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Dafna1 [17]
3 years ago
12

A retired woman has $40,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and ano

ther riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $4,000 per year from her investments?
Mathematics
1 answer:
nalin [4]3 years ago
4 0

She should invest $30000 in the 9% fund and $10000 in the 13% fund.

<u><em>Explanation</em></u>

Suppose, the amount of investment at 9% rate is  x dollar.

As the total amount of investment is $40000 , so the investment at 13% rate will be: (40000-x) dollar

So, the amount of earnings per year from 9% fund = 0.09x dollar

and the amount of earnings per year from 13% fund = 0.13(40000-x) dollar.

Given that, the <u>total earnings per year is $4000</u>. So the equation will be......

0.09x+0.13(40000-x)=4000\\ \\ 0.09x+5200-0.13x=4000\\ \\ -0.04x=4000-5200\\ \\ -0.04x= -1200\\ \\ x= \frac{-1200}{-0.04}=30000

So, the amount of investment at 9% fund is $30000 and the amount of investment at 13% fund = ($40000- $30000)= $10000

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Answer:

<u><em></em></u>

  • <u><em>Event A: 1/35</em></u>
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<u><em></em></u>

Explanation:

<u>Event A</u>

For the event A, the order of the first 4 acts does not matter.

The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.

Thus, the number of ways that the first <em>four acts</em> can be scheduled is:

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And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).

Therefore the<em> probability of Event A</em> is:

           P(A)=1/35

Event B

Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.

The number of ways in which <em>four acts </em>can be scheculed when the order matters is:

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Therefore, <em>the probability of Event B</em> is:

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