1. A large circular gear has a diameter of 20 cm and a small circular gear has a diameter of 10 cm. The ratio of the area of the large gear to the area of the small gear is ___ to 1.
2. A circular rug with a radius of 5 feet is placed in the center of a circular room with a radius of 10 feet. What is the probability that a dropped earring lands on the rug?
3. The geometric probability of a dart hitting the bullseye of a circular target is $\frac{4}{25}$. What is the ratio of the bullseye's radius to the target's total radius? Express your answer as a fraction: ___
4. Solve the system of equations using substitution to find the value of $x$. $y = x - 4$ $2x + y = 5$ The value of $x$ is ___.
5. To solve the system $x = y + 5$ and $3x + 2y = 5$ using substitution, what is the correct equation after the first step?
6. A rectangular park is 40 meters long and 30 meters wide. Inside, there is an 8-meter by 5-meter sandbox. If a toy is dropped randomly, what is the probability it lands in the sandbox? Express as a simplified fraction. ___
7. A right triangle has legs measuring 5 cm and 12 cm. What is the length of the hypotenuse in cm? ___
8. A circular target has a radius of 8 inches. The bullseye in the center has a radius of 2 inches. What is the probability of hitting the bullseye if a dart lands randomly on the target?
9. A right triangle has legs of length $x$ and $y$, and a hypotenuse of length $z$. Which equation correctly represents the Pythagorean theorem for this triangle?
10. A square board has a side length of 20 inches. A circular hole with a radius of 3 inches is in its center. What is the probability a randomly thrown point hits the hole? Express your answer in terms of $\pi$. ___