A company produces small cubic sugar cubes, each with side length 2 cm. These cubes are packed into cylindrical containers for shipping. Each cylindrical container has a radius of 5 cm and a height of 12 cm. What is the maximum number of sugar cubes that can be placed in one full cylindrical container? Round your answer to the nearest whole number. (Assume the cubes can be "melted" and poured, or consider volume packing for simplification).
117 cubes
Triangle DEF has vertices D(2,−1), E(5,3), F(1,4). If triangle DEF is reflected over the y-axis to form triangle D′E′F′, what are the vertices of triangle D′E′F′?
A. D′(2,1),E′(5,−3),F′(1,−4)
B. D′(−2,−1),E′(−5,3),F′(−1,4)
C. D′(−2,1),E′(−5,−3),F′(−1,−4)
D. D′(1,−2),E′(−3,−5),F′(−4,−1)
B. D'(-2,-1) E'(-5,3) F'(-1,4)
Question 2: Water Tank Radius
A cylindrical water storage tank has a capacity of 250 gallons. Its height is 60 inches. If one cubic foot of water is equivalent to 7.48 gallons, find the maximum possible radius for the base of the tank. Round your answer to the nearest thousandth of an inch.
Flagpole Height
From a point on the ground 75 meters away from the base of a flagpole, the angle of elevation to the top of the flagpole is 45∘. What is the height of the flagpole, to the nearest meter?
Tan x = opp/adj
75 meter
A spherical water balloon has a radius of 4 inches. It is used to fill a rectangular children's pool that measures 30 inches in length, 20 inches in width, and 10 inches in height. What is the least number of full water balloons needed to completely fill the pool? Round your answer to the nearest whole number.
23 balloons
Point Q(4,−2) is rotated 90° clockwise about the origin. What are the coordinates of Q′?
A. (−2,−4)
B. (−4,2)
C. (2,4)
D. (2,−4)
A. (−2,−4)
Question 3: Grow Tank Width
A rectangular hydroponic grow tank has a capacity of 75 gallons. Its length is 40 inches and its height is 16 inches. If one cubic foot of water is equivalent to 7.48 gallons, what is the maximum possible width for this grow tank? Round your answer to the nearest thousandth of an inch
Ramp Angle
A wheelchair ramp is 12 feet long and has a vertical rise of 2 feet. What is the angle of elevation of the ramp with the ground, to the nearest degree?
sin x = opp/hyp
Answer: Approximately 10 degrees
A cone-shaped funnel has a radius of 3 cm and a height of 10 cm. This funnel is used to transfer sand into a rectangular planter box that has dimensions of 25 cm in length, 15 cm in width, and 12 cm in height. What is the least number of full funnels of sand needed to completely fill the planter box? Round your answer to the nearest whole number.
48 funnels
Quadrilateral GHIJ has vertices G(−2,4), H(6,2), I(4,−4), J(−4,−6). If quadrilateral GHIJ is dilated by a scale factor of 21 centered at the origin to form quadrilateral G′H′I′J′, what are the vertices of G′H′I′J′?
A. G′(−1,2),H′(3,1),I′(2,−2),J′(−2,−3)
B. G′(−4,8),H′(12,4),I′(8,−8),J′(−8,−12)
C. G′(2,−4),H′(−6,−2),I′(−4,4),J′(4,6)
D. G′(−1,−2),H′(3,−1),I′(2,2),J′(−2,3)
A. G′(−1,2),H′(3,1),I′(2,−2),J′(−2,−3)
Question 4: Drum Height
A large cylindrical drum used for storing liquid has a capacity of 300 gallons. The diameter of its base is 30 inches. If one cubic foot of liquid is equivalent to 7.48 gallons, what is the maximum possible height for this drum? Round your answer to the nearest thousandth of an inch.
Airplane Approach
An airplane is at an altitude of 5,000 feet and begins its descent towards an airport. The angle of depression from the airplane to the airport is 15∘. What is the horizontal distance, in feet, from the airplane to the airport? Round your answer to the nearest foot.
Tan x = opp/ adj
Answer: Approximately 18660 feet
A cylinder with a dimension of diameter 6 inches and height 8 inches is used to fill the rectangular prims fish tank with water. What is the least number of full cylindrical containers needed to complete fill the fish tank?
31
The ABC has vertices at A(1,2) B(4,6) C(4,2) in the coordinates plane. The triangle will be reflected over the x axis and the rotated 180 degrees about the origin. What are the vertices for ABC
A. A'(1,2) B'(4,6) C'(4,2)
B. A'(1,-2) B'(4,-6) C'(4,-2)
C. A'(-1,2) B'(-4,6) C'(-4,2)
D. A'(-1,-2) B'(-4,-6) C'(-4,-2)
C. A'(-1,2) B'(-4,6) C'(-4,2)
The Pisces Place is company that makes fish tanks. Corey has sent the company a special order for a fish tank that is a rectangular prism with an open top. the dimension length 54 inches height = ? width = 18 inches and capacity = 100 gallons. one cubic foot water is equivalent to 7.48 gallons. if the capacity of the fish tank is 100 gallons find the máximum possible height for the fish tank. Round you answer to nearest thousand of an inch
V=LWH
13.369=4.5x1.5xH
H=1.981
In a right-angled triangle ABC, the hypotenuse AC measures 15 cm. If angle A is 30∘, what is the length of side BC (the side opposite to angle A)?
25.98