What is the product of \(\frac{27}{5}\), \((3)^{-3}\) and (\(\frac{1}{5})^{-1}\)?
5
3
1
\(\frac{1}{25}\)
Correct answer is C
\(\frac{27}{5} \times 3^{-3} \times \frac{(1)^{-1}}{5}\)
= \(\frac{27}{5} \times \frac{1}{3^3} \times \frac{1}{\frac{1}{5}}\)
\(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{5}{1}\) = 1
The angle of a sector of a circle radius 10.5 cm is 48\(^o\). Calculate the perimeter of the sector.
25.4cm
25.4cm
25.6cm
29.8cm
Correct answer is D
The lenght of Arc AB = \(\frac{Q}{360}\) 2\(\pi\)r
= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x 10.5 = \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)
= \(\frac{4 \times 22 \times 3}{30} \times \frac{88}{10}\) = 8.8cm
Perimeter = 8.8 + 2r = 8.8 + 2r
= 8.8 + 2(10.5)
= 8.8 + 21
= 29.8cm
30\(^o\)
60\(^o\)
112.5\(^o\)
157.5\(^o\)
Correct answer is D
Rice = 75g, Margarine = 40g, Meat = 105g
Bread = 20g
Total = 240
Angle of sector represented by meat
= \(\frac{105}{240} \times \frac{360^o}{1}\)
= 157.5
Simplify \(\frac{324 - 4x^2}{2x + 18}\)
2(x - 9)
2(9 + x)
81 - x\(^2\)
-2(x - 9)
Correct answer is D
234 - 4x\(^2\) = 18\(^2\) - (2x)\(^2\) = (18 - 2x)(18 + 2x)
2x + 18 = 2x + 18 = (2x + 18)
18 - 2x = 2(a - x) or -2(x - a)
0.3010
0.4771
0.6532
0.9542
Correct answer is C
log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 04771
log\(_{10} 4.5 = log_{10}\) (\(\frac{3 \times 3}{2}\))
log\(_{10}\) 3 + log\(_{10}\) 3 - log\(_{10}\)2 = 0.4471 + 0.771 - 0.3010
= 0.6532
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