Evaluate \((20_{three})^2 - (11_{three})^2\) in base three
101
121
202
2020
Correct answer is C
\((20_{three})^2 - (11_{three})^2\)
= \((20_{3} - 11_{3})(20_{3} + 11_{3})\)
= \((2_{3})(101_{3})\)
= \(202_{3}\)
Which of the following correctly expresses 48 as a product of prime factors?
3 x 4 x 4
2 x 3 x 8
2 x 2 x 2 x 3 x 4
2 x 2 x 2 x 2 x 3
Correct answer is D
48 = 2 x 2 x 2 x 2 x 3
\(2\frac{1}{4}\)%
4%
5%
6%
Correct answer is B
\(I = \frac{PRT}{100}\)
\(R = \frac{100I}{PT}\)
\(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\)
\(R = \frac{6000}{1500}\)
= 4%
Solve the equation 3 + 5x - 2x2 = 0
\(-\frac{1}{2},-3\)
2, 3
-2, 3
\(-\frac{1}{2},3\)
Correct answer is D
\(3 + 5x - 2x^2 = 0\\
3 + 6x - x - 2x^2 = 0\\
3(1 + 2x) - x(1 + 2x) = 0\\
(3-x)(1+2x)=0\\
3-x = 0 \hspace{1mm}or \hspace{1mm}1+2x = 0\\
x = 3\hspace{1mm} x = -\frac{1}{2}\\
x = 3 \hspace{1mm}or\hspace{1mm} x =-\frac{1}{2}\)
Find the volume (in cm\(^3\)) of the solid shown above
100cm3
150cm3
175cm3
250cm3
Correct answer is C
Total volume = (5 x 5) x 5 + (5 x 5) x 2
= 125 + 50
= 175 cm\(^3\)
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