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
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
There are 6 dogs and 12 cats in the backyard. Write the ratio of cats to total animals In 3 ways, in simplest form.
Step-by-step explanation:
12:18
12 to 18
12/18 = 2/3
Encierra todo los números que sean mayores a 18,031 2
no se me alludas a saber cual es
x² + 2xy ty = 144
(x+y)³= ?
Answer:
t=144x3+432x2y+432xy2+144y3−x2
2xy2
Step-by-step explanation:
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?
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:
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.
is it possible to have triangle with 3 cm 6 cm and 7 cm sides if yes then
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 :)
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.
Simplify the mathematical expressions and arrange them in order of their values from least to greatest. ↓ ↓ ↓ ↓
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
whats 3squared correct to 5 decimal places
Answer:
9.0000
Step-by-step explanation:
3 squared = 3*3 = 9
9 to 5 decimal places = 9.0000
pls mark as brainliest
You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?
Answer:
3
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
3 x 4 = 12
Any help is greatly appreciated but please show how to get 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
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.
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.
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?
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
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.
Answer:
Yes , it is independent
Step-by-step explanation:
independent
Can someone just please help me I beg you
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
HELP WILL GIVE BRAINLY!
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.
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.
Answer:
Equations for each salesman:
A. p(s) = 65sB. p(s) = 40s + 300C. p(s) = 900When 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) = 900The 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)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
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.
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
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
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
Answer:
plus 20 or positive
Step-by-step explanation:
-60+80= 20
positive
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.
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.
{y=5x-7
y=-2x+7 Solve the system by graphing.
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
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.
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:
Select the equation of the line of symmetry shown at the graph.
Answer choices:
X=3
Y=3
X=4
X=2
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?
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
Solve the equation w=cx-h for x.
Answer:
That's your answer. Let me know if you need an explanation.
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)
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:
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
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
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
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
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 ?
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.