Consider a firm handling concessions for a sporting event. The firm’s manager needs to know whether to stock up with coffee or col
a and is formulating policies for specific weather predictions. A local agreement restricts the firm to selling only one type of beverage. The firm estimates a $1500 profit selling cola if the weather is cold and a $5000 profit selling cola if the weather is warm. The firm also estimates a $4000 profit selling coffee if it is cold and a $1000 profit selling coffee if the weather is warm. The weather forecast says that there is a 30% of a cold front; otherwise, the weather will be warm. Build a decision tree to assist with the decision. What should the firm handling concessions do?
1 answer:
Answer: Cola is more profitable over Coffee
Step-by-step explanation:
E(cola) = 0.3 * 1500 + 0.7 * 5000
E(cola) = 450 + 3500
E(cola) = 3950
E(coffee) = 0.3 * 4000 + 0.7 * 1000
E(coffee) = 1200 + 700
E(coffee) = 1900
From the decision tree which is attached, and the calculations above, it would be advised that the firm should focus on Cola, since it has a higher expected revenue of $3950, compared to the expected revenue of $1900 for coffee.
See the attached image for the decision tree
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<u>Answer:</u>
(x - 2) is not a factor of f(x) = 3x^5 - 7x^3 - 11x^2 + 2
<u>Step-by-step explanation:</u>
According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).
So first we will divide f(x) by (x - 2) using long division to get:
(3x^5 - 7x^3 - 11x^2 + 2) / (x - 2)
= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)
= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)
= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)
=
Therefore the remainder is -2.
Now check x = 2 for 3x^5 - 7x^3 - 11x^2 + 2:
3(2)^5 - 7(2)^3 - 11(2)^2 + 2 = -2
The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.
So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .
Answer:
Using trigonometric ratio:
From the given statement:
and sin < 0
⇒ lies in the 3rd quadrant.
then;
Using trigonometry identities:
Substitute the given values we have;
Since, sin < 0
⇒
now, find :
Substitute the given values we have;
Therefore, the exact value of:
(a)
(b)