
1
1/2
1/4
Correct answer is C
(√98 - √50)/√32 = √(49x2) - √(25x2) √(16x2)
=> (7√2 - 5√2)/4√2 = 1/2
Simplify 1 - (7/3 x 5/4) + 3/5
-16/15
-79/60
-37/15
-151/60
Correct answer is B
\(1 - (\frac{7}{3} \times \frac{5}{4}) + \frac{3}{5}\)
= \(1 - \frac{35}{12} + \frac{3}{5}\)
= \(\frac{60 - 175 + 36}{60}\)
= \(\frac{-79}{60}\)