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Shtirlitz [24]
2 years ago
6

The luxury tax threshold in a professional sports league is the amount in total payroll that teams must stay under to prevent be

ing levied a competitive balance tax by the league's commissioner. One model that could be used to represent the amount of the league's luxury threshold A, in millions of dollars, t years since 2003 is A(t)=120(1.033)^t. Suppose a second model assumed that the league's luxury threshold was $117 million in 2003 and increased by 3.5% each year. How would the function A(t) change to represent the second model?
A: The coefficient changes from 120 to 117, and the base changes from 1.033 to 1.035. The function that represents the second model is A(t)=117(1.035)^t.
B: The coefficient changes from 120 to 117, and the base changes from 1.033 to 0.035. The function that represents the second model is A(t)=117(0.035)^t.
C: The coefficient changes from 120 to 103.5, and the base changes from 1.033 to 1.17. The function that represents the second model is A(t)=103.5(1.17)^t.
D: The coefficient changes from 120 to 103.5, and the base changes from 1.033 to 0.17. The function that represents the second model is A(t)=103.5(0.17)^t.
Mathematics
1 answer:
VMariaS [17]2 years ago
6 0

Answer:

A: The coefficient changes from 120 to 117, and the base changes from 1.033 to 1.035. The function that represents the second model is A(t)=117(1.035)^t.

Step-by-step explanation:

luxury tax you get only the amount that you need

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Step-by-step explanation:

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.

a) Let X represent the price of the option

<h3><u>  x                  P(X=x) </u></h3>

$1000         20/100 = 0.2

$200          50/100 = 0.5

$0              30/100 = 0.3

b) Expected option price

= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300

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Answer:

a) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}, b) x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}, x_{2} = \frac{5\pi}{3}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

Step-by-step explanation:

a) The equation must be rearranged into a form with one fundamental trigonometric function first:

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\sqrt{3} \cdot \left(\frac{1}{\sin x} \right) - 2 = 0

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Value of x is contained in the following sets of solutions:

x_{1} = \frac{\pi}{3}\pm 2\pi \cdot i, \forall i \in \mathbb{N}_{O}

x_{2} = \frac{5\pi}{6}\pm 2\pi\cdot i, \forall i \in \mathbb{N}_{O}

b) The equation must be simplified first:

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