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madam [21]
3 years ago
12

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
Mathematics
1 answer:
AfilCa [17]3 years ago
7 0

Answer:

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

Step-by-step explanation:

Consider the provided information that Avery and Caden have saved $27000.

Let <em>x</em> is the money deposit in the bank and <em>y</em> is the money deposit in stock fund.

Therefore,

<em>x</em> + <em>y</em> = 27000

<em>x</em>  = 27000 - <em>y</em>

The bank account will pay 2.4% annual interest.

\frac{2.4}{100}x+x=1.024x

Stock fund pays 7.2% annual interest.

\frac{7.2}{100}y+y=1.072y

Therefore,

1.024 <em>x</em> + 1.072 <em>y</em> = 1.06 × 27000

Substitute the <em>x</em>  = 27000 - <em>y</em> in above equation.

1.024 (27000 − <em>y</em>) + 1.072 <em>y</em> = 1.06 × 27000

27648 − 1.024 <em>y</em> + 1.072 <em>y</em> = 28620

0.048 <em>y</em> = 28620-27648

0.048 <em>y</em> = 972

<em>y</em> = 20250

Now, substitute the <em>y</em> = 20250 in <em>x</em>  = 27000 - <em>y</em>.

<em>x</em> = 27000 − 20250

<em>x</em> = 6750

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

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Step-by-step explanation:

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Which expression represents the ratio of the difference of the two means to Sidney's mean absolute deviation
prohojiy [21]

Answer:

The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

Step-by-step explanation:

P.S - The exact question is -

Given - The means and mean absolute deviations of Sidney’s and Phil’s grades are shown in the table below.

                                       Sidney’s Grades           Phil’s Grades

Mean                                     82                                    78

Mean Absolute Deviation      3.28                                 3.96

To find - Which expression represents the ratio of the difference of the two means to Sidney’s mean absolute deviation?

Proof -

Given that Mean of Sidney Grades = 82

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The difference of two means = 82 - 78 = 4

Also,

Given, Mean Absolute Deviation of Sydney = 3.28

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The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

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