A square of side length 1 inch is drawn with its center A on a circle O of radius 1 inch such that a side of the square is perpendicular to $\overline{OA}$ , as shown. What is the area of the shaded region? Express your answer as a decimal to the nearest hundredth.
Marti lives in New York and wishes to call her friend Kathy who lives in Honolulu. The chart below shows the times in several cities when it is 12:00 noon in New York. If Marti calls Kathy when the time is 6:30 p.m. in New York, what time is it in Honolulu?
Place 9 points in a unit square. Prove it is possible to select 3 points from them to create a triangle whose area is no more than $\frac{1}{8}$.
The apples collected by Ms. Pinski's class are represented in the bar graph shown. How many more red apples than yellow apples were collected?
When $(37 \times 45) - 15$ is simplified, what is the units digit?
One witness to a crime said that the suspect was 25 years old and 69 inches tall. A second witness claimed that the suspect was 35 years old and 74 inches tall. The third witness reported that the suspect was 65 inches tall and 35 years old. Each witness correctly identified either the suspect's height or age, but not both. If $a$ is the suspect's age in years, and $b$ is the suspect's height in inches, what is the value of the sum $a + b$?
Two equilateral triangles are drawn in a square, as shown. In degrees, what is the measure of each obtuse angle in the rhombus formed by the intersection of the two triangles?
Seven pounds of Mystery Meat and four pounds of Tastes Like Chicken cost \$78.00. Tastes Like Chicken costs \$3.00 more per pound than Mystery Meat. In dollars, how much does a pound of Mystery Meat cost?
The perimeter of a rectangle is 22 cm and its area is 24 $cm^2$. What is the smaller of the two integer dimensions of the rectangle?
Farmer Hank has fewer than $100$ pigs on his farm. If he groups the pigs five to a pen, there are always three pigs left over. If he groups the pigs seven to a pen, there is always one pig left over. However, if he groups the pigs three to a pen, there are no pigs left over. What is the greatest number of pigs that Farmer Hank could have on his farm?
At the school's carnival, one game featured this unique square dartboard with five smaller, shaded squares, shown here. The length of a side of the square dartboard is 4 times the length of a side of any of the five congruent, shaded squares. To win a prize, a player's dart has to land in a shaded region. If a player's dart randomly hits the dartboard, what is the probability of her winning a prize? Express your answer as a common fraction.
A line passes through the points (-2, 8) and (5, -13). When the equation of the line is written in the form $y = mx + b$, what is the product of $m$ and $b$?
Mr. Mayfeld is designing a sign for his ice cream shop. The sign will be a shape consisting of a semicircle and an isosceles triangle that he will paint to look like a cone with a scoop of ice cream. He will cut the figure out of a rectangular piece of plywood measuring 2 ft by 4 ft, as shown. The shaded regions will be cut away. If BE = 3BG and $\overline{AB}$ is parallel to $\overline{CE}$ , what is the total area of the resulting figure? Express your answer as a decimal to the nearest tenth.
A state license plate contains the state logo in the center, preceded by three letters and followed by three digits. If the first two letters must both be consonants, excluding Y, how many different license plates are possible?
A right square pyramid has a base with a perimeter of 36 cm and a height of 12 cm. At one-third of the distance up from the base to the apex, the pyramid is cut by a plane parallel to its base. What is the volume of the top pyramid?
Jay and Mike were walking home with heavy books in their backpacks. When Mike complained about the weight in his backpack, Jay remarked, "If I take one of your books, I will be carrying twice as many books as you will be carrying, but if you take one of my books, we'll be carrying the same number of books." How many books is Mike carrying in his backpack?
A right rectangular prism has a volume of 720 $cm^3$. Its surface area is 484 $cm^2$. If all edge lengths are integers, what is the length of the longest segment that can be drawn that connects two vertices? Express your answer in simplest radical form.
Avi and Hari agree to meet at their favorite restaurant between 5:00 p.m. and 6:00 p.m. They have agreed that the person who arrives first will wait for the other only 15 minutes before leaving. What is the probability that the two of them will actually meet at the restaurant, assuming that the arrival times are random within the hour? Express your answer as a common fraction.
What fraction of the first 100 triangular numbers are evenly divisible by 7? Express your answer as a common fraction.
The analog clock shown has a minute hand with an arrow tip that is exactly twice as far from the clock\u2019s center as the hour hand\u2019s arrow tip. If point A is at the tip of the minute hand, and point B is at the tip of the hour hand, what is the ratio of the distance that point B travels in 3 hours to the distance that point A travels in 9 hours? Express your answer as a common fraction.
What percent of the interval with endpoints \u22125 and 5 consists of real numbers $x$ satisfying the inequality $x + 1 > \frac{8}{x -1}$?
In the figure shown here, the distance between any two horizontally or vertically adjacent dots is one unit. What is the area of the shaded polygon? Express your answer as a decimal to the nearest tenth.
What is the mean of all possible positive three-digit integers in which no digit is repeated and all digits are prime? Express your answer as a decimal to the nearest hundredth.
Alex added the page numbers of a book together and got a total of 888. Unfortunately, he didn't notice that one of the sheets of the book was missing with an odd page number on the front and an even page number on the back. What was the page number on the final page in the book?
A circular spinner has seven sections of equal size, each of which is colored either red or blue. Two colorings are considered the same if one can be rotated to yield the other. In how many ways can the spinner be colored?
