An experiment involves picking a card from a selection of cards numbered 5, 10, and 15. In equation form, what is the probability model for this experiment? List the values of x in ascending order.(2 points)
f(x)= ?, where x= ?, ?, ?
f(x) = {1/3, if x=5; 1/3, if x=10; 1/3, if x=15}
x = 5, 10, 15
A "Caution Wet Floor” warning sign is in the shape of a rectangular pyramid. It is 31 in. tall and has a base whose dimensions are 12 in. by 20 in. What is the volume of the sign?(1 point)
__ in.3
The volume of a rectangular pyramid is given by the formula V=1/3 * base area * height.
Here, the height is 31 in, and the base dimensions are 12 in by 20 in, so the base area is 12*20 = 240 sq in.
Plugging in these values, we get:
V = 1/3 * 240 sq in * 31 in
V = 2,480 cubic inches
Therefore, the volume of the sign is 2,480 cubic inches.
Use the image to answer the question.
An illustration shows a rectangular pyramid with a length of 14 inches, a width of 6 inches, and a perpendicular height of 12 inches. The face with the length of 6 inches has a slant height of 13.89 inches. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
How many cubic inches does this rectangular pyramid contain? Round answer to the nearest whole number.
(1 point)
Responses
1,167 in.3
, , , 1,167 in. cubed
389 in.3
, , , 389 in. cubed
1,008 in.3
, , , 1,008 in. cubed
336 in.3
The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
Here, the base area is given by the product of the length and width, so it is 14 * 6 = 84 sq in.
Plugging in the values for the base area and height, we get:
V = (1/3) * 84 sq in * 12 in
V = 3,024 cubic inches
Therefore, the rectangular pyramid contains 3,024 cubic inches. Rounded to the nearest whole number, the answer is:
1,167 in.3
Use the image to answer the question.
An illustration shows a square rectangular pyramid with a side length of 12 meters, a perpendicular height of 10 meters, and a slant height of 11.66 meters. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
What is the volume of the rectangular pyramid?
(1 point)
Responses
559.68 m3
, , , , 559.68 m cubed
144 m3
, , , , 144 m cubed
1,440 m3
, , , , 1,440 m cubed
480 m3
The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
Here, the base is a square with side length 12 meters, so the base area is 12 * 12 = 144 square meters.
Plugging in the values for the base area and height, we get:
V = (1/3) * 144 sq m * 10 m
V = 480 cubic meters
Therefore, the volume of the rectangular pyramid is 480 cubic meters.
Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point)
Responses
33,034.03 in.3
400,000 in.3
924,075 in.3
308,025 in.3
The formula for the volume of a rectangular pyramid is V = (1/3) * base area * height.
Here, the base of the pyramid is a rectangle with dimensions 111 in. by 111 in., so the base area is 111 * 111 = 12,321 sq in.
Plugging in the values for the base area and height, we get:
V = (1/3) * 12,321 sq in * 75 in
V = 308,025 cubic inches
Therefore, the volume of the pyramid-shaped tent is 308,025 cubic inches.
A cell phone telecommunication tower stands in the shape of a rectangular pyramid. The tower stands 80 m tall and rests on a base that is 15 m by 20 m. What is the volume of the tower?(1 point)
Responses
12,000 m3
, 12,000 m cubed
70 m3
, 70 m cubed
24,000 m3
, 24,000 m cubed
8,000 m3
8,000 m cubed
The volume of a rectangular pyramid is given by the formula V = (1/3) * base area * height.
Here, the base of the tower is a rectangle with dimensions 15 m by 20 m, so the base area is 15 * 20 = 300 sq m.
Plugging in the values for the base area and height, we get:
V = (1/3) * 300 sq m * 80 m
V = 8,000 cubic meters
Therefore, the volume of the tower is 8,000 cubic meters.
A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.(1 point)
Responses
20.80 in.3
6.93 in.3
9.01 in.3
24.47 in.3
The volume of a square pyramid is given by the formula V = (1/3) * base area * height.
Here, the base of the pyramid is a square with side length 2.75 inches, so the base area is 2.75 * 2.75 = 7.5625 sq in.
Plugging in the values for the base area and height, we get:
V = (1/3) * 7.5625 sq in * 2.75 in
V = 6.9348958 cubic inches
Rounded to the nearest hundredth, the volume of the ornament is approximately 6.93 cubic inches.
A rectangular prism has a volume of 252 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point)
___in.3
The volume of a rectangular prism is given by the formula V = length * width * height.
Here, we are told that the volume of the rectangular prism is 252 cubic inches. We can write:
252 = length * width * height
Since the base and height of the rectangular pyramid are congruent to the prism, the base of the pyramid is a square. Let's call the side length of the square base "s". Then, the volume of the pyramid is given by the formula V = (1/3) * base area * height.
We know that the base area of the pyramid is s^2, since it is a square. We also know that the height of the pyramid is the same as the height of the rectangular prism. Therefore, we have:
V = (1/3) * s^2 * height
We can solve for "s" and "height" by using the fact that the base and height of the rectangular pyramid are congruent to the prism. Since the base of the prism is a rectangle with length "l" and width "w", we have:
l = w = s
Also, we know that:
height = height of prism
Substituting these values into the equation for the volume of the prism, we get:
252 = length * width * height
252 = s * s * height
252 = s^2 * height
Solving for "height", we get:
height = 252 / s^2
Substituting this value for "height" into the equation for the volume of the pyramid, we get:
V = (1/3) * s^2 * (252 / s^2)
V = 84 cubic inches
Therefore, the volume of the rectangular pyramid is 84 cubic inches.