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irga5000 [103]
3 years ago
8

how much must you deposit in an account that pays 8% annual interest compounded monthly to have a balance of $1,000 after one ye

ar​
Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

Answer:

\$923.36  

Step-by-step explanation:

we know that

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=1\ year\\ A=\$1,000\\ r=0.08\\n=12  

substitute in the formula above  and solve for P

\$1,000=P(1+\frac{0.08}{12})^{12*1}  

P=\$1,000/(1+\frac{0.08}{12})^{12*1}=\$923.36  

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Colin walked a distance of 15 miles in 6 hours. <br> Work out out
butalik [34]

Answer:

Colin walked 2.5 miles every hour

Step-by-step explanation:

The answer is 2.5 because 15 divided by 6 is 2.5

P.S Can I have brainliest?

8 0
2 years ago
jim walks at an average rate of 4 miles per hour. at this rate how long will it take jim to walk 10 miles?
Firdavs [7]
It would take him 2.5 hrs because when you divide 10 by 4 that's what you get
7 0
3 years ago
Read 2 more answers
A person is supposed to drink half a gallon of water every day.abby drank 15 small cups today if the capacity of the cup is 3.5
Yuki888 [10]

He needs to drink 3 cups MORE to meet his daily requirement.

Step-by-step explanation:

Here, as given in the question:

The total need for water = half a gallon = 0.5 gallon

1 gallon  = 128 oz

So, 0.5 gallon = 128/2  = 64 oz

Now, the capacity of 1 cup = 3.5 oz

The number of cups already drank by the person = 15 cups

So, the total amount of water already taken by him

= 15 cups x Capacity of 1 cup

= 15 x (3.5 oz)  = 52.5 oz

So, the amount of water left to be drink by him

= Total Need - Already covered

= 64 oz - 52 . 5 oz  =  11.5 oz

Now, as 1 cup = 3.5 oz

So, 11.5 oz  has ( \frac{11.5}{3.5} )cups  = 3.28 cup≈ 3 cups

Hence, he needs to drink 3 cups MORE to meet his daily requirement.

6 0
3 years ago
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio
JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

Initial =1\ million

6\ years\ later = 500,000

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

\frac{dA}{dt} = kA

Where k represents the constant of proportionality

\frac{dA}{dt} = kA

Multiply both sides by dt/A

\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}

\frac{dA}{A}  = k\ dt

Integrate both sides

\int\ {\frac{dA}{A}  = \int\ {k\ dt}

ln\ A = kt + lnC

Make A, the subject

A = Ce^{kt}

t = 0\ when\ A =1\ million i.e. At initial

So, we have:

A = Ce^{kt}

1000000 = Ce^{k*0}

1000000 = Ce^{0}

1000000 = C*1

1000000 = C

C =1000000

Substitute C =1000000 in A = Ce^{kt}

A = 1000000e^{kt}

To solve for k;

6\ years\ later = 500,000

i.e.

t = 6\ A = 500000

So:

500000= 1000000e^{k*6}

Divide both sides by 1000000

0.5= e^{k*6}

Take natural logarithm (ln) of both sides

ln(0.5) = ln(e^{k*6})

ln(0.5) = k*6

Solve for k

k = \frac{ln(0.5)}{6}

k = \frac{-0.693}{6}

k = -0.1155

Recall that:

\frac{dA}{dt} = kA

Where

\frac{dA}{dt} = Rate

So, when

A = 600000

The rate is:

\frac{dA}{dt} = -0.1155 * 600000

\frac{dA}{dt} = -69300

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

7 0
2 years ago
Find the product and fill in the blanks to write in standard complex number form
k0ka [10]
X^2 +2x +10 = 0

D = 4 -40 = - 36 

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x_1,2 = -1 +/- 3i   or more understandably 

x_1 = -1 -3i and x_2 = -1 +3i

hope this will help you 
3 0
3 years ago
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