Evaluate \(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)
0.013
0.014
0.14
0.13
Correct answer is B
\(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)
= \(\frac{36}{420} \times \frac{54}{90} \times \frac{63}{240}\)
= \(\frac{6}{70} \times \frac{18}{30} \times \frac{21}{80}\)
= \(\frac{27}{2000}\)
= 0.0135
\(\approx\) = 0.014
Evaluate \(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)
\(\frac{28}{39}\)
\(\frac{13}{39}\)
\(\frac{39}{28}\)
\(\frac{84}{13}\)
Correct answer is A
\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)
\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} - \frac{10}{10} + \frac{3}{4})]\)
= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-1}{10} + \frac{3}{4})]\)
= \(\frac{1}{3} \div [\frac{5}{7}(\frac{-2 + 15}{20})]\)
= \(\frac{1}{3} \div [\frac{5}{7} \times \frac{13}{20}]\)
\(\frac{1}{3} + [\frac{13}{28}]\) = \(\frac{1}{3} \times \frac{28}{13}\)
= \(\frac{28}{39}\)
29
26
25
24
Correct answer is A
Let the sum of the 12 numbers be x and the 13th number be y.
\(\frac{x}{12} = 3 \implies x = 36\)
\(\frac{36 + y}{13} = 5 \implies 36 + y = 65\)
\(y = 65 - 36 = 29\)
Solve for x if \(25^{x} + 3(5^{x}) = 4\)
1 or -4
0
1
-4 or 0
Correct answer is B
\(25^{x} + 3(5^{x}) = 4\)
Let \(5^{x}\) = y.
\((5^{2})^{x} + 3(5^{x}) - 4 = 0\)
\(y^{2} + 3y - 4 = 0\)
\(y^{2} - y + 4y - 4 = 0\)
\(y(y - 1) + 4(y - 1) = 0\)
\((y + 4)(y - 1) = 0\)
\(y = -4 ; y = 1\)
y = -4 is not possible.
y = 1 \(\implies\) x = 0.
\(\frac{5}{3}\)
\(\frac{1}{9}\)
\(\frac{4}{9}\)
\(\frac{1}{36}\)
Correct answer is C
\(\begin{array}{c|c} & W & W & W & W & B & B \\ \hline W & WW & WW & WW & WW & WB & WB \\ W & WW & WW & WW & WW & WB & WB\\W & WW & WW & WW & WW & WB & WB\\ W & WW & WW & WW & WW & WB & WB\\ B & BW & BW & BW & BW & BB & BB \\ B & BW & BW & BW & BW & BB & BB\end{array}\)
P(WW) = \(\frac{16}{36}\)
= \(\frac{4}{9}\)