Answer:
The volume = 523.3 ft.³
Step-by-step explanation:
∵ Surface area of the sphere = 4πr²
∴ 4πr² = 100π
∴ 4r² = 100 ⇒ r² = 100/4 = 25
∴ r = √25 = 5 ft.
∵ Its volume = 4/3 πr³
∴ Its volume = (4/3) × π × 5³ = 523.3 ft.³
Answer:
The results don't make sense
Step-by-step explanation:
We can solve by means of a 2x2 system of equations, we have to:
"x" is the number of children's tickets
"y" is the number of adult tickets
Thus:
8 * x + 8.75 * y = 259
x + y = 35 => x = 35 - y
replacing we have:
8 * (35 - y) + 8.75 * y = 259
280 - 8 * y + 8.75 * y = 259
- 8 * y + 8.75 * y = 259 - 280
0.75 * y = -21
y = -21 / 0.75
y = -28
Thus:
x = 35 - (-28) = 63
With these results we notice that the problem has inconsistency, since the value of the tickets cannot be given a negative number, I recommend reviewing the problem, since the approach is correct.
Answer:
a. 8 plates
b. 9 cheese puffs on each plate and 6 carrot sticks on each plate
Step-by-step explanation:
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116