Rounding off to one significant figure will be:
600,000
The remainder is five. heres the proof.
It's the distributive property. It takes the equation, 15+10 and finds the greatest common factor of 5. it divides both numbers by 5 and puts the 5 outside of the parentheses.
Since there are 128 fluid ounces in a gallon and a raindrop is 1/90, you have to multiply 128 by 90. Since it takes 90 raindrops to get to a whoke fl oz, and you need 128, you hae to multiply:
128×90=11,520
It takes 11,520 raindrops to fill the bucket.
Below is the complete solution explained step-by-step.
The answers are:
Function: c(x) = (1/2)x^2 - 2x + 18
Cost to produce 6 widgets: $24
Explanation:
The general form of a quadratic function is:
c(x) = Ax^2 + Bx + C
So, you need to find the values of A, B, C to know the quadratic function.
Those are three unknowns. Since, you have three pair of values, you can set a systmen of three equations with trhee unknown variables.
This is it:
1) x = 2 widgets, c(x) = $ 16 => A(2)^2 + B(2) + C = 16
2) x = 4 widgets, c(x) = $18 => A(4^2) + B(4) + C = 18
3) x = 10 widgets, c(x) = $48 => A(10^2) + B(10) + C = 48
Developing the expressions you get:
1) 4A + 2B + C = 16
2) 16A + 4B + C = 18
3) 100A + 10B + C = 48
Now solve the system. I recommend to eliminate C to make two equations with A and B.
Equation 2 - Equation 1=> (3) 12A + 2B = 2
Equation 3 - Equation 2 => (4) 84A + 6B = 30
Multiply equation (3) times 3 and subtract from equation (4) =>
84A + 6B = 30
36A + 6B = 6
-------------------
84A - 36A = 30 - 6
48A = 24
A = 24/48
A = 1/2
Replace A = 1/2 on 12A + 2B = 2
=> 12(1/2) + 2B = 2 => 6 + 2B = 2 => 2B = 2 - 6 = -4
=> B = -4 / 2 = -2
Replace A and B on 4A + 2B + C = 16
=> 4(1/2) + 2(-2) + C = 16
=> C = 16 - 2 + 4 = 18
Therefore, the quatratic function is c(x) = (1/2)x^2 - 2x + 18.
Answer: c(x) = (1/2)x^2 - 2x + 18
To find the cost to produce 6 widgets, substitute x = 6:
=> (1/2) (6^2) - 2(6) + 18 = 36/2 - 12 + 18 = 18 - 12 + 18 = 24
Answer: $24.
