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cricket20 [7]
3 years ago
11

A retired woman has $280,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and an

other riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $28,000 per year from her investments?
9% fund $

13% fund $
Mathematics
1 answer:
ASHA 777 [7]3 years ago
6 0

Answer:

9% fund: $ 210,000

13% fund: $70,000

Step-by-step explanation:

As she wants to have a $28,000 annual return for her $280,000 investment, she is expecting a return rate of 10%:

r=\dfrac{R}{C}=\dfrac{28,000}{280,000}=0.10

If we call x the proportion of the capital in the 9% fund, then (1-x) is the proportion of the capital in the 13% fund,and the return of the combination has to be the expected return of 10%:

0.09x+0.13(1-x)=0.10\\\\0.09x+0.13-0.13x=0.10\\\\-0.04x=0.10-0.13=-0.03\\\\x=\dfrac{0.03}{0.04}=0.75

Then, we know that 75% of the capital should be invested in the 9% fund and 25% in the 13% fund.

This correspond to a capital of:

9% fund: 0.75*$280,000 = $ 210,000

13% fund: 0.25*$280,000 = $70,000

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ycow [4]

The expression in scientific notation is given as follows:

3.5 x 10³.

<h3>What is scientific notation?</h3>

A number in scientific notation is given by:

a \times 10^b

With the base being a \in [1, 10).

For this problem, the expression is given by:

\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}

When two factors of a multiplication have the same base and different exponent, we <u>keep the base and add the exponents,</u> hence:

10^2 \times 10^4 = 10^6

5 x 4.2 = 21, hence the expression is:

\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3

Which is the simplified expression.

More can be learned about scientific notation at brainly.com/question/16394306

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6 0
1 year ago
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RideAnS [48]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
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Step-by-step explanation:

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2 years ago
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12.
Naily [24]

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

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Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy

Thus, the expression is (x² - 6y² + 3xy).

7 0
3 years ago
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