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:
The mean increases and the median changes to 4.
Step-by-step explanation:
To find the mean. You need to add all of the numbers together then divide by how many numbers there are. The median is found by the middle number.
Answer
12
Step-by-step explanation:
You need to use cosine because the side length needed is adjacent and you have the hypotenuse.Set up a proportion of "cos23 = x/13" and solve by cross multiplying. Then just round.
Answer:
The number of fringes at 
is given as 20.
Step-by-step explanation:
Question
A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression
,
where d is the number of decades after the population was measured. Evaluate the expression for d = −2
Given :
The number of finches is modeled by the expression :
⇒ 
where 
is the number of decades after the population was measured.
To evaluate the expression for d=-2
Solution:
In order to evaluate the given expression to find the number of finches at , we will plugin 
for in the expression and simplify it.
Plugging in in the expression:
⇒ 
Using negative exponent property. [
⇒ 
⇒ 
⇒ 
(Answer)
Thus, the number of fringes at is given as 20.
This means the number of fringes two decades ago was 20.
