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SIZIF [17.4K]
3 years ago
10

You deposit $3000 in a savings account that earns 2.9% annual interest compounded monthly. You also save $80 per month in a safe

at home. Write a function for the total amount of money saved C(t)=b(t)+h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. Round any decimals to three decimal places.
Mathematics
1 answer:
Jlenok [28]3 years ago
7 0

Answer:

C(t)=3000(1.002417)^12t+960t

if T=1 year then the saving will be : 4048.17

Step-by-step explanation:

3000 deposit amount, 2.9 compound monthly interest .  save 80 dollars  per month at home .

A=p(1+r)^t

A=3000(1+0.029/12)^12t

A=3000(1.002417)^12t dollars

for the amount saved at home=80*12t=960t dollars

C(t)=3000(1.002417)^12t+960t

if T=1 year then the saving will be :

C(t)=3000(1.002417)^12t+960t

     =3088.17+960= 4048.17 dollars

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Answer:

\displaystyle V = 28 \pi \ ft^3

General Formulas and Concepts:

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  5. Division
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<u>Geometry</u>

Volume of a Cylinder Formula: \displaystyle V = \pi r^2h

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Step-by-step explanation:

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Radius <em>r</em> = 2 ft

Height <em>h</em> = 7 ft

<u>Step 2: Solve for V</u>

  1. Substitute in variables [Volume of a Cylinder Formula]:                                \displaystyle V = \pi (2 \ ft)^2(7 \ ft)
  2. [Volume] Evaluate exponents:                                                                         \displaystyle V = \pi (4 \ ft^2)(7 \ ft)
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3 years ago
Which one is the greater fraction 1/2 or 19/56
vazorg [7]

1/2 is the greater fraction

5 0
3 years ago
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Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the
Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

y=Ce^{kt}. We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is \frac{dy}{dt}. Thus, the change in the concentration of salt is found in

\frac{dy}{dt}= inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

3(\frac{y}{400})

Therefore,

\frac{dy}{dt}=0-3(\frac{y}{400}) or just

\frac{dy}{dt}=-\frac{3y}{400} and in terms of time,

-\frac{3t}{400}

Thus, our equation is

y=28e^{-\frac{3t}{400} and filling in 16 for the number of minutes in t:

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3 years ago
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katrin2010 [14]

Answer:

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2 years ago
Calls to a customer service center last on average 2.8 minutes with a standard deviation of 1.4 minutes. An operator in the call
Natali5045456 [20]

Answer:

The expected total amount of time the operator will spend on the calls each day is of 210 minutes.

Step-by-step explanation:

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Problems of normal distributions can be solved using the z-score formula.

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n-values of normal variable:

Suppose we have n values from a normally distributed variable. The mean of the sum of all the instances is M = n\mu and the standard deviation is s = \sigma\sqrt{n}

Calls to a customer service center last on average 2.8 minutes.

This means that \mu = 2.8

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This means that n = 75

What is the expected total amount of time in minutes the operator will spend on the calls each day

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M = n\mu = 75*2.8 = 210

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