The were 35 child tickets sold and 3 adult tickets sold.
How did I get this?
First, let's look at what we know.
Matinee
(C)hild ticket = $1
(A)cult ticket = $2
Regular
(C)hild ticket = $4
(A)cult ticket = $6
2. We need to make two equations out of this:
1C + 2A = $41
4C + 6A = $158
The variables represent the amount of tickets, which is the unknown.
3. Process of elimination, multiply the first equation by -3 because we want to cancel out one set of variables.
-3(1C + 2A = 41)
-3C - 6A = -123
4C + 6A = 158
C = 35 child tickets
Substitute the value c into any one of the equations
1(35) + 2(A) = $41
$35 + 2A = $41
Subtract both sides by $35.
2A = $6
Divide by 2
A = 3 adult tickets
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.
<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>
<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
Answer: 11 people like vanilla.
Step-by-step explanation: There are 50 people in this question. Since 22% of them like vanilla, multiply 0.22 and 50. That gives you 11. Therefore, 11 people out of 50 like vanilla.
Answer:
Step-by-step explanation:
