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3 years ago

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Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that

pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year?

1 answer:

Thepotemich [5.8K]3 years ago

6 0

Answer:

$6750 in the bank account and $20,250 in the stock fund

Step-by-step explanation:

If B is the money they put in the bank and S is the amount they put in the stock fund, then:

B + S = 27000

1.024 B + 1.072 S = 1.06 × 27000

Solving the system of equations:

1.024 (27000 − S) + 1.072 S = 28620

27648 − 1.024 S + 1.072 S = 28620

0.048 S = 972

S = 20250

B = 27000 − S

B = 6750

They should put $6750 in the bank account and $20,250 in the stock fund.

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The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. A) Estimate how lo

VLD [36.1K]

Answer:

A) 63.36 years.

B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

$P(t)=7.1(1.011)^{t}$

$7.1 \times 2=7.1(1.011)^{t}$

$\frac{7.1 \times 2}{7.1} =(1.011)^{t}$

$2 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(2) =ln (1.011)^{t}$

$ln(2) =t \cdot ln(1.011)$

$0.6931471805599453 =t \cdot 0.0109399400383344$

$t=\frac{0.6931471805599453}{0.0109399400383344}$

$t=63.3593217267282743049\approx 63.36$

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

$7.1 \times 3=7.1(1.011)^{t}$

$\frac{7.1 \times 3}{7.1} =(1.011)^{t}$

$3 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(3) =ln (1.011)^{t}$

$ln(3) =t \cdot ln(1.011)$

$1.0986122886681097 =t \cdot 0.0109399400383344$

$t=\frac{1.0986122886681097}{0.0109399400383344}$

$t=100.4221490079915311298\approx 100.42$

Therefore, it will take 100.42 years the population to triple of its size.

6 0

3 years ago

diketahui akar akar persamaan kuadrat 2x^2-9x + 7 = 0 adalah x1 dan x2. nilai dari x1^2 + x2^2- 4x1x2 adalah...

Leviafan [203]

<span>jika xy = 0 , kemudian menganggap x dan y = 0

faktor 2x^2-9+7
(2x-2)(x-7)=0

2x-2=0
2x=2
x=1

x-7=0
x=7

</span><span>jika 1 = x1 dan 7 = x2 maka jawabannya adalah 1^2+7^2-4(1)(7)=22
</span>
jika 7 = x1 dan 1 = x2 maka jawabannya adalah
7^2+7^2-4(7)(1)=22

<span>jawabannya adalah 22</span>

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3 years ago

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Alona [7]

Answer:

Answer: A as you have indicated.

Step-by-step explanation:

Givens

There are two sides that are 3.1 cm in length
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Formula

P = 2*(b + a)
where b is the base and
where a is the side

Solution

P = 2*(6.2 + 3.1) Add what is inside the brackets
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Answer A

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3 years ago

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Answer:

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Step-by-step explanation:

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Using the Inverse Properties of In, we get

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Answer:

D

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