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3 years ago

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

1 answer:

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

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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

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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

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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.

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We have the following summary

mean = 11
median = 10
mode = 10

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

We can see that mean < mode is false, since it should be mean > median, so cross choice A off the list.
mean = median is also false, so choice B is crossed off as well.
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.
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