4 When a ball bounces, the heights of consecutive bounces form

a geometric sequence. The height of the first bounce is

121 centimeters and the height of the third bounce is

64 centimeters. To the nearest centimeter, what is the height of the

fifth bounce?

Answers

Answer 1

Answer:

34 cm

Step-by-step explanation:

The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.

Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm

Then, T₃/T₁ = ar²/a = r²

r² = T₃/T₁

r² = 64 cm/121 cm

r = √64/121

r = 8/11

So, the height of our fifth bounce T₅ = ar⁵⁻¹

= ar⁴

= 121 cm × (8/11)⁴

= 121 × 4096/14641

= 4096/121 cm

= 33.9 cm

≅ 34 cm to the nearest cm

Answer 2

Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

The height of the first bounce is of 121 cm, hence [tex]a_1 = 121[/tex].The height of the third bounce is of 64 cm, hence [tex]a_3 = 64[/tex], and this is used to find r.

[tex]a_n = a_1r^{n-1}[/tex]

[tex]64 = 121r^{2}[/tex]

[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]

[tex]r = \frac{8}{11}[/tex]

Hence:

[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]

The height of the fifth bounce is of [tex]a_5[/tex], hence:

[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]

The height of the fifth bounce is of 33.85 cm.

You can learn more about geometric sequences at https://brainly.com/question/11847927


Related Questions

Two rectangles we're used to form the following figure. Which measurement is closest to the area of the shaded region of this figure in square inches

Answers

Answer:

44 cm

Step-by-step explanation:

You have to find the area of the bigger square and find the area of the smaller one. (Width x Height). Then subtract the smaller rectangle from the bigher one

Daniel's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 1 adult ticket and 3 child tickets for a total of $39. The school took in $87 on the
second day by selling 5 adult tickets and 3 child tickets. Find the price of an adult ticket and the
price of a child ticket.

Answers

Answer:

Your answer.

Adult ticket = 12

Child ticket = 9

Thank you. And give my answer as Brainlist answer. Follow me for more

Step-by-step explanation:

9. Which of these was an example of US industrial mobilization for war? (5.1.B) A. Increased factory production of tanks and planes B. Increased farm production of wheat C. Rationing of products, like copper and rubber D. Increased production of automobiles​

Answers

Answer:

A

Step-by-step explanation:

Tanks are the Backbone of the Military, they are needed to destroy the Axis Powers during WW2, they also used Captured Enemy Tanks for studying and Produce New Tanks to Counter them.

Compare the number of friends at the beginning of a month and at the end of that month if it decreased by 60 and increased by 80

Answers

Answer:

plus 20 or positive

Step-by-step explanation:

-60+80= 20

positive

Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.

Drag and drop the choices into the boxes to correctly complete the table.

corresponding alternate interior alternate exterior none of these

Answers

Answer:

From left to right, top to bottom: 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are cooresponding angles, 1 and 2 are alterante interior angles.

Answer:

We will go in order.

first-None of them

second-Alternate exterior

third-None of them

forth-Corresponding

and Fifth-Alternate Interior

Step-by-step explanation:

just took test

is it possible to have triangle with 3 cm 6 cm and 7 cm sides if yes then​

Answers

Answer:

No

Step-by-step explanation:

Step-by-step explanation:

Yes it is possible to have a triangle with 3 cm, 6 cm and 7 cm sides because in order to form a triangle the length of two sides of a triangle should exceed the third side as shown below :

3 + 6 > 7

9 > 7( True) ✔

6 + 7 > 3

13 > 3 ( True) ✔

7 + 3 > 6

10 > 6 ( True) ✔

Hope it will help :)

There are 6 dogs and 12 cats in the backyard. Write the ratio of cats to total animals In 3 ways, in simplest form.

Answers

Step-by-step explanation:

12:18

12 to 18

12/18 = 2/3

There are 56 female performers in a dance recital. The ratio of men to women is 3:8. How many men are in the dance recital?

Answers

There are 21 men at the dance recital

Answer:

56%8=7     so then u do this  (3 is the ratio of men) 3X7=21 and thats how u do it :D

Step-by-step explanation:

uhh i don't have one lol

What is the image of M(11,-4) using the translation (x,y) →x-17, y + 2?
A. M'(-6,-2)
B. M'(6,2)
C. M'(-11,4)
D. M'(-4,11)​

Answers

Answer:

https://cdn.kutasoftware.com/Worksheets/PreAlg/Reflections%20of%20Shapes.pdf

Step-by-step explanation:

pls search this

Answer:

A. M'(-6,-2)

Step-by-step explanation:

Which problem matches the given inequality? d > 12.75 Chelsea spent $12.75. Chelsea spent about $12.75. Chelsea spent less than $12.75. Chelsea spent more than $12.75.

Answers

Answer:

Chelsea spent more than $12.75

Step-by-step explanation:

To solve this problem we should understand the meaning of signs first.

sign (<) → less than

sign (>) → more than

sign (=) → equal to

sign (≤) → Not more than

sign (≥) → At least

If the statement is,

"Chelsea spent more than $12.75"

d > 12.75

Therefore, Chelsea spent more than $12.75 is the correct statement.

Answer:

Chelsea spent more than $12.75.

Step-by-step explanation:

bc ik.

x² + 2xy ty = 144
(x+y)³= ?

Answers

Answer:

t=144x3+432x2y+432xy2+144y3−x2

2xy2

Step-by-step explanation:

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.

Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.


100 POINTS
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.

Salesman C does not earn any commission. His weekly salary is $900.
The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.

Answers

Answer:

Equations for each salesman:

A. p(s) = 65sB. p(s) = 40s + 300C. p(s) = 900

When s = 0, s= 1, s = 10 each of the gets paid:

A. p(0) = 0, p(1) = 65, p(10) = 650B. p(0) = 300, p(1) = 340, p(10) = 700C. p(0) = p(1) = p(10) = 900

The above numbers as ordered pairs:

                 A                B               C          s = 0  |    (0, 0)       | (0, 300)    | (0, 900)s = 1   |    (1, 65)      | (1, 340)     | (1, 900)s = 10 |    (10, 650) | (10, 700)   | (10, 900)

Select the equation of the line of symmetry shown at the graph.
Answer choices:
X=3
Y=3
X=4
X=2​

Answers

the answer is x=3
hope this helps !

Any help is greatly appreciated but please show how to get answers

Answers

We first calculate the front and back which are 2 congruent(equal) triangles. The 2 areas together is...

9*6/2*2=54

Now we want to calculate the 2 rectangles at the top right and top left of the shape they are also congruent(equal). The 2 areas together is...

7*5*2=70

The last part is the rectangle on the bottom with area...

9*5=45

Now we just need to add them all together...

54+70+45=124+45=169

I hope this helped you, if you have any questions about this solution just ask me in the comments :)

Answer:

223cm

Step-by-step explanation:

First you want to figure out how many faces the 3D shape has.

This has 5 faces.

Then you find the area of each face.

The front face has an area of 54cm because the length is 6cm and the width is 9cm.

Area = Length x Width

The back face will always have the same area as the front.

54cm + 54cm = 108cm (Front and Back Face)

Now the right side and left side.

The width of the side is 5cm and length is 7cm.

7cm • 5cm = 35cm

Just like the front and back, the right and left side will have the same area.

35cm + 35cm = 70cm

Now the last part.

There is no top face since this is a 3D triangle and not a square and rectangle etc.

So, you don't add it two times like the others.

The bottom's width is 5cm and the length is 9cm

5cm • 9cm = 45cm

Now you add all of it up together to find the surface area.

108cm + 70cm + 45cm = 223cm

Hope this helps dude

Susan Marciano invested part of her $27,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $1,590.​

Answers

54,000 it you add up all the profits

Can someone just please help me I beg you

Answers

Answer:

8 by 6986 = quotient  873 remainder 2

M= 800x8 =6400

N= 560/8=70

P= 26/8 =3

Q=3x8=24

R=26-24=2

I need brainliest so I can rank up

Step-by-step explanation:

yes good haware you good

Solve the equation w=cx-h for x.

Answers

Answer:

That's your answer. Let me know if you need an explanation.

w=cx-h
add h to both sides
w+h = cx
divide both sides by c
(w+h)/c = x

answer:
x = (w+h)/c

PLS PLS help!
Type an equation of a parabola that is moved down 2 units, stretched vertically by a factor of 3, and moved left 5 units.

Answers

9514 1404 393

Answer:

  y = 3x^2 +30x +69

Step-by-step explanation:

Transformations work this way:

  g(x) = k·f(x) . . . . vertical stretch by a factor of k

  g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)

__

So, the translation down 2 units will make the function be ...

  f(x) = x^2  ⇒  f1(x) = f(x) -2 = x^2 -2

The vertical stretch by a factor of 3 will make the function be ...

  f1(x) = x^2 -2  ⇒  3·f1(x) = f2(x) = 3(x^2 -2)

The horizontal translation left 5 units will make the function be ...

  f2(x) = 3(x^2 -2)  ⇒  f2(x +5) = f3(x) = 3((x +5)^2 -2)

The transformed function equation can be written ...

  y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)

  y = 3x^2 +30x +69

__

The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came before the vertical scaling.

Simplify the mathematical expressions and arrange them in order of their values from least to greatest. ↓ ↓ ↓ ↓

Answers

Answer and Step-by-step explanation:

To simplify algebraic expressions, follow the basic rules:

1. Remove brackets or parentheses by multiplying factors;

2. Use exponent rule to remove grouping, if terms have exponents;

3. Add or subtract like terms;

4. Combine constants;

In the expressions above, there only constants and scientific notations, i.e., exponents elevated on a base 10. So, to simplify, we multiply the numbers and add the exponents:

(4.27 x 10⁸)(9.2 x 10⁻⁵) = 39.28 x 10³

(6.96 x 10⁵)(8.43 x 10⁻²) = 58.67 x 10³

[tex]\frac{(7.25.10^{5})(9.36.10^{-7})}{(7.95.10^{-2})(4.13.10^{-3})}=[/tex] 2.07 x 10³

[tex]\frac{(8.32.10^{4})(9.67.10^{1})}{(7.56.10^{11})(5.79.10^{-8})}[/tex] = 1.84 x 10²

[tex]\frac{(1.89.10^{4})(5.92.10^{3})}{(2.74.10^{-2})(4.67.10^{2})}=[/tex] 0.875 x 10⁷

All the exponents are positive, which means, comma "moves" to the right.

The numbers arranged from least to greatest will be

1.84 x 10² < 2.07 x 10³ < 39.28 x 10³ < 58.67 x 10³ < 0.875 x 10⁷

Help Plz
You are playing a game that requires flipping a coin twice. Use a sample space to determine whether flipping heads and then tails are independent events.

Answers

Answer:

Yes , it is independent

Step-by-step explanation:

independent



whats 3squared correct to 5 decimal places​

Answers

Answer:

9.0000

Step-by-step explanation:

3 squared = 3*3 = 9

9 to 5 decimal places = 9.0000

pls mark as brainliest

I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.

Answers

Total student are 20

HELP WILL GIVE BRAINLY!

Answers

Answer:

The second one

Step-by-step explanation:

on the f axis you can see that f is greater than or equal to 1 and less than or equal to 5.

Encierra todo los números que sean mayores a 18,031 2 ​

Answers

no se me alludas a saber cual es

You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?

Answers

Answer:

3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3 x 4 = 12

The length of a rectangle is three times its width.
If the width is represented by x, what is the
perimeter of the rectangle, in terms of x?

Answers

Answer:

perimeter:- 8x

Step-by-step explanation:

since,

length= 3(width)

length= 3x

and, perimeter= 2(l + b)

= 2(3x + x)

= 2(4x)

perimeter = 8x

Researchers in plant growth are investigating the proportions of seedlings that sprout under two environmental settings in a lab experiment. Let pˆC represent the sample proportion of seedlings that sprout in garden C, and let pˆH represent the sample proportion of seedlings that sprout in garden H. For random samples of 100 garden C seedlings and 100 garden H seedlings, the sampling distribution of the difference between sample proportions pˆC−pˆH has σpˆC−pˆH≈0.051. Which of the following is the best interpretation of σPˆC−PˆH≈0.051 ?

Answers

Answer:

E

Step-by-step explanation:

For all random samples of 100 garden C seedlings and 100 garden H seedlings, the average distance of all possible differences between sample proportions  pˆC−pˆH  from the mean of the sampling distribution is approximately 0.051.

The means and mean absolute deviations of the amount of rain that fell each day in a local city, last week and this week, are shown below. Means and Mean Absolute Deviations of Rainfall Last Week and This Week Last Week This Week Mean 3.5 in. 2.7 in. Mean Absolute Deviation 1.2 in. 0.5 in. Which expression compares the difference of the two means to this week's mean absolute deviation?

Answers

Answer:

0.8 / 0.5

Step-by-step explanation:

Given :

Deviations of Rainfall :

______Last Week ____ This Week

Mean___ 3.5 in. ________2.7 in

MAD ___ 1.2 in _________ 0.5 in

Mean difference = 3.5 in - 2.7 in = 0.8 in

This week's mean absolute deviation = 0.5 in

Mean difference / this week's mean absolute deviation

= 0.8 / 0.5

Answer:

0.8 / 0.5

Step-by-step explanation:

Perform the indicated row operation:

2 −1 −4 7
−1 2 1 −1
0 10 8 2
equation
2 −1 −4 7

0 10 8 2

Answers

Answer:

-1,2,1,-1

3,4,5,5

The other answer is for the question after this one on the edge assignment

Answer:

1ST ANSWER

0 10 8 2

2ND ANSWER

0 3 -2 5

Got it right on edg

{y=5x-7
y=-2x+7 Solve the system by graphing.

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer: Put both equation into desmos and the crossing point will be (2,3) and the graph will be there.

Step-by-step explanation: 5x-7 = -2x+7                   y = 5(2) - 7

                                             5x = -2x + 7 + 7.              y = 3

                                             5x = -2x + 14

                                             5x + 2x = 14

                                             7x = 14

                                             x = 2

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