Mathematics High School

A ball is dropped from a height of 8 feet. If every time it bounces, it bounces 60% of its previous height, what is the total distance traveled by the ball?

Answers

Answer 1

Answer:

20feet

Step-by-step explanation:

Initial height of the ball = 8feet

If it bounces 60% of its previous height, its new height will be;

60% of 8

= 60/100 * 8

= 480/100

= 4.8 ft

If it bounces 60% of its current distance, new height will be expressed as;

60% of 4.8

= 0.6 * 4.8

= 2.88

The height of the ball will keep reducing and form a geometric progression of the form 8, 4.8, 2.88...

In order to get the total distance traveled by the ball, we need to calculate the sum to infinity of the sequence;

S∞ = a/1-r where;

a is the first term = 8

r is the common ratio

[tex]r = \frac{4.8}{8} = \frac{2.88}{4.8}\\r = 0.6[/tex]

Substitute into the formula;

S∞ = a/1-r

S∞ = 8/1-0.6

S∞ = 8/0.4

S∞ = 20feet

Hence the total distance traveled by the ball is 20feet

Related Questions

Find −523−16. Write your answer as a mixed number in simplest form.

Answers

Answer:

(-523) - 16 is -539

Step-by-step explanation:

mathmathmathmathmsthmatj

Mark the additive inverse of each integer!

Answers

Answer:

12, -12

21, -21

-11, 11

17, -17

-21, 21

additive inverse is when the sign changes either to a negative or positive.

therefore

12, -12
21,-21
-11 , 11
17, -17
-21, 21

matt is playing a game. he gains 7 points, loses 10 points, gains 2 points, and then loses 8 points. what is the final score?

Answers

Answer:

-9 points

Step-by-step explanation:

He starts at 0 but gains 7 [7] then loses 10 [-3] gains 2 [-1] and loses 8 [-9]

negative 9 points i just took it and it’s correct

Write the equation that represents a 15% increase of $120.

Answers

Answer:

$138

Step-by-step explanation:

if 100 is 15 then you add 1.15 or 1% of 15

Can someone please help me with this problem ? I would love y’all forever !

Answers

-1= 1
0= 3
1= 5
2= 7
3= 9

Tommy bought stamps at the post office. Some of the stamps had a snowflake design, some had a truck design, and some had a rose design. Tommy bought 14 snowflake stamps. He bought 5 more truck stamps than snowflake stamps, and 5 fewer rose stamps than truck stamps. How many stamps did Tommy buy in all? Show your work, how you came up with the answer.

Answers

Answer:

Step-by-step explanation:

s = Number of stamps with snowflake design = 14

Number of stamps with truck design is 5 more than snowflake design

[tex]t=s+5\\\Rightarrow t=14+5\\\Rightarrow t=19\ \text{stamps}[/tex]

Number of stamps with rose design is 5 fewer than truck stamps

[tex]r=t-5\\\Rightarrow r=19-5\\\Rightarrow t=14\ \text{stamps}[/tex]

Total number of stamps

[tex]s+t+r=14+19+14\\ =47[/tex]

So total number of stamps Tommy bought is 47.

Calcula el numero de vueltas ,por minuto que, da la polea pequeña mienta la grande da 40 vueltas . Sabiendo que cada polea gira de manera que el radio y el numero de vueltas son inversamente proporcionales

Answers

Esta pregunta esta incompleta

Pregunta completa

Calcula el número de vueltas por minuto que hace la polea pequeña mientras que la grande hace 40 vueltas. Sabiendo que cada polea gira de manera que el radio y el número de vueltas son inversamente proporcionales.

El radio de la polea pequeña = 3 cm.

El radio de la polea grande = 9 cm

Answer:

120 vueltas por minuto

Step-by-step explanation:

El radio y el número de vueltas son inversamente proporcionales.

Por lo tanto

R = Radio

T = El número de vueltas por minuto

R ∝ 1 / T

R = k / T

Donde k es constante de proporcionalidad

Polea grande

R = 9 cm

T = 40 vueltas

9 = k / 40

k = 9 × 40

k = 360

Debemos encontrar el número de vueltas para la polea pequeña, por lo tanto,

R = k / T

k = 360, R = 3 cm

3 = 360 / T

3 × T = 360

T = 360/3

T = 120 vueltas

El número de vueltas de la polea pequeña = 120 vueltas por minuto

What is the slope of the line through (-7,-8)(−7,−8)

Answers

Answer:

the slope would be 0

Step-by-step explanation:

this is because those are the same 2 points

Estimate 7 x 522 ns

Answers

3.866 microseconds? 7 x 522 nano seconds = 3.86600 ms

3.86400 hope that helped

how do you write 6.4 × 10^1 in standard form?

Answers

Answer:

Step-by-step explanation:

6.4 * 10^1

is the same as:

6.4 * 10

= 64

Given: m∠PRS = 2x + 12
m∠SRT = 6x + 8
∠PRS and ∠SRT are a linear pair

Prove: m∠PRS = 52

-make sure to include statements and reasonings like it shows in the screenshot

Answers

Answer:

See Below.

Step-by-step explanation:

1) Given:

[tex]\angle PRS\text{ and } \angle SRT \text{ are a linear pair.}[/tex]

2) Definition of Linear Pair:

[tex]m\angle PRS+m\angle SRT=180[/tex]

3) Given:

[tex]m\angle PRS=2x+12[/tex]

4) Given:

[tex]\displaystyle m\angle SRT=6x+8[/tex]

5) Substitution Property:

[tex](2x+12)+(6x+8)=180[/tex]

6) Combine Like Terms:

[tex]8x+20=180[/tex]

7) Subtraction Property of Equality (subtract 20 from both sides):

[tex]8x=160[/tex]

8) Division Properety of Equality (divide both sides by 8):

[tex]x=20[/tex]

9) Given (this step is optional. You don’t have to include this):

[tex]m\angle PRS=2x+12[/tex]

10) Substitution:

[tex]\displaystyle m\angle PRS=2(20)+12[/tex]

11) Multiplication:

[tex]m\angle PRS=40+12[/tex]

12) Addition:

[tex]m\angle PRS=52[/tex]

Answer:

sorry i dont realy understand that

Step-by-step explanation:

A line has a slope of -3/4 and passes through the point (-5, 4). Which is the equation of the line?

Answers

Answer: A

Step-by-step explanation:

y-4 = -3/4(x+5)

y = -3/4x+1/4

Answer: the equation is y= 3/4 times + 1/4 is your answer

The ratio of blueberries to strawberries in a fruit salad is 4:3. If there are 45 strawberries in a salad, how many blueberries are there.. Blueberries 4 Strawberries 3

Answers

Answer:

60 blueberries

Step-by-step explanation:

Given the ratio of blueberries to strawberries in a fruit salad to be 4:3. The total ratio = 4+3 = 7

If there are 45 strawberries in the salad then we can first calculate the total mixture of both as shown;

amount of strawberries = 3/7 * x = 45

x is the total amount of mixture

from the expression;

3x/7 = 45

cross multiply

3x = 7*45

3x = 315

x = 315/3

x = 105

The amount of blueberries present = 105 - 45 = 60

Hence the amount of blueberries present is 60 blueberries

Which of the following expressions is equal to (2g)5?

10 · g · g · g · g · g

2g · 2g · 2g · 2g · 2g

2 · g · g · g · g · g

10g

Answers

Answer:

The answer is choice b.

Step-by-step explanation:

I took a quiz with the exact same question on it. hopefully I'm not too late ! <3

The expression is;

⇒ 2g * 2g * 2g * 2g * 2g

Option 2 is true.

Given that;

The expression is;

⇒ (2g)⁵

We have to find the equivalent expression.

What is Powers of a number?

The powers of a number is express how many time the numbers are repeated.

The expression is;

⇒ (2g)⁵

Since, The power of 2g is five.

Hence, It can be repeat five times as,

(2g)⁵ = 2g * 2g * 2g * 2g * 2g

Hence, The equivalent expression is;

⇒ 2g * 2g * 2g * 2g * 2g

Option 2 is true.

Learn more about Powers of a number visit:

https://brainly.com/question/28400450

#SPJ2

What is the simple interest that is missing from the table?

Answers

Answer:

Calculate simple interest on the principal only, I = Prt. Simple interest does not include the effect of compounding.

What is the square root of 40000 step by step
Thx for everything that answers

Answers

The answers 200 of u have an iPhone u can ask siri what the square root of whatever number is and it will tell u the correct answer

pls help ill give brainlist

Answers

Answer:

Step-by-step explanation:

The rise is 8 and run is 6

Answer:

The answer is J) y=-4/3x+8

IM IN NEED OF HELP .!!Antonio is at Best Buy and all TV's are 30% off. He finds a 75" OLED that he
wants, the price is $1500. What is the discount amount and how much did he
pay for the TV? Write and equation

Answers

Answer:

$450. The amount Antonio bought the tv for was $450.

Step-by-step explanation:

If all the tv's are 30%, multiple 30 by the price of the tv he wants, giving you 45000. Then, divide by 100 because a percent is out of a hundred, giving you $450

Formula:

(30x1500)/100

Please Help!!!!!!!!!!
Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is 2/5?
line n, with slope -5/2
line m, with slope 5/2
line p, with slope 2/5

Answers

Answer:

Step-by-step explanation:

n is perpendicular. - 1/(2/5) = - 5/2. n is the negative reciprocal of the given line.

m is neither.

p is parallel to the given line. For example y = 2/5x

and y = 2/5 x + 9 are parallel to each other.

Solve 2|x + 2| – 3 ≥ 0

Answers

Answer:

2x+1

Step-by-step explanation:

Answer

[tex]x[/tex] [tex]\geq[/tex] [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

I'm learning this to but I hope this helps :)

What are the x-intercepts of the function y = x2 - X - 6?

Answers

Answer:(3,0) , (-2,0)

Step-by-step explanation:To find the x-intercept, substitute in 0 for y and solve for x

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[tex]f(x) = {x}^{2} - x - 6 [/tex]

[tex]f(x) = (x - 3)(x + 2)[/tex]

[tex]0 = (x - 3)(x + 2)[/tex]

_________________________________

Hint :

[tex]a \times b = 0[/tex]

[tex]a = 0 \: \: \: or \: \: \: b = 0[/tex]

_________________________________

Thus ;

[tex] x - 3 = 0[/tex]

Add sides 3

[tex]x - 3 + 3 = 0 + 3[/tex]

[tex]x = 3[/tex]

[tex]x + 2 = 0[/tex]

Subtract sides 2

[tex]x + 2 - 2 = 0 - 2[/tex]

[tex]x = - 2[/tex]

Thus the x-intercepts are (( - 2 )) and (( 3 )) .

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A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was $125,000. What is the Population?

Answers

Answer:

The population is the total number of the universities graduates i.e [tex]N = 300,000[/tex]

Step-by-step explanation:

From the question we are told that

The number of students that are consider is n = 10,000

The total number of graduates is [tex]N = 300,000[/tex]

The mean is [tex]\= x = \$125 , 000[/tex]

Here the population is The total number of graduates with value [tex]N = 300,000[/tex], this is because a population is the pool from with a sample is drawn and in this case the pool is [tex]N = 300,000[/tex] while the sample with is drawn is n = 10,000

私はこれをGoogle翻訳を使って書き留めています。地面からうんちをすくい取ります。今やれ！

Answers

Answer:

yessssss

Step-by-step explanation:

thanks ;p;p;

The area of a circle, in terms of π, is 196π m2.
Find the value of the radius.

Answers

Step-by-step explanation:

if area of circle = pi times radius^2,

area of circle divided by pi = radius^2

so, square root (area of circle divided by 2) = radius.

so, 196pi = m2

approx 616

616=m2

sqrt 616 =m

approx value of radius is 25 or 24.8

pls mark this as brainliestttt

HELP PLEASE ILL GIVE U 26 POINTS

Christo graphs AB with endpoints A( -3, -2 ) and B ( -1, -2 ) what are the endpoints of the image after a reflection of AB across the x axis?

1. (-3,2) and (-1,2)

2.(-3.-2) and (-1,-2)

3. (1,-2) and (3,-2)

4. (2,3) and (2,1)

5. none of the above

Answers

Answer:

1. (-3,2) and (-1,2)

Step-by-step explanation:

Reflection over x axis results in change y-coordinates to opposite sign and x-coordinates remain as is

So the coordinates become:

A(-3, -2) → A'(-3, 2)B(-1, -2) → B'(-1, 2)

Correct option is the first one

2(t+1)=10 what does t equal

Answers

Answer:

t = 4

Step-by-step explanation:

1. 2*t = 2t

2. 2*1 = 2

3. 2t+2 = 10

4. 10-2 = 8

5. 2t = 8

6. 8/2 = 4

7. t = 4

Answer:

t = 4

Step-by-step explanation:

2(t + 1) = 10

2t + 2 = 10

2t = 10 - 2

2t = 8

t = 8 ÷ 2

t = 4

-TheUnknownScientist

What is the answer for X (geometry)

Answers

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In the lower triangle, one of the angles of which is 45 degrees, we know:

In the triangle, the side facing the angle 45° is √2 / 2 times the hypothenuse.

Thus ;

[tex]10 = hypothenuse \times \frac{ \sqrt{2} }{2} \\ [/tex]

[tex]hypothenuse \times \frac{ \sqrt{2} }{2} = 10 \\ [/tex]

Multiply sides by 2

[tex]hypothenuse \times \sqrt{2} = 2 \times 10[/tex]

Divide sides by √2

[tex]hypothenuse = \frac{2 \times 10}{ \sqrt{2} } \\ [/tex]

[tex]hypothenuse = \frac{ \sqrt{2} \times \sqrt{2} \times 10 }{ \sqrt{2} } \\ [/tex]

[tex]hypothenuse = 10 \sqrt{2} [/tex]

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The common side of the triangles is hypothenuse for both.

[tex]hypothenuse \times \cos(60) = x[/tex]

[tex]10 \sqrt{2} \times \frac{1}{2} = x \\ [/tex]

[tex]x = \frac{2 \times 5 \sqrt{2} }{2} \\ [/tex]

[tex]x = 5 \sqrt{2} [/tex]

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The correct answer is the Third Option .

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The three-digit number "ab5" is divisible by 3. How many different three-digit numbers can "ab5" represent?

Answers

Answer:

Step-by-step explanation:

I can't prove this, but I can tell you the answer.

30.

a = 100 s digit

b = 10 s digit

5 is always the units digit.

I'm pretty sure that 30 is the correct answer.

What an interesting question. If I find out how it is done, I'll post it in the comments.

I can say this much.

a + b + 5 must be divisible by 3.

a = 1 b = 9 + 5

a = 1 b = 6 + 5

a = 1 b = 3 + 5

a = 1 b = 0 + 5

===============

Three more are obtained by interchanging the 100s and 10s digit except for b = 0

a = 9 b=1 + 5

a = 6 b =1 + 5

a = 3 b= 1 + 5

==================

a = 2 b = 2 + 5

a = 2 b = 5 + 5

a = 2 b = 8 + 5

only 2 more are obtained by interchanging the 10s and 100s digit

=============

a = 3 b = 4 +5

a = 3 b = 7 +5

You can't go any further. You get 2 more by interchanging the b and a digits.

=============

I hope you see what I've done here. I don't think this is an exact proof, but it is an exhaustive search.

I need help I dont wear to start

Answers

Answer:

Yes! it is there are straight across from each other and will never touch Hope I helped!

What is the solution to the equation?
Pls help ASAP

Answers

Answer: 12 1/2

Step-by-step explanation:

its easy bruh what grade you in this is 6th grade stuff

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