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il63 [147K]
3 years ago
6

Fran purchased an annuity that provides $5,400 quarterly payments for the next 10 years. The annuity was purchased at a cost of

$135,000. How much of the first quarterly payment will Fran include in her gross income?
Mathematics
1 answer:
guajiro [1.7K]3 years ago
4 0

Answer:

$5400

Step-by-step explanation:

Gross income is any interest, wage etc(money received) given to someone which they account for before any deductions and tax. Fran will have to include all $5400 of her first quarterly payment into her gross income because there are no deductions yet and tax when you consider what is put in gross income. Fran would have earned this amount as a payment from the purchasing of the annuity as it serves as a payment back for purchasing an annuity which to Fran, is an investment.

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13. Find a cubic function with the given zeros. 7, -3, 2
emmainna [20.7K]

\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y

5 0
3 years ago
A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu
Novosadov [1.4K]

Answer:

A(t)=240-220e^{-\frac{t}{40}}

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

  • Volume of the tank = 240 liters
  • Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

R_{in}=(concentration of salt in inflow)(input rate of fluid)

R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}

R_{out}=(concentration of salt in outflow)(output rate of fluid)

R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}

Rate of change of the amount of salt in the tank:

\dfrac{dA}{dt}=R_{in}-R_{out}

\dfrac{dA}{dt}=6-\dfrac{A}{40}

We then solve the resulting differential equation by separation of variables.

\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}

Taking the integral of both sides

\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}

Recall that when t=0, A(t)=20 (our initial condition)

20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}

3 0
3 years ago
Is this correct?<br> Need help!!!!!<br> plz
atroni [7]

Answer:

150

Step-by-step explanation:

the bases are 60 and the sides are 90

4 0
3 years ago
In which function does an increase of 1 in quantity x correspond to an increase of 8 in
OLga [1]

Answer:

C. y = 8x

Step-by-step explanation:

When x = 1

y = 8(1) = 8

when x = 2

y = 8(2) = 16

x increased by 1

y increased by 8

8 0
2 years ago
Please HELP me !!!! <br> No LINKS!!!!!
11111nata11111 [884]

Answer:

I think its A

Step-by-step explanation:

The graph shows its number are getting greater than -4 and i think solid dots mean greater than or equal to the number

8 0
3 years ago
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