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19mcgough
20.05.2021 •
Mathematics
Which expression should you simplify to find the 90% confidence interval,
given a sample of 80 people with a sample proportion of 0.75?
A. 0.75 +1.645 .
0.75(1-0.75)
80
B. 0.75 +1.645 •
10.75(1–0.75)
80
C. 0.75 + 80 •
0.75(1-0.75)
1.645
O D. 0.75 +
1.645.0.75
80
SUBMIT
Solved
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Ответ:
The surface area of the rocket is 76π inches² ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- A firework rocket consists of a cone stacked on top of a cylinder
- The radii of the cone and the cylinder are equal
∴ Their bases are equal
- The diameter of the cylindrical base of the rocket is 8 inches
∴ The radius of the cylinder = 8 ÷ 2 = 4 inches
- The height of the cylinder is 5 inches
- The height of the cone is 3 inches
- The surface area of the rocket is the sum of the lateral area of the
cylinder , area of one base of the cylinder and the lateral area of
the cone
∵ The lateral are of the cylinder = perimeter of its base × its height
∵ The base of the cylinder is circle
∵ The perimeter of the circle (circumference) = 2πr
∵ r = 4 and h = 5
∴ The lateral area of the cylinder = 2π(4)(5) = 40π inches²
- Lets calculate the area of the base of the cylinder
∵ The area of the circle = πr²
∴ The area of the circle = π(4)² = 16π inches²
- To find the lateral area of the cone you must find the slant height l
∵ The slant height of the cone = √ (r² + h²) , where r is the radius of
the base of the cone and h is the height of the cone
∵ r = 4 and h = 3
∴ l = √(4² + 3²) = √(16 + 9) = √25 = 5 inches
∵ The lateral area of the cone = 1/2 Cl , where C is the circumference
of the base and l is the slant height
∵ C = 2πr
∴ C = 2π(4) = 8π
∵ l = 5
∴ The lateral area of the cone = 1/2 (8π)(5) = 20π inches²
- Lets find the surface area of the rocket
∵ The S.A of the rocket = L.A of the cylinder + A of the base of the
cylinder + L.A of the cone
∵ L.A of the cylinder = 40π inches²
∵ A of the base of the cylinder = 16π inches²
∵ L.A of the cone = 20π inches²
∴ The S.A = 40π + 16π + 20π = 76π inches²
* The surface area of the rocket is 76π inches²