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SIZIF [17.4K]
2 years ago
8

Serena is single. She purchased her principal residence three years ago. She lived in the home until she sold it at a $300,000 g

ain this year. Serena was allowed to exclude $250,000 of the $300,000 gain. What is the character of the $50,000 gain she was not able to exclude?
Mathematics
1 answer:
Lesechka [4]2 years ago
7 0

Answer: Long -term capital gain

Step-by-step explanation:

Serena is single, so based on the Taxpayer Relief Act of 1997, she would pay no capital gains tax on the first $250,000 gain.

Therefore, $300,000 - $250,000 =  $50,000

<em>The remaining $50,000 gain is taxable because of her being single and it has been her principal residence for three years.</em>

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The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the
navik [9.2K]

Answer:

a) 0.019

b) 0.563

c) x = 1.966 hours

Step-by-step explanation:

E(X) = 1

Exponential random variable's probability function is given as

P(X=x) = λ e^(-λ.x)

The cumulative distribution function is given as

P(X ≤ x) = 1 - e^(-λ.x)

a) The time between the arrivals of small aircraft at a county airport that is exponentially distributed.

But the number of planes that land every hour will be obtained using the Poisson distribution formula.

It is the best for discrete systems.

Poisson distribution formula is given as

P(X = x) = (e^-λ)(λˣ)/x!

λ = 1 aircraft per hour.

The probability that more than three aircraft arrive within an hour = P(X > 3)

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

P(X > 3) = 1 - 0.98101 = 0.01899 = 0.019 to 3 d.p

b) If 30 separate one-hour intervals are chosen, what Is the probability that no interval contains more than three arrivals

Probability of one 1-hour interval not containing more than 3 arrivals = 1 - P(X > 3)

= 1 - 0.01899 = 0.98101

Probability that thirty 1-hour intervals will not contain more than 3 arrivals = (0.98101)³⁰ = 0.5626 = 0.563 to 3 d.p

c) Determine the length of an interval of time (In hours) such that the probability that no arrivals occur during the interval is 0.14

We can now use the cumulative distribution function for exponential random variable for this

P(X ≤ x) = 1 - e^(-λ.x)

P(X > x) = 1 - P(X ≤ x)

P(X > x) = e^(-λ.x)

λ = 1, x = ?,

0.14 = e⁻ˣ

e⁻ˣ = 0.14

In e⁻ˣ = In 0.14 = -1.966

-x = -1.966

x = 1.966 hours

Hope this Helps!!!

4 0
2 years ago
Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the co
Aleksandr-060686 [28]

Answer:

length of the photograph will be 4.2 in. after pressing the button 5 times.

Step-by-step explanation:

By pressing the button, every time size of the photograph gets reduced by 12%.

Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,

L = l(1-\frac{12}{100})^{n}

Where l = Actual length of the photograph

L = length of the reduced image

n = Number of times the button has been pressed

For l = 8 in. and n = 5

L = 8(1-0.12)^{5}

  = 8(0.88)^{5}

  = 4.22 in

L ≈ 4.2 in.

Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.

3 0
2 years ago
The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimens
Rom4ik [11]

cubed root of 4896 = 16.98

round to 17

17-1 = 16

17 +1 = 18

16* 17 *18 = 4896

 bin is 16 in x 17 in x 18 in

7 0
2 years ago
Read 2 more answers
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the
Flauer [41]
This is substitution, it's very simple once you get the hang of it! 

okay, what you want to do is plug in the numbers you already have, to get the number you don't have(r).

First, you plug in the numbers.

1.  P= $2000  
    A=$2543
    t= 4(years)
    r=? 

2543=2000^r(4) 

Secondly, you want to solve the equation.


5 0
2 years ago
Read 2 more answers
Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each
gayaneshka [121]

Answer:

Thinker Toys

Step-by-step explanation:

8 0
2 years ago
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