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
List all the different combinations with total cost:
Airplane + van = 350 + 60 = $410
Airplane + cab = 350 + 40 = $390
Bus + van = 150 + 60 = $210
Bus + cab = 150 + 40 = $190
Train + van = 225 + 60 = $285
Train + cab = 225 + 40 = $265
There are 6 different combinations.
There are 2 that are more than $300
The probability would be quantity higher than 300 / total combinations.
Probability = 2/6 = 1/3
Answer:
7 miles / hour
Step-by-step explanation:
I'm taking this to mean she walked 3.5 miles. She did this 1/2 hour.
Givens
d (distance ) = 3.5 miles
t (time) = 1/2 hour
r (rate) = ?
Formula
r = d/t
Solution
The easiest way to do this is to change the fractions to decimals.
t = 1/2 = 0.5 hours
r = 3.5 / 0.5
r = 7 miles per hour.
Answer:
The second one (2) is a lie
Step-by-step explanation:
The quantities are all proportional, with 4 donuts costing one dollar being consistant. With this, we can multiply the amount of donuts to 40, and through what we know, we can find that the donuts will cost 10 dollars. This leaves only (2) left.
Answer:
Option (4)
Step-by-step explanation:
Definition of a ray states that a segments which connects two points but extending only in one direction infinitely is called as Ray.
Opposite rays will have a common end but the direction of the arrows will be different.
Therefore, from the picture attached,
Opposite rays will be PA and PB.
Option (4) will be the correct option.
