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

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?

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.

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.

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?

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?

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?

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

The two sides of a triangle are 25 cm and 26 cm, while the altitude to the third side is 24 cm. Find the area of the triangle.

The diagonals of a parallelogram are 16 cm and 28 cm, respectively. One side of the parallelogram is 12 cm. Find the area of the parallelogram.

After M students took the test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70%?

How many integers between 18 and 70 inclusive are divisible by either 7 or 9 but not both?

If the power of an engine grows by 10% when the number of its cylinders is increased by one, which of the following is closest to the ratio of the power of a 9-cylinder engine to that of a 12-cylinder engine?

A lead pencil whose ends are regular hexagons was cut from a cylindrical piece of wood with the least waste. If the original piece was 8 in. long and 1/2 in. in diameter, find the volume of the pencil.

Kate and David each have \$10. Together they flip a coin 5 times. Every time the coin lands on heads, Kate gives David \$1. Every time the coin lands on tails, David gives Kate \$1. After the coin is flipped 5 times, what is the probability that Kate has more than \$10 but less than \$15.

10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?

To make lemonade, a recipe requires 4 lemons, 30 ounces of sugar, and 2 pints of water. One can squeeze out 0.4 cups of 5% citric acid from an average lemon. Marta does not have lemons, but wants to make lemonade from 4 cups of 12% citric acid. She has sugar and water in abundance. How much water will Marta use?

If each expression under the square root is greater than or equal to 0, calculate

$$ \sqrt{x^2 - 6x + 9} + \sqrt{2 - x} + x - 3 $$

A construction company wants to number new houses using digit plates only. If the company puts an order for 1212 plates how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).

Point P has cylindrical coordinates of (8, 30°, 5). Find the value of x in the Cartesian coordinates.

At an ordinary rate a man can row the distance from Pasig to Manila, about 15km, in 5 hours less time than it takes him to return. Could he double his rate, his time to Manila would only be one hour less than his time to Pasig. What is the rate of Pasig River?

Find the volume of the sheet iron in cubic meter.

Find the weight of the tank when empty, in kilo Newton.

Find the weight of the tank when full of salt water in, kilo Newton.

Find the amount of salt in the tank at any time, t.

Find the time at which the brine leaving will contain 1 lb/gal of salt.

Determine the limiting value for the amount of salt in the tank after a long time.

How much work is done in winding-up the upper half of the chain?

How much work is done in winding-up the full length of the chain?

If the bucket is leaking at a uniform rate so that it is half-full when no chain is out, how much work is done in winding-up the 30-m length?