June 2021

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

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

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?

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?

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.

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.

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?

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

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%?

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.

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.