Ask question

Ask question

All categories

2 years ago

11

An author published a book which was being sold online. The first month the author sold 21000 books, but the sales were declinin

g steadily at 12% each month. If this trend continues, how many total books would the author have sold over the first 9 months, to the nearest whole number?

1 answer:

Wittaler [7]2 years ago

4 0

Answer: 119,616

You may have to erase the comma when inputting the answer.

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

Explanation:

The author sells 21,000 books in the first month.

Then they sell 21,000*(1-0.12) = 21,000*(0.88) = 18,480 in the second month.

Then they sell 18,480*(1-0.12) = 18,480*(0.88) = 16,262.4 = 16,262 in the third month.

And so on. These values follow a geometric sequence with first term a = 21,000 and common ratio r = 0.88

We can think of the 0.88 as 88% of the original value (since losing 12%, we keep the remaining 88%)

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

Use the formula below to sum the first 9 terms of the geometric sequence

Plug in a = 21000 and r = 0.88

$S_n = a*\frac{1-r^n}{1-r}\\\\S_9 = 21000*\frac{1-0.88^9}{1-0.88}\\\\S_9 \approx 21000*\frac{0.6835216}{0.12}\\\\S_9 \approx 21000*5.6960133\\\\S_9 \approx 119,616.2793\\\\S_9 \approx 119,616\\\\$

The author sold about 119,616 books over the course of the first nine months.

You might be interested in

Area of a triangle with points at (-9,5), (6,10), and (2,-10)

Ann [662]

First we are going to draw the triangle using the given coordinates.
Next, we are going to use the distance formula to find the sides of our triangle.
Distance formula: $d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Distance from point A to point B:
$d_{AB}= \sqrt{[6-(-9)]^2+(10-5)^2}$
$d_{AB}= \sqrt{(6+9)^2+(10-5)^2}$
$d_{AB}= \sqrt{(15)^2+(5)^2}$
$d_{AB}= \sqrt{225+25}$
$d_{AB}= \sqrt{250}$
$d_{AB}=15.81$

Distance from point A to point C:
$d_{AC}= \sqrt{[2-(-9)]^2+(-10-5)^2}$
$d_{AC}= \sqrt{(2+9)^2+(-10-5)^2}$
$d_{AC}= \sqrt{11^2+(-15)^2}$
$d_{AC}= \sqrt{121+225}$
$d_{AC}= \sqrt{346}$
$d_{AC}= 18.60$

Distance from point B from point C
$d_{BC}= \sqrt{(2-6)^2+(-10-10)^2}$
$d_{BC}= \sqrt{(-4)^2+(-20)^2}$
$d_{BC}= \sqrt{16+400}$
$d_{BC}= \sqrt{416}$
$d_{BC}=20.40$

Now, we are going to find the semi-perimeter of our triangle using the semi-perimeter formula:
$s= \frac{AB+AC+BC}{2}$
$s= \frac{15.81+18.60+20.40}{2}$
$s= \frac{54.81}{2}$
$s=27.41$

Finally, to find the area of our triangle, we are going to use Heron's formula:
$A= \sqrt{s(s-AB)(s-AC)(s-BC)}$
$A=\sqrt{27.41(27.41-15.81)(27.41-18.60)(27.41-20.40)}$
$A= \sqrt{27.41(11.6)(8.81)(7.01)}$
$A=140.13$

We can conclude that the perimeter of our triangle is 140.13 square units.

3 0

2 years ago

QUICK QUICK PLEASE! 1 MINUTE ONLY! WITH EXPLANATION PLEASE!

Dmitriy789 [7]

Answer:

Step-by-step explanation:

<h2>first you add 60 plus 40 equals 100 then add 80 plus 50 equals 130.add 130 + 100 =230 then add 90 which is 320 next add 9 the you get 329</h2>

5 0

3 years ago

Prove that x=2 if 4^x=8x...where ^ stands for "to the power of".

Romashka [77]

In order to prove this, you simply plug in the number 2 everywhere you see X:

4^(2) = 8(2).

Simplify

16 = 16 √

Since this checks out, x is proven to be 2.

4 0

3 years ago

How to round 42.6598 to the barest hundredths place

NeX [460]

To round to the nearest hundredth is 42.66

6 0

3 years ago

Read 2 more answers

At a concert, 20% of the audiences is sitting in the balcony. If there are 450 people sitting in the balcony, what is the total

elena-14-01-66 [18.8K]

....................

3 0

3 years ago

Read 2 more answers