Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50
Answer:
0.750714286
Step-by-step explanation:
For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
Here our function is:
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
Evaluating this in our function we get:
Remember that the thing above must be equal to x, so we get:
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
If you want to learn more, you can read:
brainly.com/question/10300045
Answer:
3 over 8
Step-by-step explanation:
The total of box numbers is 8 and there are 3 white boxes. So, the total goes on the bottom and the amount of white boxes goes on top.
Hope this helped!
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
