Find the 8th term of the sequence whose common ratio is 1/3 and whose first term is 3

Answers

Answer 1

Answer:

The 8th term is [tex]\frac{1}{729}[/tex].

Step-by-step explanation:

Let's begin with the formula for a geometric sequence. We know this is geometric because we are working with a common ratio, or the number we multiply to find each term.

[tex]a_n=a_0(r)^{n-1}[/tex]

In this formula, [tex]a_0[/tex] is the first term, [tex]r[/tex] is the common ratio, and [tex]n[/tex] is the desired term. We know the values of [tex]r[/tex], [tex]a_0[/tex], and [tex]n[/tex] from the given information:

[tex]a_0=3\\r=\frac{1}{3}\\n=8[/tex]

Substituting those values we get:

[tex]a_8=3(\frac{1}{3})^{8-1}[/tex]

[tex]a_8=3(\frac{1}{3})^7\\a_8=3(\frac{1}{2187})\\a_8=\frac{3}{2187}\\a_8=\frac{1}{729}[/tex]


Related Questions

expression that is equivalent to 27e+24

Answers

Answer:

3(9e + 8)

Step-by-step explanation:

the highest common factor is 3 so factor it out.

Answer:

[tex]\displaystyle 3[9e + 8][/tex]

Explanation:

Sinse you were not specific in your approach, it is safe to assume that you were probably looking for how to factour this expression, and the way to do to this is to factour a 3 out the expression sinse both quantities have a common divisour of 3:

24: 1, 2, 3, 4, 6, 8, 12, 24

27: 1, 3, 9, 27

I am joyous to assist you at any time.

How many times larger is 8 x 106 than 2 x 103?
Х

Answers

Answer: ~4.12 times larger

Step-by-step explanation:

1. find the values for both equation, (8*106=848) and (2*103=206).

2. divide the larger number by the smaller one. 848/206

which gives us 4.11650485, or 4.12 rounded.

hope this helped! ♡

Is this a function pls someone tell me

Answers

Functions must pass the vertical line test. This means that for every x value there must be ONLY ONE y value.

We can see in this table that the x value 25 has two different y values. Therefore, this is NOT a function.

Hope this helps!

Answer:

yes

Step-by-step explanation:

If the line only goes through one point once than yes. Vertical line test.

Note: "While a function may NOT have two y-values assigned to the same x-value, it may have two x-values assigned to the same y-value. Function: each x-value has only ONE y-value!"

Find the slope of the line y=7x–6.

Answers

Answer:

slope: 7

y-intercept:  (0,−6)

Step-by-step explanation:

please help fast!!! a shirt is regularly priced at $35.50 if it is discounted by 45% what is the sales price

Answers

Might be 15 but good luck

BRAINLIEST For the fastest answer
Hello I need help on this math question​

Answers

Answer:

Choice a 10 cm

Step-by-step explanation:

Volume of a sphere; 4/3 x 3.14(r^3)

Since we dont know the radius aka r, we can put in the different values until we get what we are looking for :)

!!!used an online calculator for this!!!

Choice a: 4188.79

Choice b: 50965.01

Choice c: 38792.39

Choice d: 5575.2

Since none of the answers are coming out as 4846.59, I would go with the closest one, choice a.

I really hope this helps!!

Please rate!!

Have a wonderful day!!

In diagram below?FG bisects

Answers

Answer:

107 should be your answer

Step-by-step explanation:

so to simplify it, its as simple as 180-146=34 and then 73+34=107, because BGC is vertical to AGD giving you most of the line, and from more math you can figure out that FGA is equal to 73 and vertical to EGB giving you the rest that you need.

∠A and ∠B are supplementary. The measure of ∠A is 96°. What is the measure of ∠B? Enter your answer in the box. °

Answers

Answer:

∠B = 84

Step-by-step explanation:

Supplementary angles add up to 180°, You would subtract 96 from 180 to find angle B.

Answer:

=> ∠B = 84

Step-by-step explanation:

Given :

∠A + ∠B = 180°

∠A = 96°

=> 96° + ∠B = 180

=> ∠B = 180-96

=> ∠B = 84

Helpppppp!!!
(Show work)

Answers

Answer:

Step-by-step explanation:

Part B: A"C

The angle of elevation to a nearby tree from a point on the ground is measured to be 65 degrees. How tall is the tree if the point on the ground is 92 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Answers

Answer:

102feets

Step-by-step explanation:

sin 65=92÷x

0.906=92÷x

x=102

Angelina wins money in a competition. She is given the choice as to how she is paid.
Choice 1: Get $1 the 1st day, 2$ the 2nd day, $4 the 3rd day, 8$ the 4th day, and so on
Choice 2: Get 1,000,000 today.
a) With which method of payment will angelina get more money?
c) After how many days will the money Angelina gets from Choice 1 be approximately $1, 000, 000?

Answers

Answer:

Choice 120 days

Step-by-step explanation:

You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.

__

a)

Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.

__

c)

For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...

  Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r

We want to find n such that ...

  Sn ≥ 1,000,000

  1 × (2^n -1)/(2 -1) ≥ 1,000,000

  2^n ≥ 1,000,001 . . . . add 1

  n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm

  n ≥ 19.93

The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.

LAY
STOP
Solve using the Zero Product Property.
15. The height of a football after it has been kicked from the top of a hill can be modeled
by the equation h= 2(-2-4t) (2t - 5), where h is the height of the football in feet
and tiltihe time in seconds. How long is the football in the air?
A
A. t=2.5 seconds
B.
B. t=-0.5 seconds
с
C. t=1.5 seconds

Answers

Answer:

A

Step-by-step explanation:

how long is the ball in the air ?

that is the same as asking : after how many seconds will the ball hit the ground (= reach the height of 0) ?

so, that means we need to find the zero solution of h(t).

at what t is h(t) = 0 ?

when at least one of the factors is 0 :

2(-2 - 4t)(2t - 5)

we have 3 factors

2 : can never be 0.

(-2 -4t) : can only be 0 for negative t, which does not make sense in our scenario (we cannot go back in time, only forward).

(2t - 5) : is 0 when 2t = 5 or t = 2.5

so, A is the right answer.

FYI : the starting height (on the hill) is given by t = 0 :

2(-2 - 0)(0 - 5) = 2×-2×-5 = 20 ft

Please help on this

Answers

Answer:

5.025m

Step-by-step explanation:

The clothesline also creates an upside-down triangle with two sides being 5m, 0.5m, and the hypotenuse being the clothesline.

We can use the pythagorean theorem to find the length of the clothesline.

5 squared +.5 squared= the length of the clothesline squared

25+.25= the square root of 25.25

= 5.025

Answer:

Your answer would be:
5.025m


Step-by-step explanation:

5 sq + 0.5sq = the length of the clothesline sq

25 + 0.25= the square root of 25.25

= 5.025m



Have a great rest of your day
#TheWizzer

20 points, A right rectangular prism is 9.5 inches long, 4 yards wide and 3 yards tall what is its volume?

Answers

Answer:

114

Step-by-step explanation:

You first have to do L x W x H

which will be 9.5 x 4 x 3

that gives you 114

which is the answer 114!!

What is the coefficient for the 5th term of (2x-y)^8

Answers

Answer:

256x^8

Step-by-step explanation:

Hope this helped

Maybe mark brainiest?

Help? im confused plss!
Find the area of the regular polygon with the given radius or apothem.

Answers

Answer:

okay so think of the polygon as like a rectangle in a way now use the method of finding a area with a triangle  

Step-by-step explanation:

A= bxh divide by 2 then A= bxh x 2

it worked for me

BRAINLIEST For the fastest answer
Hello I need help on this math question​

Answers

Answer:

23

Step-by-step explanation:

EASY GIVING BRAINLIEST JUST GRAPH TO FIND ANSWER While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the first player's ball can be represented by the function g(x) = –2x2 + 13x + 7, where x represents the distance from the coach. The path of the second player's ball can be represented by the function h(x) = –x2 + 4x + 21.

Part A: Find the distances in which the two basketball paths will cross. Show all necessary calculations.

Answers

Answer:

  2 ft, 7 ft

Step-by-step explanation:

We are interested in the values of x such that g(x) = h(x). These will be solutions of the difference g(x) -h(x) = 0. Hence the x-intercepts of a graph of g(x) -h(x) will be solutions to the problem.

__

The graph shows the difference between the paths will be zero at distances of 2 feet and 7 feet.

Which one doesn’t belong? A B C D

Answers

Answer:

A

Step-by-step explanation:

because its not an angle

Answer:

i would say a

Step-by-step explanation:

because b c and d sort of have an angle to them but a is straight

A model of a house is 6 inch wide and 8 inches long. If the actual house is
20 yards long, how wide is the actual house?
OA) 2.4 yd
OB) 4.8 yd
OC) 15 yd
OD 26 yd

Answers

Answer:

its 15 <3

Step-by-step explanation:

i did the quiz.

What is the area of this figure?
3 mi
7 mi
4 mi
2 mi
5 mi
12 mi
3 mi
2 mi
Write your answer using decimals, if
necessary.
square miles

Answers

Answer:

38.5

Step-by-step explanation:

I would give explanation but it's kind of hard

The diagram shows the entrance to a tunnel.
The circular arc has a radius of 3m and center O.
AB is horizontal and angle AOB = 120°.

During a storm the tunnel filled with water, to the level shown by the shaded area in the diagram.
Calculate the shaded area.

Answers

Step-by-step explanation:

it filled up half the circle (up to the center point) - if we had a full circle. but a little bit is cut off (below AB).

what we see is that the shaded area is the sum of the area of the triangle AOB and 2 equally sized circle segment areas left and right of AOB.

since we are dealing with a half-circle, we have 180° in total. 120° are taken by AOB, so, that leaves us with 180-120 = 60° for both circle segments (so, one has an angle of 30°).

and 2×30° = 1×60°, so we can calculate the area of one 60° segment instead of two 30° segments.

AOB is an isoceles triangle (the legs are equally long, and therefore also the 2 side angles are equal).

the area of this triangle AOB is

1/2 × a × b × sin(C) = 1/2 × 3 × 3 × sin(120) =

= 3.897114317... m²

a circle segment area of 60° is 60/360 = 1/6 of the full circle area (as a full circle = 360°).

so, it's area is

pi×r² × 1/6 = pi×3²/6 = pi×3/2 = 4.71238898... m²

so, the total area of the shaded area is

3.897114317... m² + 4.71238898... m² =

= 8.609503297... m²

The area of the shaded portion of the circle is A = 8.61 m²

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the area of the shaded region be A

Let the radius of the circle be r = 3 m

The triangle ΔAOB is an isosceles triangle with side lengths = 3m

The area of the triangle ΔAOB = ( 1/2 ) x 3 x 3 x sin (120)

On simplifying the equation , we get

The area of the triangle ΔAOB = 3.897 m²

Now ,

There are 2 sectors , with sector angle = 30°

The area of the two sectors = 2 x ( 30/360 ) x π x 3²

On simplifying the equation , we get

The area of the two sectors = 2 x 2.357

The area of the two sectors = 4.714 m²

Now ,

The area of the shaded region of circle A = area of the two sectors + area of the triangle ΔAOB

Substituting the values in the equation , we get

The area of the shaded region A = 4.714 + 3.897

The area of the shaded region A = 8.611 m²

Therefore , the value of A is 8.611 m²

Hence , the area is 8.611 m²

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ2

Please help!!!
Mr. Johnson's class will study one sea animal for the next week. Which group should Mr. Johnson survey to find the type of sea animal his students should study?
A: His students
B: Teachers at his school
C: Parents of his students
D: Workers at a sea animal park

Answers

Answer:

A He should ask his students to know what they prefer

Step-by-step explanation:

Ten tubs of dried cranberries cost $40 how many runs can u buy for $20

Answers

Answer:

5 tubs

Step-by-step explanation:

This because if we divided 10 in half we get 5 and if we divide 40 in half we get 20

I hope this helps :)!!  

Can someone please help me?

Answers

Question 4:

   2x + 3y = 17    -- equation 1

   5x + 6y = 32  -- equation 2

    (equation 1) * 2

    4x + 6y = 34 -- equation 3

    (equation 2) - (equation 3)

     x = -2 -- equation 4

     plug (equation 4)'s value of x into (equation 1)

     2(-2) + 3y = 17

     3y - 4 = 17

      3y = 21

         y = 7

      Thus the answer is x = -2 and y = 7

Question 5:

  The vertex form of a quadrilateral looks like this:

      [tex]y = a(x-h)^2 + k[/tex]

a : coefficient of [tex]x^2\\[/tex](h,k): coordinate of the vertex.

    The x-coordinate of the vertex is equal to '-b/2a'. Where b is the

     coefficient of x, so:

          [tex]h = -\frac{b}{2a} =-\frac{-8}{2*1} =4[/tex]

     

    There is also another formula to find the y-value of the vertex

    coordinate, but the easier way to find it is to plug it into the original

    equation:

        [tex]k=(4)^2-8(4) + 12= 16 -32 + 12 = -16 + 12 = -4[/tex]

    Since we know now that h = 4 and k = -4 and that a = 1, lets plug it into

    the original equation.

       [tex]y = 1*(x-4)^2 - 4 =(x^2-4)-4[/tex]

     Thus the answer is [tex]y = (x-4)^2 -4[/tex]

Hope that helps!

       

 

Please guys help me , i need help with this math work im not doing so good un math

Answers

Answer: If you need help on both here are both answers.... Answer 1- f(x)=6.50x+48.00 because Let

x ----> the number of adult tickets

f(x) ----> amount of money collected

To find the amount collected multiply the number of adult tickets by the cost and multiply the number of student tickets  by the cost, and then sum the two quantities

The linear equation that represents this problem is

f(x)=6.50x+4.00(12)

f(x)=6.50x+48.00

and for Answer 2- Is 4

Make x the subject K(x-a)=t

Answers

Answer:

x = t+ka/k

Step-by-step explanation:

First you take letter k and place it after =sign which brings (x-a) = t/k because if you shift any number or letter after the = sign it has to be the opposite sign. for instance if it's positive, it will turn negative after the equal sign and if it is multiplication, it will turn division

Then you open the brackets which makes x-a = t/k

Now you shift "a" after the equal sign which leads to our answer, x= t +ka/k

Answer:

x = [tex]\frac{t+ka}{k}[/tex]

Step-by-step explanation:

k(x - a) = t ← distribute parenthesis on the left side by k )

kx - ka = t ( add ka to both sides )

kx = t + ka ( divide both sides by k )

x = [tex]\frac{t+ka}{k}[/tex]

Can anyone help me with this one Question on volume The diameter of a cylinder is 1 yd. The height is 12 yd. Find the volume of the cylinder.

Answers

Answer:

9.42 cube.yd

Step-by-step explanation:

Volume of cylinder= πr^2h

3.14 × 0.5 × 0.5 × 129.42 cube.yd

Find the solution to the equation:
f(x)=x^2-4x+3
Please show work!

Answers

Answer:

UM make a graph if you want so yea

Step-by-step explanation:

[tex]\\ \rm\rightarrowtail x^2-4x+3[/tex]

Use quadratic formula

[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm\sqrt{16-12}}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{4\pm 2}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=2\pm 1[/tex]

[tex]\\ \rm\rightarrowtail x=3,1[/tex]

Which best describes the range of the function f(x) = 2(3)x?

y > 0
y ≥ 0
y > 2
y ≥ 2

Answers

Answer:

y > 0

Step-by-step explanation:

if x = 0, y = 2

if x > 0, y > 0

if x < 0 , y > 0

The option that describes the range of the function f(x) = 2(3)x is A. y > 0.

How to illustrate the function?

It should be noted that a function whose value us constant raised to the power of the argument especially the function where the constant is e.

The range of the value of y depends on x. Here, the option that describes the range of the function f(x) = 2(3)x is y > 0.

In conclusion, the correct option is A.

Learn more about functions on:

brainly.com/question/25638609

#SPJ9

Other Questions
Find the missing numerator that will make the rational expressions equivalent.82x+7=?6(2x+7) A piece of writing should be appropriate to the writer's audience and.A. purpose.B. style.C. development. D.organization Explain why your brother/ sister is unable to come i think of a number multiply it by seven then add 8 to it and the results is 29 find the number Tina's teacher wrote 7/8 on the whiteboard. What percentage is equivalent to the fraction that Tina's teacher wrote on the whiteboard? How long does a koala joey stay in its moms pouch after birth?. What is the simplified expression of (4-5r+8s)(5r-9) In what year did John O'Sullivan coin the term Manifest Destiny Darren has borrowed $100$ clams from ethan at a $10\%$ simple daily interest. meanwhile, fergie has borrowed $150$ clams from gertie at a $5\%$ simple daily interest. in how many days will darren and fergie owe the same amounts, assuming that they will not make any repayments in that time period? How were American people influenced by television broadcasts of the Vietnam War?1. They joined the military in record numbers.2. They distrusted the truth of the newscasts.3. They became more concerned for people affected by the war.4. They increasingly supported the war.Please help 4.Choose the option that makes the sentence correct.Michelangelo, an artist of the Italian Renaissance, was born in Caprese in 1475 he becamean apprentice when he was a teenager.O The sentence is correct.O 1475, and heO 1475, but heO 1475, so he Pls help i will give 5 starts and brainliest question is down below 9:22 The height of the prism is the Blank between the bases. Benjamin wants to purchase a new bike, but he does not have enough money in his bank account to pay for one.Which of these is not an option for Benjamin?He can save money and write a check once there is enough money in his account.He can use his debit card to purchase the bike now.He can save money and pay cash once he has enough.He can use his credit card to purchase the bike now. Debate on topic Success brings happiness Speak In favour of this topic What is the next time: 8:45, 6:15, 3:45, _______?A) 11:15B) 12:15C) 1:15D) 2:15 Five widgets and three gadgets cost $109. 90. One widget and four gadgets cost $75. 70. How much does one gadget cost? Given the expression which operation would you perform first? Do basketball players hit a higher proportion of free throws when they're playing at home or when they're playing away this best is assessed by using Which concept is exemplified by being able to distinguish a slight change in light when a dimmer is used to adjust the brightness