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wolverine [178]
2 years ago
15

Angela’s grandfather gave her all the cash he had in his pocket to buy raffle tickets that cost $1

Mathematics
1 answer:
daser333 [38]2 years ago
5 0

In this problem situation:

  • the independent quantity is <em><u>the money</u></em> Angela's grandfather gave her
  • the dependent quantity is the <em><u>number of raffle ticket</u></em> Angela will buy.

An independent quantity is the quantity that affects or brings a change in a dependent quantity.

The dependent quantity is affected by the independent quantity. If the independent quantity changes, the dependent quantity will change.

The dependent quantity is dependent on the independent quantity.

<em><u>Let's relate it to the </u></em><em><u>problem situation</u></em><em><u>:</u></em>

  • The amount of money Angela's grandfather gave her is unknown, therefore, the number of raffle tickets Angela can buy cannot be ascertain.

  • If we know <em>how much Angela's grandfather gave her</em>, we can determine <em>how many </em><em>raffle tickets </em>Angela can buy.

  • This implies that the number of raffle ticket Angela will buy is dependent on how much money her grandfather gave her.

Therefore, in this problem situation:

  • the independent quantity is <em><u>the money</u></em> Angela's grandfather gave her
  • the dependent quantity is the <em><u>number of raffle ticket</u></em> Angela will buy.

Learn more here:

brainly.com/question/19967540

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Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for reg
Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) <u>Optimal solution</u>: 40.000 units of R and 10.000 of PC = $17.000

c) <u>Slack variables</u>: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) <u>Binding Constaints</u>:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

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3 years ago
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SVETLANKA909090 [29]

Rewrite 5% as a decimal and then multiply by 60.

X = 0.05 x 60

8 0
3 years ago
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1 is also equal to 100/100. What percent is equal to both 1 and 100/100?
Delvig [45]

Answer:

100%

Step-by-step explanation:

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2 years ago
PLEASE ANSWER I DO NOT UNDERSTAND... PLEASE AND THANK YOU
scZoUnD [109]

Answer:

7) First Circle

8)Also First Circle

Step-by-step explanation:

For the first one simplify the bottom expression to get (x-3)(x+7), then cancel out the numerator and x+7 to get 1/x-3. The restrictions are when you solve for x-3 and x+7

The second one is the same thing but this time we simplify the numerator to get (x+2)(x-5). Then, cancel out both x+2. Then you get x-5 as the answer and the restriction is -2 because x+2 is the denominator.

Hope this helps!

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Solve.<br> 2log(x+1)-log(x+3)=log1
guapka [62]

Answer: x = 1

Step-by-step explanation:

2log(x+1) - log (x+3) = log 1

log(x+1)^2 - log (x+3) = log 1

log [(x+1)^2 / (x+3)] = log 1

(x+1)^2 / (x+3) = 0

(x+1)^2 = 0

x = 1 or x = -1 (rejected, as log0 does not exist)

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