Which function has the same y-intercept as the line graphed below?
1 answer:
Answer:
D. y + 4 = 2x
Step-by-step explanation:
The graph has a y-intercept at (0, -4).
A. y=16 - 3x/4
if x = 0, y = 16. FALSE.
B. 24 + 3y = 6x
If x = 0, 24 + 3y = 0
3y = -24
y = -8. FALSE.
C. 4y + x = 16
If x = 0, 4y = 16
y = 4. FALSE.
D. y + 4 = 2x
If x = 0, y + 4 = 0
y = -4. TRUE.
y = 4 + 2x has the same y-intercept as the graphed line.
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The maximum earning is v(r,b)
Let v(r,b) be the expected value of the game for the player, assuming optimal play, if the remaining deck has r red cards and b black cards.
Then v(r,b) satisfies the recursion
and
The stopping rule is simple: Stop when v(r,b)=0.
To explain the recursion . . .
If r,b>0, and the player elects to play a card, then:
- The revealed card is red with probability
, and in that case, the player gets a score of +1, and the new value is V(r-1,b)
- The revealed card is black with probability
, and in that case, the player gets a score of −1, and the new value is V(r,b-1)
Thus, if r,b>0, electing to play a card yields the value f(r,b).
But the player always has the option to quit, hence, if r,b>0, we get v(r,b)=max(0,f(r,b)).
Implementing the recursion in Maple, the value of the game is
v(26,26)=41984711742427/15997372030584
v(26,26) ≈2.624475549
and the optimal stopping strategy is as follows . . .
- If 24≤b≤26, play while r≥b−5.
- If 17≤b≤23, play while r≥b−4.
- If 11≤b≤16, play while r≥b−3.
- If 6≤b≤10, play while r≥b−2.
- If 3≤b≤5, play while r≥b−1.
- If 1≤b≤2, play while r≥b.
- If b=0, play while r>0.
So, The maximum earning is v(r,b)
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Answer:
The increase in Arthur's operating profits would be <u>$1120</u>.
Step-by-step explanation:
Given:
The Arthur Company manufactures kitchen utensils. The company is currently producing well below its full capacity. The Benton Company has approached Arthur with an offer to buy 16,000 utensils at $0.70 each. Arthur sells its utensils wholesale for $0.80 each; the average cost per unit is $0.78, of which $0.15 is fixed costs.
If Arthur were to accept Benton's offer.
Now, to find the increase in Arthur's operating profits.
The average cost per unit = $0.78.
The fixed costs = $0.15.
So, to get the variable cost we subtract the fixed cost from the average cost per unit:
Thus, the variable cost is $0.63.
As, the Benton Company has approached Arthur with an offer to buy 16,000 utensils at $0.70 each.
So, to get the profit per unit we subtract $0.70 from the variable cost:
Profit per unit = $0.07.
Number of utensils = 16,000.
Now, to get the total profit we put formula:
<u><em>Total profit = Number of utensils × Profit per unit.</em></u>
Therefore, the increase in Arthur's operating profits would be $1120.