Find the sum of the geometric series
1+ 0.8 + 0.8^2 + 0.8^3 + ... + 0.8^19

Answers

Answer 1
Answer: Approximately 4.94235392476964

Work Shown:

a = first term = 1

r = 0.8 = common ratio

We know the common ratio is 0.8 because we multiply this common ratio by each term to get the next term. The easiest to spot this is going from term1 to term2. Put another way, term2/term1 = 0.8/1 = 0.8 is our common ratio.

The general form of the nth term of a geometric sequence is [tex]a(r)^{n-1}[/tex] and because the last term has an exponent of 19, this means n-1 = 19 solves to n = 20. Therefore, we are summing exactly n = 20 terms here.

Use the formula below to take a shortcut rather than painstakingly find all 20 terms and then summing them.

[tex]S = \frac{a*(1-r^n)}{1-r}\\\\S = \frac{1*(1-0.8^20)}{1-0.8}\\\\S \approx \frac{1*(1-0.01152921504607)}{1-0.8}\\\\S \approx \frac{1*(0.98847078495393)}{0.2}\\\\S \approx \frac{0.98847078495393}{0.2}\\\\S \approx 4.94235392476964\\\\[/tex]

This value is approximate.

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

To check your answer, you could type the following into your calculator

1+0.8+0.8^2+0.8^3+0.8^4+0.8^5+0.8^6+0.8^7+0.8^8+0.8^9+0.8^10+0.8^11+0.8^12+0.8^13+0.8^14+0.8^15+0.8^16+0.8^17+0.8^18+0.8^19

Though as you can see, this is very tedious to type in. This is why the formula in the previous section above is preferred.


Related Questions

PLZ help I don't understand!!!!

Answers

Answer:

The answer is 24.4.

Step-by-step explanation:

You use tan to figure it out as we they have given us the opposite value and we need to find out the adjacent value. and tan tan(x) = opposite over adjacent.

x is the value we need to find

tan(16) =7÷x

xtan(16) = 7

x= 7 ÷ tan(16)

x = 24.4

Hope this helped!

Mathematics question

Answers

So the answer of question no 4 is 2

The answer of question no 5 is 5

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

Step-by-step explanation:

number 4 :  x=2

number 5:  x=5

percentage increase from 14 to 40

Answers

Answer:

185.714% increase

Step-by-step explanation:

To find the percentage increase, take the new amount and subtract the original amount

40-14 = 26

Divide by the original amount

26/14

1.857142857

Multiply by 100% to change to percent form

185.714%

Answer:

185.714%

Step-by-step explanation:

Evaluate 3|-3|
if you could do it step by step I’d appreciate

Answers

Answer:

9

Step-by-step explanation:

the absolute value of -3 is 3

so; 3*|-3| =3*3 =9

Jaylen rents bowling shoes for $6 and pays $5 per bowling game. Is the relationship a proportional relationship? Explain

Answers

Answer:

yes

Step-by-step explanation:

the easy explanation is that the graph is straight so it means its proportional. the more detailed one is that you don't care about those 6$, cause its only says to you where the graph starts from (if you'll see it isn't from 0 there its from 6). you do care about the 5$ detail. and they say its for every game which is the definition of proportional (for every *blank amount of x* youll need *blank amount of y* ) you can see that after 1 game youll pay 5$ and then 10$ and so on....

√(25 - 10 √(3) + 3)
(not as a decimal)

Answers

Answer:

[tex]\huge\boxed{\sqrt{25-10\sqrt3+3}=5-\sqrt3}[/tex]

Step-by-step explanation:

[tex]\sqrt{25-10\sqrt3+3}=(*)\\\\25=5^2\\3=(\sqrt3)^2\\10\sqrt3=(2)(5)(\sqrt3)\\\\(*)=\sqrt{5^2-(2)(5)(\sqrt3)+(\sqrt3)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(5-\sqrt3)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|5-\sqrt3|=5-\sqrt3\\\\^{\text{because}\ 5>\sqrt3\to5-\sqrt3>0}[/tex]

Which set includes all of the integers?
{1,2,3,4,5...)
{...-3.-2, -1.0, 1, 2, 3,...)
{0, 1, 2, 3, 4, 5,...)​

Answers

Answer:

its {0,1,2,3,4,5......}

Step-by-step explanation:

Answer:

whoops wrong question srry

Step-by-step explanation:

A single candy is picked
randomly from a bag
containing 5 red, 4 Green, and
3 blue. Give the probability of
picking a candy that is not blue.

Answers

Answer:

9/12 or 3/4 (it's the same)

Step-by-step explanation:

You have to guve the probabiloty of picking a candy that is not blue, so you have to do:

5 red + 4 green = 9

total = 5 + 4 + 3 = 12

9/12 is equal to 3/4

Step-by-step explanation: the  answer is3/12

it is 3/12 because if you add 5+4+3 you will get 12 so out of that 12 which are blue which is 3 so it would be three

if it is wrong sorry but if it right hope its was correct :)

HELPPPPPPPPPPPPPPP MEEEEE

Answers

Answer:

-2

Step-by-step explanation:

Answer:

the number is the third one -2

A classroom has 14 blue chairs, 5 green chairs and 11 red chairs. If a chair is selected from the classroom at random, which color is most likely to be choses?

Answers

Answer:

Blue, and with a 7/15 chance

Step-by-step explanation:

14+5+11=14+16=30

b=14/30=7/15

r=11/30

g=5/30=1/6

Please mark as Brainliest! :)

Have a nice day.

An aircraft carrier left Port 35 traveling north five hours before a container ship. The container ship traveled in the opposite direction going 8 km/h faster than the aircraft carrier for seven hours after which time the ships were 303 km apart. What was the aircraft carrier's speed ?

Answers

Answer:

Aircraft carrier speed = 4.97 km/h

Step-by-step explanation:

Given that the time taken by the aircraft = 5 hours

Let the distance covered = X

Speed = V

Time taken by the ship = 7 hours

Let the distance covered = Y

Speed = 8V

Since it is 8 km/h faster than the aircraft carrier.

Using the speed formula

Speed = distance/time

Distance = speed × time

For the aircraft;

X = 5V

For the ship:

Y = 7 × 8V = 56V

Since they are 303km distance apart,

X + Y = 303

5V + 56V = 303

61V = 303

V = 303/61

V = 4.97 km/h

Aircraft carrier speed = 4.97 km/h

Which measurement would not be used to calculate the area of this triangle?
16 cm
12 cm
24 cm
1.
12 cm
2.
16 cm
3.
24 cm
pls someone help this is due in 10 minutes and i have a lot more to do​

Answers

Answer:

Im not sure but i think 2 is the answer

Step-by-step explanation:

Please help answer this asap!
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the y term is eliminated?

1/4x - 1/6y = 5
4/5x + 3/8y = 10

1. 18 times the first equation and 8 times the second equation
2. –18 times the first equation and 8 times the second equation
3. 8 times the first equation and 6 times the second equation
4. –8 times the first equation and 6 times the second equation

Answers

Answer:

try answer 3 its been a minute hun but im pretty sure its 3. im sorry if the answer is wrong.

Step-by-step explanation:

Which operations could you use to solve this word problem? Check all that

apply

STEP 2: PLAN

The entire school, 250 students, went to the soap

box derby. The Math Club went in 2 vans, and

each van held 6 students. How many students

from the Math Club went to the soap box derby?

O

A. Multiplication

B. Subtraction

C. Division

D. Addition

Answers

Answer:

A and D

Step-by-step explanation:

if each van held 6 students and the math club went in two vans, then you can use multiplication to figure it out. each van held 6 students, the math club went in two vans, so the equation can be 6 x 2. BUT you can do addition as well. because 6 plus 6 will give you the same answer as 6 x 2 because each van holds six students, there were two vans so 6 plus 6 is another way to solve this problem.

what is the maximum volume of water a hamster bath could hold with a depth of 1 2/3 inches, a length of 2/13 inches and a width of 2 inches

Answers

Answer:

I'm glad you asked.

Step-by-step explanation:

The max volume would be 70/9 or 7 7/9.

John and David have a rectangular piece of property. The length is 8 more miles than the width, the perimeter is 60. What are the possible dimensions?​

Answers

Answer:

Length: 19

Width: 11

Step-by-step explanation:

19 miles is 8 miles longer than 11 miles.

With these dimensions, the perimeter is equal to 60 miles.

I will give you brainliest if you answer pleaseee

Answers

Answer: The area of the banner is 100 in^2

Step-by-step explanation:

so let say the banner was still a rectangle with the triangle still  attached to it so if we needed to find the area of the whole rectangle we will need to multiply the length times the width

so  14 * 8 =  112    

But now a triangle is being cut out of the rectangle so we need to find the area of the triangle being cut out and subtract it from the area of the whole rectangle.  But first we need to find the base and the base is 8  since the other side  base is 8  too and the height will be 3 since 14- 11= 3  

Now find the area of the triangle by multiplying the base times the height and divide it by 2.

8 * 3= 24

24/2= 12

subtract 12 from 112

112- 12 = 100

What type of correlation is shown in the graph?
A) Positive
B) negative
C) no correlation

Answers

Answer:

No correlation

Step-by-step explanation:

This is because they are all spread out and aren't all consistently going up or down.

Answer:

C

Step-by-step explanation:

What is a like radical to cube root 54 after simplifying

Answers

Answer:

3√128

Step-by-step explanation:

Which is NOT true regarding the hypotenuse? *
O It is the longest side of the right triangle
It helps form the right angle.
It is across from the right angle

Answers

Answer:

It helps form the right angle.

Step-by-step explanation:

The hypotenuse is across from the right angle formed by the shorter sides.

Answer:

B: It helps form the right angle.

Step-by-step explanation:

Solve the equation for x : x3=64

Answers

Answer:

x=21.3333

Step-by-step explanation:

its right

Answer:

X=4

Step-by-step explanation:

Hope I helped:)

Heyguys can soeom plzz help meee?? IDK how to do this!! 20 Points? plz write all details of the problem plzz!

Math problem: An airplane traveled 5.7 x 102 miles per hour for 1.4 x 101 hours. How far did the airplane travel?

Answers

Answer:

The distance travelled is 7.98×10³ miles.

Step-by-step explanation:

Given that the formula to find distance is Distance = Speed×Time. Then you have substitute the values into the formula :

[tex]distance = speed \times time[/tex]

Let speed = 5.7×10²,

Let time = 1.4×10¹,

[tex]d = (5.7 \times {10}^{2} ) \times (1.4 \times 10)[/tex]

[tex]d = (5.7 \times 1.4) \times ( {10}^{2} \times 10)[/tex]

[tex]d = 7.98 \times {10}^{3} miles[/tex]

I need help finding the area of the polygons.

Answers

Answer:

hope it helps

Step-by-step explanation:

1. area = 15*15 - 5*6 = 195

2. area = (8+16)*8 /2   -     5*3  =  96 - 15 = 81

3. area = 12*3 + 9 * (12 - 4 - 4) = 36 + 9*4 = 36+36 = 72

4. x = 6-3 = 3

   y = 3- (-1) = 4

   z = 7-3 = 4

area = 2*x*y/2 + y*z = 2*3*4/2 +4*4 = 12+16 = 28

1. If you deposit $9200 into an account paying 7% annual interest
compounded quarterly, how much money will be in the account after 10 years? a
A) $20,123.85
B) $ 8,549.75
C) $18,414.70
D) $10,487.20

Answers

Answer:

C) $18,414.70

Step-by-step explanation:

  [tex]A = 9,200 (1 +\frac{0.07}{4}) ^{4 x 10}[/tex]

      = $18, 414.70

Lines r and a are parrallel.if m<2=110,what is m<7?

Answers

Answer:

m< 7 = 70

Step-by-step explanation

m< 2 + m< 1 = 180

180 - 110 = 70

m< 1 = 70

because the lines are parallel m< 1 = m< 7

so m< 7 = 70

Robert wants to put lights around the edge of his deck.the deck is 46 feet long and 29feet wide .how many yards of lights does he needs.

Answers

Answer:

1334feet

Step-by-step explanation:

46x29

Determine between which consecutive integers the real zeros of f(x) = x2 – 3x + 1 are located.
between -1&0,0&1 and 2&3
between -1&0,0&1 and 1&2
between -28-1,0&1 and 1&2
between -2&1, 0&1 and 1&2

Answers

Answer:

between -2&1,0&1 and 1&2

Maria is four times as old as Frank. In two years Maria will be 3 times as old as Frank. Find their present ages?

Answers

Answer:

Maria is 16 and Frank is 4

Step-by-step explanation:

Determine if a linear, exponential, or quadratic function is the best model for the data given in the table below.

Answers

Answer:

linear

Step-by-step explanation:

yes it is linear since I did this question and got it right

Please help me with this question i am struggling

Answers

Answer:

x would be 7 units because 4 × 7 = 28 And 28 + 10 = 38

Step-by-step explanation:

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