Answer:
The radius of the pie is 6.17 in.
Step-by-step explanation:
The formula for arc length as a function of radius is
s = r·Ф, where Ф is the central angle in radians.
Here we know that the arc length is 7.85 in. Assuming that the whole pie has been cut into 8 equal pieces, the central angle of one such piece is
2π / 8, or π /4 (radians).
thus, s = r·Ф, solved for r, is r = s/Ф
and in this instance r = (7.85 in)/(π/4). Evaluating this, we get:
r = 6.17 in
The radius of the pie is 6.17 in.
6x+1 = 3(2x-4)
-4(x+3) = 4(x-1)
Answer: 0.3125.
Step-by-step explanation:
- The chance of having a boy is 0.5,
- the chance of having a girl is also 0.5.
<u>Outcome 1: all boys</u>
boy boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 2: first child is a girl, all others are boys</u>
girl boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 3: second child is a girl, all others are boys</u>
boy girl boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 4: third child is a girl, all others are boys</u>
boy boy girl boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
<u>Outcome 5: fourth child is a girl, all others are boys</u>
boy boy boy girl
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Therefore,
0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125
Simplify the expression
-10
Hope this helps! :)
The surface area of the figure is 96 + 64π ⇒ 1st answer
Step-by-step explanation:
* Lats revise how to find the surface area of the cylinder
- The surface area = lateral area + 2 × area of one base
- The lateral area = perimeter of the base × its height
* Lets solve the problem
- The figure is have cylinder
- Its diameter = 8 cm
∴ Its radius = 8 ÷ 2 = 4 cm
- Its height = 12 cm
∵ The perimeter of the semi-circle = πr
∴ The perimeter of the base = 4π cm
∵ The area of semi-circle = 1/2 πr²
∴ The area of the base = 1/2 × π × 4² = 8π cm²
* Now lets find the surface area of the half-cylinder
- SA = lateral area + 2 × area of one base + the rectangular face
∵ LA = perimeter of base × its height
∴ LA = 4π × 12 = 48π cm²
∵ The dimensions of the rectangular face are the diameter and the
height of the cylinder
∴ The area of the rectangular face = 8 × 12 = 96 cm²
∵ The area of the two bases = 2 × 8π = 16π cm²
∴ SA = 48π + 16π + 96 = 64π + 96 cm²
* The surface area of the figure is 96 + 64π
