0 < n < 60
\(4n\equiv 2\pmod 6\)
\(n\equiv \frac{2}{4}\pmod6\)
\(n\equiv \frac{2+6}{4}\equiv2\pmod6\)
n = 6k + 2
k = 0, 1, 2, ..., 9
total : 10
\(\frac{2}{3}\times m=w\)
\(\frac{5}{8}\times \frac{1}{3}\times m=\frac{5}{24}\times m=b\)
\(m(1-\frac{2}{3}-\frac{5}{24})=6\) => \(\frac{1}{8}\times m=6\) => \(m=48\)
\((\sqrt{8^2+x^2})^2+(\sqrt{5^2+x^2})^2=(5+8)^2\)
\(64+x^2+25+x^2=169\)
\(2x^2=80\)
\(x^2=40\)
\(x=2\sqrt{10}\)
probability red die shows odd number : 3/6 = 1/2
probability green die shows even number : 3/6 = 1/2
total : 1/2*1/2 = 1/4
Lev's age = L
Mina's age = M
Naomi's age = N
\(\frac{L}{M}=\frac{1}{2}=\frac{3}{6}\) => \(\frac{M}{N}=\frac{3}{4}=\frac{6}{8}\)
L = 3a
M = 6a
N = 8a
a = 1
M = 6
42 - 36 = 6
60 - 42 = 18 = 6 + 6+ 6
=> 60, 54, 48, 42, 36
4x = 24
x = 6
y - 10 = 32
y = 42
\((101+97)(101-97)+(93+89)(93-89)+...+(5+1)(5-1)=4(101+97+93+89+...+5+1)\)
\(4\times \frac{(1+101)}{2}\times 26\)
\(4\times 51\times 26=5304\)
\((x^2+y^2)^2=1^2\)
\(x^4+y^4+2(xy)^2=1\)
\(\frac{17}{18}+2(xy)^2=1\)
\(xy=\sqrt{\frac{1}{36}}=\frac{1}{6}\)
\(CA=\sqrt{20^2+16^2}=\sqrt{656}\)
\(BD^2+20^2=BA^2\)
\(AC^2+BA^2=(DC+BD)^2\) =>\(656+(BD^2+20^2)=(16+BD)^2\)
\(656+BD^2+400=256+32BD+BD^2\)
\(1056-256=800=32BD\)
\(BD=25\)
