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tankabanditka [31]
3 years ago
13

Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 1

3 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Mathematics
1 answer:
Alex777 [14]3 years ago
3 0

Answer:

<h2>$1344.9</h2>

Step-by-step explanation:

This problem can be solved using the compound interest formula

A= P(1+r)^t

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87

To the nearest cent the in 13 years the CD will be worth $1344.9

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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108
Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

4x+L=108

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

V=x^2L

If we express L in function of x using the restriction equation, we get:

4x+L=108\\\\L=108-4x

We replace L in the volume formula and we get

V=x^2L=x^2*(108-4x)=-4x^3+108x^2

To maximize the volume we derive and equal to 0

\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18

We can replace x to calculate L:

L=108-4x=108-4*18=108-72=36

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0
3 years ago
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If the sum of the measures of the interior angles of a polygon is twice the sum of its exterior angles, how many sides does it h
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<span>The measure of angle KJM is 108°.</span>
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A recipe calls for 6 quarts of water. Michael put 1 gallon of water in the bowl and realized that he made a mistake. Michael sho
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The answer to this to add 2 quarts.
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Can someone explain me how do i do (ii)?
Varvara68 [4.7K]

Answer:

(only ii right?)

Since we have the total number is 360° and our section is 72°, we know that the percentage of students who choose the cinema should be the number that we have divided to the total amount and then multiply the result by 100 ( it's fine if you write 100%, but when you actually calculate it, it's only 100, not 100%):

(72/360) . 100 = 20%

6 0
3 years ago
What is an example of when you would want consistent data and, therefore, a small standard deviation?
steposvetlana [31]

Answer:

12.1, 12.3,12.4,12.5,12.3,12.1,12.2

\bar X= \frac{12.1+12.3+12.4+12.5+12.3+12.1+12.2}{7}=12.271

And for the standard deviation we can use the following formula:

s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And after replace we got:

s = 0.1496

And as we can ee we got a small value for the deviation <1 on this case.

Step-by-step explanation:

For example if we have the following data:

12.1, 12.3,12.4,12.5,12.3,12.1,12.2

We see that the data are similar for all the observations so we would expect a small standard deviation

If we calculate the sample mean we can use the following formula:

\bar X=\frac{\sum_{i=1}^n X_i}{n}

And replacing we got:

\bar X= \frac{12.1+12.3+12.4+12.5+12.3+12.1+12.2}{7}=12.271

And for the standard deviation we can use the following formula:

s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

And after replace we got:

s = 0.1496

And as we can ee we got a small value for the deviation <1 on this case.

8 0
3 years ago
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