June 2021

Find the angle between $2x - y + z = 10$ and $x + y + 2z = 11$.

A person buys a piece of property for P100,000 down payment and ten deferred semi-annual payments of P8,000 each starting three years from now. What is the present worth of the investment if the rate of interest is 12 percent compounded semi-annually?

From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?

What time between 2 and 3 o 'clock will the angle between the hands of the clock be bisected by the line connecting the center of the clock and the 3 o 'clock mark?

The top of the tower signal at B 2000 m away from A was sighted through a transit with recorded vertical angle of 3°30'. The height of the mast is 12 m and the HI of the transit above the point where it is set is 1.10 m with elevation 133.3 m. What is the elevation of the base of the signal B.

From point A on level ground, the angles of elevation of the top D and bottom B of a flagpole situated on the of a hill are measured as 47°54' and 39°45'. Find the height of the hill if the height of the flagpole is 115.5 ft.

Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get

1. at least 1 six when 6 dice are rolled
2. at least two sixes when 12 dice are rolled, or
3. at least 3 sixes when 18 dice are rolled.

What is the answer?

A circle has its center at (3, -27). It is tangent to the line $3x + 4y - 26 = 0$. Locate the point of tangency.