36. Find the sum of the infinite geometric series if it exists.
1+\frac{3}{2}+\frac{9}{4}+\frac{27}{8}+\cdots

Answers

Answer 1

Answer:

[tex]=2\times \left( \frac{3}{2} \right)^{n+1} -2[/tex]

Step-by-step explanation:

[tex]1+\frac{3}{2} +\frac{9}{4} +\frac{27}{8} +\cdots[/tex]

[tex]=1+\left( \frac{3}{2} \right)^{1} +\left( \frac{3}{2} \right)^{2} +\cdots +(\frac{3}{2})^n[/tex]

[tex]=\frac{1-\left( \frac{3}{2} \right)^{n+1} }{1-\frac{3}{2} }[/tex]

[tex]=-2\times \left( 1-\left( \frac{3}{2} \right)^{n+1} \right)[/tex]

[tex]=2\times \left( \left( \frac{3}{2} \right)^{n+1} -1\right)[/tex]


Related Questions

Explain the difference between center and shape of a data set.

Answers

The center is the median and/or mean of the data. And, the shape describes the type of graph.

There are many shapes data sets could show. One example would be asymmetric data set. In this case, both sides of the picture would look almost exactly or could be exactly (rarely) alike. In this case, the mean could be used as a measure of center.

When the data is skewed right or left, the pictorial representation of the data will show fewer data points on the side where it is skewed and more data on the opposite side. The tail will be longer on the right if it is skewed right and vice versa.

In skewed right data, the mean will be greater than the median, and if the data is skewed left, the mean will be less than the median. The mean is not the measure of the center when the data is skewed.

A box of oranges has a mass of 4 kg. If one orange is 80 g, how many oranges are in the box?

Answers

Total mass of box = 4 kg or 4000 grams

Number of oranges= 4000/80

= 50 oranges

Answer:

50 oranges are in the box

Step-by-step explanation:

First, find the converting of 1 kg to grams (1kg = 1000g)

Then, convert how many kg is the box of oranges (4kg = 4000g)

Finally, divide the total grams of the box by the total grams per EACH orange in the box (4000g ÷ 80g = 50)

Therefore, there are 50 oranges in the box

The only reason you may have got confused with this question is from not knowing the conversions or measurements. This is a 2-step questions were you have to convert then do the main equations to solve.

HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!1

Answers

Answer:

1/3

Step-by-step explanation:

From the given diagram of the spinner, we can infer that blue occupies 1/3 of the space and green occupies the remaining space.

Hence, the probability of spinning blue :

1/3

Answer:

1/3

Step-by-step explanation:

The blue one occupied one-third of the spinner, means when it got divided into three parts, the blue get one of them.

how do i tell my ex i miss them and what we had but what if they don’t miss me?

Answers

Answer:

So basically just try to make em miss you or say "haha get pranked loser" and roast em hard

Step-by-step explanation:

Answer: I miss her too, I miss her smile every second of my life

Step-by-step explanation:

Item 16
In a survey of 600 people, 54% said they ate at a restaurant the previous week.

How many people said they ate at a restaurant the previous week?


276 people

288 people

324 people

348 people

Answers

it’s 324 because 50% is 300 and 4% is 24
The answer is 324 people

A storage box has a base area of 314.5 square inches and a height of 8.5 inches.

What is the volume of 5 of these boxes?

Enter your answer as a decimal in the box.

Answers

Volume is base x height, and since you have 5 boxes, it’s the volume of 1 box, times 5. The base area x the height is 2,673.25, and when you multiply this by 5, you get 13,366.35 cubic inches.

Answer:

13366.25in cubed

Step-by-step explanation:

To find the volume of a rectangular prism, you need the formula:

V = (L × H) × W

Luckily, L × H is the base of the shape. So we can change it into:

V = B × W

Step 1

Plug in the values! That’s what we do everytime!

V = 314.5 × 8.5

Step 2

Multiply 314.5 by 8.5.

V = 2673.25

BUT ITS NOT THE ANSWER YET!

Step 3

Because you need  to find the volume of 5 of the boxes, multiply 2673.25 by 5.

2673.25 × 5 = 13366.25

Thus, the volume of 5 of the boxes is 13366.25in cubed.

Help me with this
Another similar question​

Answers

Step-by-step explanation:

you do know that 1 cm = 10 mm, right ?

so,

6 cm = 6×1 cm = 6×10 mm = 60 mm

and that is the ultra-ultra long form of doing this ...

Answer:

60mm

Step-by-step explanation:

This is conversion, so, to find this, we will have to convert 6cm to milimeters.

1cm = 10mm

So [tex]6cm *10mm=60mm[/tex]

Hence, the tail length is 60mm

Have a great day!

Remember to be Kind!

In the figure below, the m∠2 is 50°.

∠1 and ∠3 are a pair of ? angles.

Answers

Answer:

adjacent

Step-by-step explanation:

Adjacent I think because that’s what my papa said to me when he went to go get milk

It costs $22 to enter an amusement park and $0.50 to ride a ride. You have $23. Write an equation that represents the number r of rides you can ride.


If you get it correct I will give you an brainliest!

Answers

You would have to do 20.50 + 0.25r + 21.50 I think

Answer:

[tex]23=0.50r+22[/tex]

Step-by-step explanation:

y=total amount of money

b=cost of admission

m=cost per ride

r= amount of rides

How to solve:

Step 1: Set up the equation in [tex]y=mx+b[/tex] format.

[tex]23=22+0.50r[/tex]

Step 2: Subtract 22 from both sides of the equation.

[tex]23-22=22+0.50r-22[/tex]

Step 3: Divide both sides by 0.50

[tex]\frac{1}{0.50} =\frac{0.50r}{0.50}[/tex]

Step 4: You are left with your answer.

[tex]r=2[/tex]

A right rectangular pyramid is sliced perpendicular to the base through the vertex.

What is the resulting shape of the cross section?


trapezoid

rectangle

triangle

Answers

triangle, try using a model to help you !

George is working on a math assignment. He needs to identify which point on the coordinate plane below is located at (7,5). Help George locate the correct point by sharing what you know about the coordinate plane.

Answers

Answer:

A is correct.

Explanation:

Given: (7,5) where (x, y)

Identify:

x = 7

y = 5

Go 7 units through x-axis, then move up 5 units along the y-axis.

Answer:

An address on a coordinate plane is made up of an x value and a y value that correspond to the x- and y-axes. This "address" is called a coordinate point, and is written in the form: (x,y). So, you would need to move 7 spaces right and 5 spaces up.

Hope this helps

What is the area of the triangle below?

Answers

Answer: 36

Step-by-step explanation:

area of a triangle = [tex]\frac{1}{2}[/tex] length × width

12 × 6 = 72

72 ÷ 2 = 36

Answer:

A = 36 in²

Step-by-step explanation:

To find the area of a triangle use this formula A =  A=hb/b

Plug your numbers inA = [tex]\frac{6 * 12}{2}[/tex] = 36

What is the surface area of a square pyramid that has a base of 12 cm. and the sides of the pyramid have a slant height of 9 cm. to the nearest whole number?

Answers

Answer:

108

Step-by-step explanation:

just multiply the base and the heigth so 12x9=108

answer :
108
just Multiply the base and the height so 12x9=108

PLS HELP!! GIVING BRAINLIEST TO FIRST CORRECT ANSWER!!+50 POINTS

Answers

Answer(s):

154 in²3168/7 km²38.5 m²

Revising the area of a circle formula

We already know that the area of a circle is expressed as [tex]\pi r^{2}[/tex].

The "r" variable is known as the radius.Solving each problem given:Solving Problem 4:

We are given the radius of circle, which is 7 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

[tex]\implies \pi (7)^{2}[/tex]

Take π as 22/7

[tex]\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)^{2}[/tex]

[tex]\implies \huge\text{(}\dfrac{22}{7} \huge\text{)}(7)(7)[/tex]

[tex]\implies (22)(7)[/tex]

[tex]\implies 154 \ \text{in}^{2}[/tex]

Solving Problem 5:

In this problem, we are given the diameter to be 24 kilometers. Since the radius of the circle is half the diameter, we can tell that the radius of the circle is 24/2 kilometers, which is 12 kilometers.

[tex]\implies \pi (12)^{2}[/tex]

Take π as 22/7

[tex]\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)^{2}[/tex]

[tex]\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (12)(12)[/tex]

[tex]\implies \dfrac{3168}{7} \ \text{km}^{2}[/tex]

Solving Problem 6:

We are given the radius of circle, which is 3.5 in. Let us substitute the radius in the formula. Once substituted, we can simplify the expression obtained to determine the area of the circle shown in the picture.

[tex]\implies \pi (3.5)^{2}[/tex]

Take π as 22/7

[tex]\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (3.5)^{2}[/tex]

[tex]\implies \huge\text{(}\dfrac{22}{7}\huge\text{)} (3.5)(3.5)[/tex]

[tex]\implies \huge\text{(}\dfrac{22}{2}\huge\text{)} (3.5) = (11) (3.5)[/tex]

[tex]\implies 38.5 \ \text{m}^{2}[/tex]

Note: The radius given in this problem was not clearly stated. If the radius I stated here, is incorrect, please notify me in the comments. Thanks!

Learn more about area of circles: https://brainly.com/question/12414551

Plot the following points on the coordinate plane: Point A: (3, 5) Point B: (0, 3) Point C: (1, 8) Point D: (7, 2) Point E: (0, 9)

PLEASE HELP WILL GIVE BRAINLIEST (88 POINTS)

Answers

Answer:

I got you I saved the image and wrote on it :)

Step-by-step explanation:

just look at the image it has all the coordinates labeled.

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPWILL MARK BRAINLIEST

Answers

1. 4x' = 36 in

x' = 9 in

As it's increased by 6 inches we get x = 9-6 = 3 in.

An equation for this is 4x'/4-6 = x

2. 2x-26=4 ==> x = (4+26)/2 (which is $15 each)

answer

1. 9 inches and 2. $18

Step-by-step explanation:

The area of the shaded region is . What is the area of the unshaded region?


A.7ft2
B.21ft2
C.42ft2
D.84ft2

Answers

You didn’t add any numbers for me to work with
can you post a picture of the actual problem on the paper

Breaking a cookie in half creates a straight side 10 cm long.

Answers

Answer:

whats the question

Step-by-step explanation:

ill give brainly
80% of what number is 48?

Enter your answer in the box.

Answers

Answer:

38.4

Step-by-step explanation:

to find a percentage of a number all you have to do is divide the percentage by a 100 then multiply it by the total which in this case is 48

0.8 × 48 = 38.4

Answer:

The answer is 38.4

Step-by-step explanation:

first divide 80 by 100

then multiply 0.8 times 48

then you get 38.4

Pls help me do today

Answers

Answer:

[tex]\overline{OT}=\textsf{line segment OT}[/tex]

Step-by-step explanation:

[tex]\overline{OT}=\textsf{line segment OT}[/tex]

[tex]\angle OT=\textsf{angle OT}[/tex]

[tex]\longleftrightarrow\\OT=\textsf{line OT}[/tex]

[tex]\overrightarrow{OT}=\textsf{ray OT}[/tex]

OT means "ray OT."

Explanation:

"Line segment OT" refers to a part of a line between two endpoints, excluding the endpoints."Angle OT" refers to the measure of the angle at point O formed by rays OA and OT."Line OT" refers to the straight path that extends indefinitely in both directions through point O and T."Ray OT" refers to the straight path that starts at point O and extends indefinitely through point T in one direction.

What is the best way to describe the center of the data represented in this line plot?

Select from the drop-down menus to correctly complete the statement.

Answers

Answer:

The number of inches is 1

Step-by-step explanation:

The median

5. Write an expression.

a. 2 less than s
c. 5 times the quantity y - 2
b. the quantity 7 + x, squared
d. the quotient of 4 and x²

Answers

a. s - 2

b. (7+x)^2

c. 5y - 2

d. 4/x^2
a. s-2
c. 5(y-2)
b. (7+x)^2
d. 4/x^2

What is the surface area of the green shapes?

Answers

Answer:

10

Step-by-step explanation:

4 x 5 ÷ 1/2 = 10

Answer:6

B=base H=height /=divided by

Bxh/2

B=3 H=4

3x4/2=?

12/2=6

Answer:6

Desmos
Is it Fair?

Explain your answer.

Answers

Answer: yes
It is fair
Hope this helps
Yes it is fair because the line stays consistent threwout the graph chart

( brainliest ) Susan is buying 5 and a half pies from the market. Write this amount as a mixed number, improper fraction, decimal and percent.

Answers

The amount of pies in mixed numbers is 5*1/2   and  in the improper fraction is 11/2 and in decimal is 5.5 and in percentage is 5.5%

Given: Susan buys 5 and a half pies from the market.

To find the value of the pies in the following ways:

Mixed fractionImproper fractionDecimalPercent

The mixed fraction is represented as a whole number and also as a fraction. It is the mixture of a whole number and a fraction. The simple way to find out the mixed fraction is, first multiply the value in the denominator by the value of the whole number in the mixed fraction. Later add the obtained number. Here is the problem the mixed fraction can be written as 5*1/2.

The improper fraction is identified when the numerator is greater than the denominator. From the given question the value of pies in the improper fraction is given by 11/2. Here 11 is greater than 2.

Next, the decimal number is represented by a whole number that is separated from the decimal point of the fractional part. In question 5 and a half is represented as 5.5, where 5 is a whole number with a decimal point and the fractional part is 0.5.

The value of the percent is obtained by dividing the total value and multiplying it by 100. So from the question, we get 5*1/2*100 is equal to 250 or 5.5%.

To learn more about decimals, fractions, and percentages follow the link below:

https://brainly.com/question/12715980?referrer=searchResults

Ordering the points by their coordinate values, from least to greatest, spells,

Answers

It’s axes I’m pretty sure good luck

Consider the two-way table.

Group A Group B
Category 1 80 170
Category 2 90 84
Complete the table below to show the relative frequencies of the data in the first row.

Enter numbers in the boxes as decimals to the hundredth place.

Please give an explanation instead of just stating the answer!

Answers

Answer: Group A: 0.32 Group B: 0.68.

Explanation: I dont really have one, but a while ago i took the test and it was right.

Have a great day/night. :)

Answer:

Group A: 0.32 Group B: 0.68.

Step-by-step explanation:

The cylinder and the cone have the same volume and the same height. If the radius of the base of the cone is 3 cm, then the radius of the base of the cylinder is _____ cm.

Answers

Step-by-step explanation:

I hope you understood if yes mark me brainliest

Pls help me with this problem

Answers

Answer:

it is number 3

Step-by-step explanation:

i am just putting something here so it will not get taken down

hope this helps

The answer is 3 I’m just doing the same as the other person

HURRY PLEASE I WILL MARK BRAINLIEST!!!!!!!!!!!(Bible)
List three ways that man is called to respond to God’s plan in Christ.

a. b. c.

Answers

Answer:

a. be messengers of hope

b. be bothers and sisters in Christ

c. for us to not judge and love thy neighbor

Step-by-step explanation:

bible, yea.

hope this helps:)

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