✔A cylindrical bottle with radius 15cm is half-half filled with water. A spherical stone is dropped inside the bottle (completely submerging into the water) and the water level rises by 2.5 cm without spilling over. What is the radius of the stone?

✔Chris drives from city A to City B on an expressway. After driving for 2.5 hrs, Chris saw a sign that reads City A-225 km: City B-198km. Continuing at the same constant speed, what is his total travel time from City A to City B?

✔If 0.15a = 0.33b, what should be the value of x in the proportion a:bx = 11:10?

✔Twice a certain Number is the average of \(\frac{7}{8}\) and \(1\frac{3}{4}\). What is the number?

✔In a class, the ratio of the number of girls to boys is 5:4. If only 15 more girls had enrolled in the class, the ratio would have been 25:8. How many girls are in the class?

✔What is the distance between \( -1\frac{1}{6}\) and \(-\frac{3}{4}\)?

✔if \(f(x) = 2x^2 -1\) and \(g(x) = 8-2x\), what is the value of (f+g)(2)?

✔If \(f(x) = x^2+2x-1\), what is f(2)?

✔Find the values of x such that \(f(x) = 4\) in the equation \( f(x) = 2x^2 -3x +5\)

✔Solve for x in \( \frac{5}{x+2} - \frac{2}{x+1} = \frac{1}{2}\)

✔Solve for x in \( \sqrt{2-x} -4 = 0\)

✔Find the range of value of b if \(2x^2 +bx +8 = 0\) has no real roots. Express your answer in interval.

✔List down all possible values of the constant k so that \( 3x^2 -2kx + 2 = 0\)

✔Find the sum of the distinct roots of \( (x+\frac{2}{x})^2-6(x+\frac{2}{x})+9 = 0\)

✔Solve the inequality \(2x^2 -7x -4 \leq 0 \). Express your answer in interval notation.

✔Find the larger root of \(10x^2 -x = 3 \)

✔What constant should be added to \( x^2 -10x\) to make it perfect square?

✔Simplify \( \sqrt{72} +\sqrt{32}-\sqrt{2}\)

✔Simplify \( (\frac{b^{4x-3y}}{b^{3x+2y}})^{x} (\frac{b^{3x+6y}}{b^{-2x+4y}})^y\)

✔Rationalize the denominator of \(\frac{\sqrt{15} - 3}{\sqrt{5} -\sqrt{3}}\)

✔Simplify \(\frac{3^0 - 3^{-2}}{3^{-1} + 3^{-3}}\)

✔Find the next two terms of the elements of the sequence 1, 8, 9, 32, 49, ...

✔Show that: \(1 + {\left( {\cot \theta } \right)^2} = {\left( {\csc \theta } \right)^2}\)

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