\(\frac{1}{4}\)
\(\frac{3}{11}\)
\(\frac{1}{2}\)
\(\frac{3}{4}\)
Correct answer is A
Y = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
Number of prime numbers = 3
Prob(picking a prime number) = \(\frac{3}{12}\)
= \(\frac{1}{4}\)
3.5cm
5cm
7cm
9cm
Correct answer is D
From \(V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}\\
462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \\
h = \frac{3 \times 462}{22 \times 7}\\ h = 9\)
5cm
7cm
10cm
15cm
Correct answer is C
\(\frac{1}{2}(a+b)\times h = 105cm^2\\
\frac{1}{2}(9+12)\times h = 105\\
h = \frac{105 \times 2}{21} = 10cm\)
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\)
\(\frac{x+3}{1-x^2}\)
\(\frac{x-3}{1+x^2}\)
\(\frac{3-x}{1-x^2}\)
\(\frac{3-x}{1+x^2}\)
Correct answer is C
\(\frac{1}{1-x} + \frac{2}{1+x}\\
\frac{1+x+2-2x}{(1-x)(1+x)} = (\frac{3-x}{1-x^2})\)
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
\(\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3\)
\(\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3\)
\(\frac{2}{3} \hspace{1mm}or \hspace{1mm}3\)
\(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\)
Correct answer is D
The equation \(\frac{3x - 2}{4x^2 + 9x - 9}\) is undefined when the denominator = 0.
\(4x^2 + 9x - 9 = 0\)
\(4x^2 + 12x - 3x - 9 = 0\)
\(4x(x + 3) - 3(x + 3) = 0\)
\((4x - 3)(x + 3) = 0\)
x = \(\frac{3}{4}\) or x = -3.