4x = 7(x-3)
1. Distribute that multiplicand 7: 4x = 7x - 21
2. Group the x terms together: Subtract 4x from both sides: 0 = 3x - 21
3. Solve for x: Add 21 to both sides: 21 = 3x
4. Divide both sides by 3 to obtain x = 7 (answer)
The cubic centimeter one container can hold is 2,878.33 cm³.
<h3>What is the cubic centimeter one
container can hold ?</h3>
In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.
Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)
Volume of the cylinder = πr²h
Where:
- π = 3.14
- r = radius
- h = height
3.14 x 5² x 30 = 2355 cm³
Volume of a hemisphere = (2/3) x π x r³
2 x (2/3 x 3.14 x 5³) = 523.33 cm³
Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³
To learn more about the volume of a hemisphere, please check: brainly.com/question/26840364
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Answer:
x = 7
y = 3
z (max) = 4950/3 = 1650
Step-by-step explanation:
Let call
x numbers of church goup and
y numbers of Union Local
Then
First contraint
2*x + 2*y ≤ 20
Second one
1*x + 3*y ≤ 16
Objective Function
z = 150*x + 200*y
Then the system is
z = 150*x + 200*y To maximize
Subject to:
2*x + 2*y ≤ 20
1*x + 3*y ≤ 16
x ≥ 0 y ≥ 0
We will solve by using the Simplex method
z - 150 *x - 200*y = 0
2*x + 2*y + s₁ = 20
1*x + 3*y + 0s₁ + s₂ = 16
First Table
z x y s₁ s₂ Cte
1 -150 -200 0 0 = 0
0 2 2 1 0 = 20
0 1 3 0 1 = 16
First iteration:
Column pivot ( y column ) row pivot (third row) pivot 3
Second table
z x y s₁ s₂ Cte
1 -250/3 0 0 200/3 = 3200/3
0 - 4/3 0 -1 2/3 = -20/3
0 1/3 1 0 1/3 = -20/3
Second iteration:
Column pivot ( x column ) row pivot (second row) pivot -4/3
Third table
z x y s₁ s₂ Cte
1 0 0 750/12 700/6 = 4950/3
0 1 0 3/4 -1/2 = 7
0 0 1 -1/4 1/2 = 9/3
The answer to the question
