The height h(n) of a bouncing ball is an exponential function of the number n of bounces.

One ball is dropped and on the first bounce reaches a height of 6 feet. On the second

bounce it reaches a height of 4 feet.

PLEASE HURRY

Answers

Answer 1

Answer:

The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].

Step-by-step explanation:

According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:

[tex]h = h_{o}\cdot r^{n-1}[/tex], [tex]n \in \mathbb{N}[/tex], [tex]0 < r < 1[/tex] (1)

Where:

[tex]h_{o}[/tex] - Height reached by the ball on the first bounce, measured in feet.

[tex]r[/tex] - Decrease rate, no unit.

[tex]n[/tex] - Number of bounces, no unit.

[tex]h[/tex] - Height reached by the ball on the n-th bounce, measured in feet.

The decrease rate is the ratio between heights of two consecutive bounces, that is:

[tex]r = \frac{h_{1}}{h_{o}}[/tex] (2)

Where [tex]h_{1}[/tex] is the height reached by the ball on the second bounce, measured in feet.

If we know that [tex]h_{o} = 6\,ft[/tex] and [tex]h_{1} = 4\,ft[/tex], then the expression for the height of the bouncing ball is:

[tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex]

The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].

Answer 2

Answer:

9 (2/3) ² but insted of 2 its n

Step-by-step explanation:


Related Questions

!! PLEASE HELP, TIMED!!Multiple choice, BRAINLIEST for correct answer

Answers

Answer:

I dont see the question

Step-by-step explanation:

soryy

Sorry there’s no question or picture attached. ://

Help ASAP being timed please.

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Answer:

Its the third one

Step-by-step explanation:

Plot all of the points onto the graph, and draw a line through all of the points. It most closely resembles the third one

the Elephants at the zoo eat 2 3/4 buckets of bananas each day. The zookeeper bought 5 1/2 buckets of bananas. For how many days will.the bananas last ?

Answers

Answer:

1/8

Step-by-step explanation:

2 3/4= 11/4

5 1/2= 11/2

11/2 divided by 11/4 = 1/8

3.) The ratio of dogs to cats at the animal shelter is 4:1. If there are a total of 85 dogs and cats
at the shelter, how many dogs are at the shelter?

Answers

Answer:

Step-by-step explanation:

The ratio of dogs to cats is

quantities relative to each other. There are two cats and one dog. This means there are twice as many cats as dogs, or half as many dogs as cats.

...

Equivalence.

cats : dogs

8 : 4

Answer:

d

Step-by-step explanation:

yes

A container has 360 gallons ; daniel took 1/3 of water to give to the animals in the ranch; how many gallons of water are left? I NEED IT TO BE EXPLAINED AND I WILL MAKE YOU THE BRAINLIEST

Answers

Answer: 240 gallons

Step-by-step explanation:

From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:

= 1/3 × 360

= 120 gallons

Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:

= 360 - 120

= 240 gallons

Forty families gathered for a fund-raising event. Suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $120 and $24, respectively. The organizers would call this event a success if the total contributions exceed $5,200. What is the probability that this fund-raising event is a success?

Answers

Answer:

3.51% probability that this fund-raising event is a success

Step-by-step explanation:

In a set with mean  and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

3.51% possibility (20 characters aaa)

2) Egbert's twin sister Egberta runs her own small business making pies. She delivers all
her own orders. For each order, she charges a flat delivery fee, and a cost per pie. Client 1
makes orders 2 pies and it costs $62. This is expressed as the ordered pair (2, 62).
a) Client 2 orders 11 pies for a total cost of $287. Express this as an ordered pair.
I
b) Find the slope between these 2 points.
c) Write a linear equation to represent this scenario where x is the number of pies
and y is the total charges
d) What is the cost per pie?
What is the delivery fee?
e) Use the equation to find out how much she would charge for 8 pies
f) How many pies would result in a total charge of $262 ?
Focus

Answers

Answer:

Step-by-step explanation:

a. (11,287)

b. 25

c. y = 25x + 12 (not sure if this is correct)

d. $25 and $12

e. $212

f. 10 pies

Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).

Answers

Answer:

[tex]\displaystyle r = \sqrt{10}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)

Geometry

Definition of a radius - the center of a circle to any point to the circumference

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Center (2, -3) → x₁ = 2, y₁ = -3

Circumference point (-1, -2) → x₂ = -1, y₂ = -2

In this case, the distance d from the center to the circumference point would be the radius r of the circle.

Step 2: Find Radius r

[Distance Formula] Define equation [Radius]:                                               [tex]\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute in points [Radius]:                                                                         [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}[/tex][Radius] [√Radical] (Parenthesis) Simplify:                                                     [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}[/tex][Radius] [√Radical] (Parenthesis) Subtract/Add:                                           [tex]\displaystyle r = \sqrt{(-3)^2+(1)^2}[/tex][Radius] [√Radical] Evaluate exponents:                                                       [tex]\displaystyle r = \sqrt{9+1}[/tex][Radius] [√Radical] Add:                                                                                 [tex]\displaystyle r = \sqrt{10}[/tex]

SOMEONE PLZZ HELP, I HAVE A TEST AND DONT KNOW HOW TO DO THIS!!

Answers

I believe it is C.
Good luck!

At a deli, Joe bought 2.2 pounds of coleslaw for $7.15. What was the unit price?

Answers

Answer:

$3.25 for 1 pound of coleslaw

Step-by-step explanation:

i think,.

Determine the value of a.

A) 6
B) 70
C) 7
D) 10


Answers

Answer:

C

Step-by-step explanation:

SU/UR = ST/QT

10/7=10/x

70=10x

7=x

A=7

Have a nice day :)

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 10 more than the second.

Answers

Answer:

first angle be 30°

second angle be 70°

third angle be 80°

Step-by-step explanation:

first angle be x

second angle be y

third angle be z

x+y+z=180

given, y+z = 5x; z=5x-y

also, z=y+10

5x-y = y+10

5x= 10+y+y = 10+2y

x= (10+2y)/5

x+y+z=180

(10+2y)/5 + y + y+10 = 180

(10+2y)/5 = 180 -2y -10

(10+2y)/5 = 170-2y

multiply both sides by 5

10+2y = 5(170-2y)

10+2y= 850-10y

2y+10y = 850-10

12y= 840

y= 840/12 = 70°

z=y+10 =70+10= 80°

5x= (10+2y) = 10+2(70) = 10+140= 150

x = 150/5 = 30°

Tom makes jewelry boxes containing drawers of equal size. The number of drawers in three different jewelry boxes and the corresponding total volumes of the drawers are shown in the table below. Write an equation for the relationship between the number of drawers in the jewelry box, X, and the total volume of the drawers in the jewelry box, V. Use your equation to determine the number of drawers in a jewelry box with a total volume of 12 cubic inches. Show your work.

Answers

Answer:

Step-by-step explanation:

what is 16 to the power of a half

Answers

Answer:

4

Step-by-step explanation:

SHOW work
5.3 divided by 0.25 = ?

Answers

Answer:

5.3 divided by 0.25 is 21.2

Answer: 21.2______________________________________Divide 5.3 ÷ 0.25 = 21.2______________________________________

Sorry, Loves.

But I can't really type my work-

I'm on a chrome book so I don't have a camera.

Help, please it's due soon?

Answers

9514 1404 393

Answer:

  398,765

Step-by-step explanation:

If s represents the number sold to date, the given relation is ...

  0.081s = 32300

  s = 32300/0.081 ≈ 398,765 . . . . . . divide by the coefficient of s

398,765 copies have been sold to date.

Classify the following triangle. Check all that apply.
98
419
O A. isosceles
I B. scalene
C. obtuse
U
D. equilateral
I E. acute
F. right

Answers

Answer:

obtuse and isosceles

angle greater than 90° and 2 equal sides

A large discount store wants to determine the average yearly income of its shoppers. A researcher chooses 100 shoppers at random between 1:00 p.m. and 5:00 p.m. on a Saturday to survey. Identify the population.
A. All shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
B. The 100 surveyed shoppers at the discount store between 1:00 p.m. and 5:00 p.m. on this particular Saturday.
C. All shoppers at the discount store on this particular Saturday.
D. All shoppers at the discount store during a year's time.
E. None of the above.

Answers

Answer:

The population is:

D. All shoppers at the discount store during a year's time.

Step-by-step explanation:

Since the discount store wants to determine the average yearly income of its shoppers, the population of interest here is all the shoppers that visit the discount store during a year's time.  The population includes all the individual shoppers.  However, this number may be too difficult to obtain and work on their data.  This is the researcher can choose a sample, calculating its statistics to approximate the population parameters.

what unfortunate mistake did the champion ice skater make with his gold medal

Answers

Answer:

He Had It Bronzed

Step-by-step explanation:

Hope this help pls mark as brainlest!!

Ahn had walked 8 blocks. He was 25% of the way to school. How many total blocks was his walk to school?

Answers

He had walked 8 blocks, and that was 25% (or .25) of the distance to the school. Let’s let “D” represent the total distance...
D x .25 = 8 blocks
Divide both sides of the equation to solve for D...
D = 8 / .25 = 32
So the total number of blocks to his school is 32.

Amphibian populations are in decline worldwide due to the increasing prevalence of ranavirus infections. Herpetologists (those that study amphibians and reptiles) are especially concerned with how ranavirus infections may be affecting Ozark and eastern hellbender populations.

Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%. Suppose a random sample of size 118 is taken of the eastern hellbender population and a random sample of size 177 is taken of the Ozark hellbender population. Every hellbender in each sample is tested for ranavirus, and the sample proportions for each of the two samples are calculated.

Required:
Which of the two sample proportions is more likely to exceed 22% ?

Answers

Answer:

The sample proportion of size 177 is more likely to exceed 22%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%.

This means that [tex]\mu = p = 0.25[/tex]

Sample of size 118:

[tex]n = 118, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0399[/tex]

Probability of sample proportion above 22%.

This is 1 subtracted by the pvalue of Z when X = 0.22. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.25}{0.0399}[/tex]

[tex]Z = -0.75[/tex]

[tex]Z = -0.75[/tex] has a pvalue of 0.2266

1 - 0.2266 = 0.7734

0.7734% probability that a random sample of size 118 exceeds 22%.

Sample of size 177:

[tex]n = 177, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0325[/tex]

Probability of sample proportion above 22%.

This is 1 subtracted by the pvalue of Z when X = 0.22. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.25}{0.0325}[/tex]

[tex]Z = -0.92[/tex]

[tex]Z = -0.92[/tex] has a pvalue of 0.1788

1 - 0.1788 = 0.8212

0.8212 = 82.12% probability that a random sample of size 177 exceeds 22%.

82.12% > 77.34%, so the sample proportion of size 177 is more likely to exceed 22%.

The sample proportion that is more likely to exceed 22% is; the sample proportion with a sample size of 177

Central Limit Theorem

We are given;

Population proportion; p = 25% = 0.25

Now, in central limit theorem, the formula for standard deviation is;

σ = √(p(1 - p)/n)

For a sample size of 118, we have;

σ = √(0.25(1 - 0.25)/118)

σ = √0.001588983

σ = 0.03986

Similarly, for a sample size of 177, we have;

σ = √(0.25(1 - 0.25)/177)

σ = √0.001059322

σ = 0.032547

Since we want to find which of the two sample proportions will likely exceed 22% which is p₀ = 0.2, we will use the formula;

z = (p₀ - p)/σ

For sample size of 118, we have;

z = (0.22 - 0.25)/0.03986

z = -0.75

From online p-value from z-score calculator, we have;

p-value = 0.7734 or 77.34%

For sample size of 177, we have;

z = (0.22 - 0.25)/0.032547

z = -0.92

From online p-value from z-score calculator, we have;

p-value = 0.8212 or 82.12%

The p-value of the sample of 177 is higher than the p-value for the sample of 118 and so we can say that the sample proportion with a sample size of 177 is more likely to exceed 22%

Read more about Central Limit theorem at; https://brainly.com/question/25800303

I am once again asking for your help

Convert the expression (√3)(∜3) to exponential form. Show your work.

Answers

Answer:

(3^1/2)(3^1/4)

Step-by-step explanation:

Use the formula

[tex]\sqrt[n]{a} ^x[/tex] = [tex]a^{\frac{x}{n} }[/tex]

[tex]\sqrt{3}[/tex]

a = 3

n = 2, we do not write it because square root is basically replacing it

x = is a period in this case period is 1

[tex]\sqrt[4]{3}[/tex]

a = 3

n = 4

x = 1

Exact Form:

[tex]3^{\frac{3}{4} }[/tex]

Decimal Form:

2.27950705

Hope it helps:)

what is the equivalent property of 8(4x - 3)

Answers

Answer:

=32x−24

Step-by-step explanation:

Write 0.0065 in standard form.

Answers

Answer:

It is just 65.

Step-by-step explanation:

Find the square root of the following decimal numbers.​

Answers

Answer:

[tex] \huge \boxed{ \tt i)1.6} \\ \huge \boxed{ \tt ii)4.3} \\ \huge \boxed{ \tt iii)8.3} \\ \huge \boxed{ \: \: \: \: \tt iv)9.2 \: \: \: }[/tex]

Step-by-step explanation:

to understand thisyou need to know about:square rootfinding square root by division methodconverting decimal to a fractionPEMDAStips and formulas:

tips for finding square root by division method

Group the digits in pairs, starting with the digit in the units placeThink of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient.Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. Repeat steps till all the periods have been taken up

tips for converting decimal to a fraction

Write down the decimal divided by 1Multiply both top and bottom by 10 for every number after the decimal pointreduce the fractionlet's solve:

solve the square roots using division method:

the picture is attached

solve the square roots by converting decimals into fraction:

[tex] \tt i) \sqrt{2.56} \\ \tt \sqrt{ \frac{256}{100} } \\ \tt \sqrt{ \frac{1 {6}^{2} }{ {10}^{2} } } \\ \tt\frac{16}{10} \\ \tt \: 1.6[/tex]

[tex] \tt ii) \sqrt{18.49} \\ \tt \sqrt{ \frac{1849}{100} } \\ \tt\sqrt{ \frac{ {43}^{2} }{ {10}^{2} } } \\ \tt \frac{43}{10} \\ \tt 4.3[/tex]

[tex] \tt iii) \sqrt{ 68.89} \\ \tt \sqrt{ \frac{6889}{100} } \\ \tt \sqrt{ \frac{ {83}^{2} }{ {10}^{2} } } \\ \tt \frac{83}{10} \\ \tt 8.3[/tex]

[tex] \tt iv) \sqrt{84.64} \\ \tt\sqrt{ \frac{8464}{100} } \\ \tt\sqrt{ \frac{ {92}^{2} }{ {10}^{2} } } \\ \tt \frac{92}{10} \\ \tt9.2[/tex]

Answer:

1.6

4.3

8.3

9.2

Step-by-step explanation:

Hope it is helpful....

Hi! 8th grade math problem for you. Please see the screenshot

Answers

Answer:

r=4/2=2cm

total volume=volume of cylinder + cone=πr²h+1/3πr²h'=πr²(h+1/3 h')=2²π((10-3)+1/3× 3)=4π(7+1)=8×4π=32πcm³

Atoms are made up of subatomic particles including protons and electrons. The mass of a proton is about 1.6726 x
10-27 kg and the mass of an electron is about 9.1094 x 10-31 kg. Determine how much mass a proton and electron
has combined. Express the result in scientific notation.
O 1.6717 x 10-27
O 16,717 * 10-31
O 1.6735 x 10-27
O 16,735 x 10-31

Answers

Answer:

C

Step-by-step explanation:

I got a 100%

Write formula for the following mathematical statement.
The force acting on a body is equal to the product of the mass of the body and the acceleration produced by it

Answers

Answer:

F=ma

Step-by-step explanation:

F is force and its measured in Newtons (N)

m is mass measured in kg

a is acceleration measured in metres per second per second


Solve y^3 =-28 where y is a real number.
Simplify your answer as much as possible.

Answers

Answer:

YOU GOT THIS!!

Answer:

y=[tex]\sqrt{28}[/tex] i

Step-by-step explanation:

What is the measure of angle x?

A right angle is shown divided into two parts. The measure of one part of the right angle is 30 degrees. The measure of the other part is 3x.

10
20
30
40

Answers

Step-by-step explanation:

Right angle=90°

90-30= 3x

3x=60

x=20

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