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babymother [125]
4 years ago
7

Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years. Approximately what is the minimum

simple interest rate Maggie needs to reach her goal? a. 2.89% b. 3.55% c. 4.95% d. 5.18%
Mathematics
2 answers:
iragen [17]4 years ago
6 0

Answer

Find out the what is the minimum simple interest rate Maggie needs to reach her goal .

To proof

Formula

Simple\ interest = \frac{principle\times rate\times time}{100}

As given

Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years.

put all the values in the formula

4000 = \frac{14100\times rate\times 8}{100}

Solving

rate = \frac{4000\times 100}{14100\times8}

solving the above

rate = \frac{400000}{112800}

rate =3.55% (approx)

the minimum simple interest rate Maggie needs to reach her goal is 3.55% .

Option (b) is correct .

Hence proved


jolli1 [7]4 years ago
6 0
$14,100 * 8 * i = <span>$4,000 
$112,800 * i = </span>$4,000 
i = $4,000  /  $112,800
<span>i = 0.0355

i = 3.55%

answer is </span><span>b. 3.55%</span><span>

</span>
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c)0.2402

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Step-by-step explanation:

Let X_i be an item passed by inspector i

Let Y be the event that there is a fault in an item

The probability that an item has a flaw is 0.1 i.e. P(Y)=0.1

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If a flaw is present ,it will be detected by the second inspector with probability 0.7 i.e.P(\bar{X_2}|Y)=0.7

So,P(X_2|Y)=1-0.7=0.3

If an item does not have a flaw, it will be passed by the first inspector with probability 0.95 i.e. P(X_1|\bar{Y}) = 0.95

So, P(\bar{X_1}|\bar{Y}) = 1-0.95=0.05

If an item does not have a flaw, it will be passed by the second inspector with probability 0.8 i.e. P(X_2|\bar{Y}) = 0.8

So, P(\bar{X_2}|\bar{Y}) = 1-0.8=0.2

a)P(found by atleast one inspector | It has flaw )=1-P(found by none inspector | It has flow )

P(found by atleast one inspector | It has flaw )=1-P(X_1|Y) P(X_2|Y)

P(found by atleast one inspector | It has flaw )=1-0.08 \times 0.3

P(found by atleast one inspector | It has flaw )=0.976

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b)P(Y|X_1)=\frac{P(X_1|Y) P(Y)}{P(X_1|Y) P(Y)+P(X_1|\bar{Y}) P(\bar{Y})}

P(Y|X_1)=\frac{0.08 \times 0.1}{0.08 \times 0.1+0.95 \times 0.9}=0.00926

C)P( two inspectors draw different conclusions on the same item)=P(X_1 \cap \bar{X_2} \cap Y)+P(\bar{X_1} \cap X_2 \cap Y)+P(X_1 \cap \bar{X_2} \cap \bar{Y})+P(\bar{X_1} \cap X_2 \cap \bar{Y})

P( two inspectors draw different conclusions on the same item)=0.2402

D)

P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2)}\\P(Y|(X_1 \cap X_2))=\frac{P(Y \cap X_1 \cap X_2)}{P(X_1 \cap X_2 \cap Y)+P(X_1 \cap X_2 \cap \bar{Y})}\\P(Y|(X_1 \cap X_2))=0.35

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You can work from the bottom up and define the outer function (f(x)) to be any of these operations. In our answer above, we have elected to include the "square root" and the "8 divided by that root" in our definition of f.

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<u>Step 1</u>

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<u>Step 2</u>

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<u>Step 3</u>

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<u>The answer:</u>

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