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Aleksandr-060686 [28]
3 years ago
7

3. The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy. Lola sold $2030 in ads, Ahmed sold $1540, and

Tommy sold $1800. (a) What fraction of the total sales did each salesperson sell? (b) A $100 bonus was awarded to the three salespeople, which they had to share. It was awarded so that each salesperson received the same fraction of $100 as he or she sold of the total sales. How much did each person receive? Round to the nearest whole cent.
Mathematics
1 answer:
dalvyx [7]3 years ago
6 0
A.) First, you find the total sales. $2030 + $1540 + $1800 = $5370. Then, divide each with the total. The answer would be:

Lola: 203/537
Ahmed: 154/537
Tommy: 60/179

b.) Divide 100 by 3 for equal shares. Each person receives $33.3.
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A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs
iogann1982 [59]

Answer:

r=3.628cm

h=12.093cm

Step-by-step explanation:

For this problem we are going to use principles, concepts and calculations from multivariable calculus; mainly we are going to use the Lagrange multipliers method. This method is thought to help us to find a extreme value of a multivariable function 'F' given a restriction 'G'. F represents the function that we want to optimize and G is just a relation between the variables of which F depends. The Lagrange method for just one restriction is:

\nabla F=\lambda \nabla G

First, let's build the function that we want to optimize, that is the cost. The cost is a function that must sum the cost of the sides material and the cost of the top and bottom material. The cost of the sides material is the unitary cost (0.03) multiplied by the sides area, which is A_s=2\pi rh for a cylinder; while the cost of the top and bottom material is the unitary cost (0.05) multiplied by the area of this faces, which is A_{TyB}=2\pi r^2 for a cylinder.

So, the cost function 'C' is:

C=2\pi rh*0.03+2\pi r^2*0.05\\C=0.06\pi rh+0.1\pi r^2

The restriction is the volume, which has to be of 500 cubic centimeters:

V=500=\pi r^2h\\500=\pi hr^2

So, let's apply the Lagrange multiplier method:

\nabla C=\lambda \nabla V\\\frac{\partial C}{\partial r}=0.06\pi h+0.2\pi r\\\frac{\partial C}{\partial h}=0.06\pi r\\\frac{\partial V}{\partial r}=2\pi rh\\\frac{\partial V}{\partial h}=\pi r^2\\(0.06\pi h+0.2\pi r,0.06\pi r)=\lambda (2\pi rh,\pi r^2)

At this point we have a three variable (h,r, λ)-three equation system, which solution will be the optimum point for the cost (the minimum). Let's write the system:

0.06\pi h+0.2\pi r=2\lambda \pi rh\\0.06\pi r=\lambda \pi r^2\\500=\pi hr^2

(In this kind of problems always the additional equation is the restricion, in this case, V=500).

Let's divide the first and second equations by π:

0.06h+0.2r=2\lambda rh\\0.06r=\lambda r^2\\500=\pi hr^2

Isolate λ from the second equation:

\lambda =\frac{0.06}{r}

Isolate h from the third equation:

h=\frac{500}{\pi r^2}

And then, replace λ and h in the first equation:

0.06*\frac{500}{\pi r^2} +0.2r=2*(\frac{0.06}{r})r\frac{500}{\pi r^2} \\\frac{30}{\pi r^2}+0.2r= \frac{60}{\pi r^2}

Multiply all the resultant equation by \pi r^{2}:

30+0.2\pi r^3=60\\0.2\pi r^3=30\\r^3=\frac{30}{0.2\pi } =\frac{150}{\pi}\\r=\sqrt[3]{\frac{150}{\pi}}\approx 3.628cm

Then, find h by the equation h=\frac{500}{\pi r^2} founded above:

h=\frac{500}{\pi r^2}\\h=\frac{500}{\pi (3.628)^2}=12.093cm

4 0
3 years ago
A scientist measured the energy of a system and found that it was increasing. The data shown represent the energy taken every bi
DiKsa [7]

At start ( t = 0 nanoseconds ) :

E ( t = 0 ) = 2.645 J

E ( t = 1 ) = 6.290 J

E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37

Also:

E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37

E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37

Therefore, the formula for calculating the energy of the system is:

E ( t ) = 2.645 * 2.37 ^ t

The answer is 4) exponential growth.


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olga nikolaevna [1]

A. there are 20 boys and 30 girls.

B.

68.7 out of 100 Boys

Girls im not sure, maybe someone else can answer that sorry




Hope I'm right and this helps sorry i didn't get girls.

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Joan had 227 dollars to spend on 8 books. After buying them she had 11 dollars. How
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The correct answer is 27
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Nat2105 [25]
<span>Cost = Pounds of Sugar X 0.59

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