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sergejj [24]
3 years ago
11

What does the interest rate have to be, if a bank pays interest, compounded continuously and the amount doubles in 5 years?

Mathematics
1 answer:
allochka39001 [22]3 years ago
3 0
Let the original amount be A.  Double that would be 2A.

Then, 2A = Ae^(r*5), or 2 = e^(5r).

Taking the natural log of both sides:  ln 2 = 5r.  Then r = (ln 2)/5 = 0.14

The interest rate would have to be 13.86% per year, written here as r=0.14.
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Using the data in the table, which statement is true?
horsena [70]

Answer:  Choice C.  mean > median

================================================

Explanation:

Multiply each measure with their corresponding frequency.

  • 8*1 = 8
  • 10*3 = 30
  • 14*2 = 28

Add up those products: 8+30+28 = 66

Then divide by the total frequency n = 1+3+2 = 6 to get 66/6 = 11 as the mean.

mean = 11

----------------

Since we have n = 6 values in this list, this means the median is between slot n/2 = 6/2 = 3 and slot 4.

Note how that places us in the middle row because 1+3 = 4 encapsulates both of those slots mentioned. So the median is 10.

Or you could list out the values in roster notation {8, 10, 10, 10, 14, 14} to see that {10,10} occupy the middle most slots. So the median is (10+10)/2 = 20/2 = 10.

median = 10

-----------------

The mode is simply the most frequent value. The table shows that mode = 10 since it occurs 3 times, compared to 8 showing up 1 time and 14 showing up twice.

-----------------

We have the following summary

  • mean = 11
  • median = 10
  • mode = 10

With that in mind, let's go through the answer choices.

  1. We can see that mean < mode is false, since it should be mean > median, so cross choice A off the list.
  2. mean = median is also false, so choice B is crossed off as well.
  3. mean > median is true since 11 > 10 is true. Choice C is the answer. Note how this being true directly contradicts choice B, which is another reason to see why choice B is false.
  4. median > mode is false because 10 > 10 is false. It should be median = mode. Choice D is crossed off the list.
4 0
3 years ago
A rectangle that is 6 feet by 9 feet has been scaled by a factor of 1/3.
OleMash [197]

The side lengths of the scaled copy are 2 feet by 3 feet and  to scale the copy back to its original size, the scale factor to use is 3

<h3>1. What are the side lengths of the scaled copy? feet by feet</h3>

The given parameters are:

Length = 6 feet

Width = 9 feet

The scale factor is given as:

k = 1/3

So, the side lengths of the scaled copy are

Length = 1/3 * 6 feet = 2 feet

Width  = 1/3 * 9 feet = 3 feet

Hence, the side lengths of the scaled copy are 2 feet by 3 feet

<h3>2. Suppose you want to scale the copy back to its original size. What scale factor should you use?</h3>

In (1), we have:

The scale factor is given as:

k = 1/3

To scale the copy back to its original size, the scale factor to use is:

Scale = 1/(1/3)

Evaluate

Scale = 3

Hence, to scale the copy back to its original size, the scale factor to use is 3

Read more about scale factors at:

brainly.com/question/10253650

#SPJ1

6 0
2 years ago
Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the coefficient 'k' in the factored form? 6x3 + 4x2 − 6x − 4 = 2(x
anastassius [24]

6x^3+4x^2-6x-4 =\\ 2(3x^3+2x^2-3x-2) =\\ 2(x^2(3x+2)-1(3x+2))=\\ 2(x^2-1)(3x+2)=2(x+1)(x-1)(3x+2).

So k=1.

5 0
3 years ago
What is 6.38 to 1 decimal place​
agasfer [191]

Answer: Is 6.4

Step-by-step explanation: I hope I helped in some way shape or form.

7 0
2 years ago
- Mr. Rodriguez's construction company built an
ioda

Answer:

132 Floors

Step-by-step explanation:

1,848 ÷ 14 = <em>x</em>

<em>x </em>= 132

4 0
3 years ago
Read 2 more answers
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