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If the area of the square is 196, when what is the area of the shaded area?

Each of the four semicircles shown in the figure has a side of the square as its diameter and has exactly one point in common with the larger circle. If each side of the square has length 4,what is the sum of the areas of the shaded regions?

Four same circles with a radius of 4 are inscribed in a larger circle. What`s the area of the larger circle?

The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?

Quantity A: x
Quantity B: y

Quantity A: AB
Quantity B: BC

A triangle is inscribed in a semi-circle with a radius of r
Quantity A: $$x^{2}+y^{2}$$
Quantity B: $$4r^{2}$$
The length of each side of a smaller cube is 2. What is the surface area of the bigger cube formed out of 125 such cubes?
A gardener plans to cover a rectangular plot of land with pine bark mulch to a depth of 4 inches.The plot measures 8 feet by 12 feet, and the gardener will buy mulch packed in bags. If each bag contains 3.5 cubic feet of mulch and costs $6,what is the cost of the least number of bags that the gardener will need to cover the plot? (Note: 1 foot=12 inches.)
______dollars

For the rectangular solid below, find the following. What is the surface area of the solid?

In the rectangular solid above, TU=3, VU=4,and VR=2. What is the area of the shaded rectangular region?
A rectangular solid box has a height, width and length ratio of 1:2:3 and a surface area of 550. What is the volume of the box?
317.5 m^3 of water needs to be added to a right cylinder tank. The diameter of the base of the cylinder is 10m.

Quantity A

The overall height of the water in the cylinder

Quantity B

7 meters
The radius of the base of right cylinder A is 2 times that of right cylinder B, while the height of cylinder A is also 2 times that of cylinder B. What is the ratio of volume of cylinder B to the volume of cylinder A?
Give your answer as a fraction.

In a right circular cylinder, the radius of the base circle is 1, the height is 8.

Quantity A

The outside area (top ,down and lateral surface) of a section of the cylinder with a central angle of 100°

Quantity B

5π
There are two right circular cylinder oil drums. In the first cylinder, the base area is 4π and the oil height is 5, while in the second cylinder, the base area is 10π, and the oil height is 6. Mark gradually pours oil from the second cylinder into the first one, so that the oil height in both cylinders will become the same. What will be the oil height at last?
Give your answer as a fraction.

In the above circular cone, point V is its apex, point P is on the circle of its base, and point O is the center of its base. The length of segment VP is 2 and the measure of angle OVP is 30. Which of the following is the volume of this solid?

The table above shows the frequency distribution of the values of a variable Y. What is the expected value of the distribution?
Give your answer to the nearest 0.01.


What is the ratio of the number of people in Group 2 with the ailment sneezing and itchy eyes to the total number of people in both groups with the ailment sneezing and itchy eyes?
Give your answer as a fraction.

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