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Allushta [10]
3 years ago
13

You want to have $25,000 for a down payment on a house 6 years from now. if you can earn 6.5 percent, compounded annually, on yo

ur savings, how much do you need to deposit today to reach your goal?
Mathematics
1 answer:
STatiana [176]3 years ago
6 0
Use compound interest formula:
Future value, F 
25000=P(1+i)^n
where
P=present value to be found
i=annual interest rate = 0.065
n=number of years = 6
so
25000=P(1.065)^6
=>
P=(25000/1.065^6)=$17133.353
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The sum of twice a number and 18 less than the number is the same as the difference between -30 and the number
maksim [4K]
2x + x - 18 = -30 - x
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3 years ago
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-17 times a number -29 is equal to -32 less than a number
Airida [17]

Step-by-step explanation:

-17x = -32 - <em>x</em>

Collect like terms

-17x + <em>x</em><em>=</em><em> </em><em>-</em><em>32</em>

<em>-</em><em>16x</em><em> </em><em>=</em><em> </em><em>-</em><em>32</em>

<em>Divide</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>-</em><em>16</em>

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3 years ago
A 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. Brine containing 3 lb of salt per
gulaghasi [49]

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is \dfrac{dx}{dt}= Rate \ of \  \ inflow - rate \ of \  \ outflow

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank  × flow rate

= x/250 ×  9

= 9x/250  lb/s

∴

\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}

\dfrac{dx}{dt} + \dfrac{9x}{250}= 21

This is a 1st order linear differentiation,

The integrating factor if e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}

∴

e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C

e^{^{ \dfrac{9t }{250}}} \ \ x(t) =  21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C

x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}     at  t = (0) and x(0) = 100 lb

Hence;

100 = \dfrac{1750}{3}+C

C = \dfrac{1750}{3} -100

C = - \dfrac{1450}{3}

∴x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}

after time t = 1 minute i.e 60 s

x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}

x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}

x(t) = 581.66 lb

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3 years ago
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Answer:

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Hi, I need help with this question.
elena-14-01-66 [18.8K]

Answer:

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Step-by-step explanation:

<u>Each member marches:</u>

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<u>Find the number of steps:</u>

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3 years ago
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