Answer:
Function: C = 500 / n
Jane must recruit 20 more contributors or 25 contributors in total for the cost of each share to be $20.
Step-by-step explanation:
1. Cost per share, C, with respect to the number of contributors, n is
C = 500 / n
So, with 5 contributors, the price is $100 per share. $100 = 500/5
2. C= $20
20= 500 / n
20 * n = 500 * n
20n = 500
n= 25
She already has 5 contributors, so she needs 20 more.
A minimum of 220 backpacks must be produced to obtain the desired benefits.
Since a company making backpacks charges $ 29.99 for each backpack, and it costs $ 6.45 to make each backpack, and the company can make backpacks in multiples of 10 and there is $ 1,000 in fixed costs, and the company wants to make at least $ 4,000 profit each week, to determine how many backpacks should be produced, the following calculation must be performed:
- 29.99 - 6.45 = 23.54
- 500 x 23.54 - 1000 = 10,770
- 250 x 23.54 - 1000 = 4.885
- 220 x 23.54 - 1000 = 4,178.80
- 210 x 23.54 - 1000 = 3,943.40
Therefore, a minimum of 220 backpacks must be produced to obtain the desired benefits.
Learn more in brainly.com/question/15713474
Answer
(a) 
(b) 
Step-by-step explanation:
(a)
δ(t)
where δ(t) = unit impulse function
The Laplace transform of function f(t) is given as:

where a = ∞
=> 
where d(t) = δ(t)
=> 
Integrating, we have:
=> 
Inputting the boundary conditions t = a = ∞, t = 0:

(b) 
The Laplace transform of function f(t) is given as:



Integrating, we have:
![F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.](https://tex.z-dn.net/?f=F%28s%29%20%3D%20%5B%5Cfrac%7B-e%5E%7B-%28s%20%2B%201%29t%7D%7D%20%7Bs%20%2B%201%7D%20-%20%5Cfrac%7B4e%5E%7B-%28s%20%2B%204%29%7D%7D%7Bs%20%2B%204%7D%20-%20%5Cfrac%7B%283%28s%20%2B%201%29t%20%2B%201%29e%5E%7B-3%28s%20%2B%201%29t%7D%29%7D%7B9%28s%20%2B%201%29%5E2%7D%5D%20%5Cleft%20%5C%7B%20%7B%7Ba%7D%20%5Catop%20%7B0%7D%7D%20%5Cright.)
Inputting the boundary condition, t = a = ∞, t = 0:

The area of a triangle is 1/2*base*height
So make your equation: 1/2*b*12=42
6*b=42
b=7
So the base is 7 inches long
Hope that helped!
8x - 27 ≤ -x +18
No more than means that it could either be less than or equal to, which is why we used that symbol.