child is being pushed on a swing by his father spotted at Imus Plaza, reaching a maximum height of 4 feet. The father stops pushing, and the maximum height of the swing decreases by 15% on each successive swing. What is the maximum height during the 5th swing?​

Answers

Answer 1

Answer:

1.7748 feet

Step-by-step explanation:

maximum height after 1 swing = 4 feet x (1 - 15%) = 3.4 feet

maximum height after 2 swings = 3.4 feet x (1 - 15%) = 2.89 feet

maximum height after 3 swings = 2.89 feet x (1 - 15%) = 2.4565 feet

maximum height after 4 swings = 2.4565 feet x (1 - 15%) = 2.088025 feet

maximum height after 5 swings = 2.088025 feet x (1 - 15%) = 1.7748 feet

Answer 2

Using a geometric sequence to model this situation, it is found that the maximum height during the 5th swing is of 2.09 feet.

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

The nth term of a sequence is given by:

\(a_n = a_1q^{n-1}\)

In which:

\(a_1\) is the first term.q is the common ratio.

In this problem:

During the 1st swing, maximum height of 4 feet, thus \(a_1 = 4\).Each swing, the height decreases by 15%, thus, the maximum height is 100 - 15 = 85% of the previous swing, which means that \(q = 0.85\).

Thus, the nth term is:

\(a_n = 4(0.85)^{n-1}\)

For the 5th swing:

\(a_5 = 4(0.85)^{5-1} = 2.09\)

The maximum height during the 5th swing is of 2.09 feet.

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Related Questions

in the market for a bag of socks, what happens if the price of cotton falls?

Answers

A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.

When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:

1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.

2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.

3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.

It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.

Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

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When London runs the 400 meter dash, her finishing times are normally distributed with a mean of 83 seconds and a standard deviation of 1 second. If London were to run 40 practice trials of the 400 meter dash, how many of those trials would be between 84 and 85 seconds, to the nearest whole number?

Answers

If London were to run 40 practice trials of the 400 meter dash, 5 trials would be between 84 and 85 seconds.

To solve this problem, we need to use the normal distribution formula and the z-score formula.

First, we need to calculate the z-scores for 84 and 85 seconds:

z₁ = (84 - 83) / 1 = 1

z₂ = (85 - 83) / 1 = 2

Next, we need to look up the area under the standard normal distribution curve between these two z-scores. We can do this using a standard normal distribution table.

we can find the area between these two z-scores by subtracting the area to the left of z₁ from the area to the left of z₂:

area = P(z₁ < Z < z₂) = P(Z < z₂) - P(Z < z₁)

area = P(Z < 2) - P(Z < 1)

area = 0.9772 - 0.8413

area = 0.1359

This means that approximately 13.59% of the practice trials will be between 84 and 85 seconds. To find the actual number of trials, we can multiply this percentage by the total number of trials:

number of trials = 0.1359 * 40

number of trials ≈ 5.44

Rounding to the nearest whole number, we get that about 5 of the 40 practice trials will be between 84 and 85 seconds.

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perimeter describe in your own words​

Answers

Answer:

adding up all the sides

Step-by-step explanation:

Answer:

I LIKE BAKED BEANS (ToT)

Step-by-step explanation:

A right triangle is formed by line segments
KM, MP, and KP.

Based on the diagram, which describes the
best method to determine the area of the
shaded region?

A: The area of the shaded region is equal to
the sum of the areas of the two unshaded
regions.

B: The area of the shaded region is equal
to the difference in the areas of the
unshaded regions.

C: The area of the shaded region is equal
to the sum of the side lengths of the
unshaded regions.

D: The area of the shaded region is equal to
the difference in the side lengths of the
unshaded regions

A right triangle is formed by line segmentsKM, MP, and KP.Based on the diagram, which describes thebest

Answers

Answer:

B: The area of the shaded region is equal

to the difference in the areas of the

unshaded regions.

Step-by-step explanation:

i got this write on my homework :D

last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them and I know they're not the correct answer. Please these are urgent and I know its kind of tedious but i need help. Thank you so much to the kind smart person who ends up answering this.

last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them
last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them
last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them
last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them
last time, TO ALL AMAZING MATHMATICIANS PLS HELP ASAP, please do not put links in I won't click them

Answers

Answer:

I just answered these with your most recent post.

Solve the equation for x.
1=0.4x - 0.8x - 35
What does x equal

Answers

Answer:

x = - 90

Step-by-step explanation:

1 = 0.4x - 0.8x - 35 ( add 35 to both sides )

36 = - 0.4x ( divide both sides by - 0.4 )

- 90 = x

Which set is of whole numbers but not natural numbers?

Answers

Step-by-step explanation:

The set of Natural numbers: {1, 2, 3, 4, 5, ...}

The set of Whole numbers: {0, 1, 2, 3, 4, 5, ...} ← it has the number 0

simplfiy the equation and show your work







dont mind the lil typing space bar thing its not apart of the equation

simplfiy the equation and show your workdont mind the lil typing space bar thing its not apart of the

Answers

1234 get out i beat you before

Britt has decided that she wants to earn $4,000 over the next 10 months to set aside for a down payment on a car. Britt currently works some afternoons and evenings babysitting. She makes $8 per hour. At this pay rate, how many hours will Britt need to work each month to accomplish her goal?

Answers

She needs to work 8 hours per hour to work the rate of hours

This question is dealing with rates. Rates are just to show a measure of what we are to use, give or pay e.t.c per time as the case may be.

Britt needs to work 50 hours each month to accomplish her goal.

She wants to make $4,000 and she makes $8 per hour.

This means, amount of hours she need to make $4,000 is;

4000/8 = 500 hours

Since she wants this money over 10 months, it means every month she needs to work; 500/10 = 50 hours per month.

In conclusion, britt needs to work 50 hours each month to accomplish her goal.

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O No; there are y-values that have more than one x-value.
• No; the graph fails the vertical line test.
• Yes; the graph passes the vertical line test.
Yes; there are no y-values that have more than one x-value.

O No; there are y-values that have more than one x-value. No; the graph fails the vertical line test.

Answers

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

How do functions work?

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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I need help with this math problem please!

I need help with this math problem please!

Answers

AB is most likely 8 because you can solve for the missing half length with Pythagorean theorem which gives 4 and then double because of the inherent properties of the lines

Can you help it’s due today

Can you help its due today

Answers

The function is linear because as x increases, the y values change by a consistent amount. In this case, as x increases by 1, y decreases by 3. This is a linear relationship because the rate of change is constant.

To calculate this, we can take the difference between the first two values. The difference between -28 and -31 is -3. We can then take the difference between the next two values. The difference between -31 and -34 is also -3. Since the difference between each pair of values is the same, this is a linear function. We can also calculate the slope of the line. The slope is the change in y over the change in x. We can calculate this by taking the difference of the y values and dividing it by the difference of the x values. In this case, the slope would be -3/-1 = -3. This is the rate of change of the linear function.

Therefore, the function is linear because as x increases, the y values change by a consistent amount. The slope of this function is -3.

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Can you answer number 29 please?

Can you answer number 29 please?

Answers

Answer:

a. 90

b. 40

c. 55

d. 6

e. 72

Step-by-step explanation:

a: This is a rectangle so all the full corners are 90 degrees. ABC is a corner angle.

b: 1 and 3 are the congruent angles so 3 has the same measure as 1.

C: 1 is a part of the corner, which adds up to 90 degrees. That means angle 2 and angle 1 should add up to 90. They say m<1= 35, so 90-35=55.

d. In a rectangle, the interesecting lines have the same length. AC is 12, so then DB is 12. However, DE is halfway. Half of 12=6.

e. This one has a few steps. Angle 1 is 36, and angle 2 is the other part to the 90 degree corner. 90-36= 54. That gives us angle 2. We know all angles in a triangle add up to 180 degrees. The angle across from angle 2 in the same triangle is the same value, so that is also 54. To find angle 5, it must add up to 180 degrees. 54+54+x=180, in other words. 54+54=108. 180-108=72.

(3×108)(2×106) pls help me ;-;

Answers

Answer:

68688

Step-by-step explanation:

Need help asap! Tyyy

Need help asap! Tyyy

Answers

The answer would be B. 28

write an equation that shows the formation of the sulfide ion from a neutral sulfur atom.

Answers

To show the formation of a sulfide ion from a neutral sulfur atom, we need to add two electrons to the sulfur atom, as sulfide ion has a charge of -2. Therefore, the equation for this process is: S + 2e- → S2-

In this equation, S represents the neutral sulfur atom, while S2- represents the sulfide ion that is formed after the addition of two electrons. This reaction is a reduction reaction, as sulfur is gaining two electrons to form a negatively charged ion.
In summary, the equation S + 2e- → S2- shows the formation of the sulfide ion from a neutral sulfur atom by adding two electrons to it. This equation highlights the importance of electron transfer in chemical reactions and how it can lead to the formation of new compounds.

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please help me on this will give brainliest

please help me on this will give brainliest

Answers

Answer:

(m x 2)+10

Step-by-step explanation:

Answer:

2m+10

Step-by-step explanation:

First you write down 10. Then, you see that the “More than” is there and that indicates that the expression is flipped, but added to the next part of the word problem, which makes it +10. Next you see that it‘s twice Mabel’s height which is 2*m which is then 2m. Then you put the expressions together and get 2m+10. Hope this helps.

(Help Please It would be greatly appreciated) Which of these are true statements about the sine function? Choose all that are correct.

(Help Please It would be greatly appreciated) Which of these are true statements about the sine function?

Answers

Answer:

A is wrong

B is correct

C is correct

D is wrong

E is wrong

F is correct

Step-by-step explanation:

Here, we want to select the correct options about the sine function.

A. is wrong

Let’s use a case of 30 degrees angle

Sin(-30) = -0.5

Sin(30) = 0.5

B is correct

sin(-30) = -0.5

-sin(30) = -0.5

C. C is correct

Sine function is an odd function.

By mathematical definition, we say a function is odd if for any value x of the function; f(-x) = -f(x)

This is obtainable and clear about the sine function from earlier options

D. Is wrong

E. is wrong

F. is correct

The period of the sine function is 2 pi

The period of a function is the time distance between two peaks or crests

if x + y = 180 and y = 45, then x + 45 = 180 an example of substitution?

Answers

Answer:Yes. This is an example of substitution.Reason:

This is an example of substitution because you have substituted the 'y' variable to find the 'x' variable.

Hoped this helped.

\(BrainiacUser1357\)

help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The answer to your question is x=9

Answer: x=9

Step-by-step explanation:

First we need to realize that a triangle and all 3 of its angles must equal to 180°

Let's take 67°+74=141°

Now we will take 180°-141°=39

Now we know the missing angle is 39°, but we are still unsure of what x is

So let us plug in 9

4(9)+3

36+3

39

x=9

A bicycle traveled 150 meters west from point a to point b. then it took the same route and came back to point a. it took a total of 2 minutes for the bycycle to return to point a. what is the average speed and average velocity of the bycle

Answers

The average speed is 300m/2min that’s 150m per minute or 2.5m per second the average velocity is zero

How to write in Simplified slope intercept form

How to write in Simplified slope intercept form

Answers

Answer:

y = -5/3x + 8

Step-by-step explanation:

So the y - intercept is 8 and from that point the line goes down by 5 and right by 3.

Given that 1 euro is £1 how much is the exchange rate for pounds to euros

Answers

The exchange rate for pounds to euros is 1 GBP = 1 EUR.

Based on the information provided, where 1 euro is equal to £1, we can infer that the exchange rate for pounds to euros is 1:1. This means that 1 British pound (GBP) is equivalent to 1 euro (EUR). The exchange rate indicates the value of one currency in relation to another. In this case, the exchange rate suggests that the pound and the euro have equal value.

Exchange rates can fluctuate due to various factors such as economic conditions, interest rates, and political stability. However, if the given exchange rate of 1 GBP = 1 EUR is accurate, it implies that the pound and the euro have a fixed parity, where their values are considered equal. This is relatively uncommon, as currencies typically have different exchange rates due to various factors impacting their economies. It's important to note that exchange rates can vary and it's always advisable to check with current market rates or financial institutions for the most up-to-date exchange rate information.

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Solve the equation for y. Then find the value of y for each value of x. 2x - 7y = 19; X = - 2, 0, 2

PLEASE HELP​

Answers

Answer:

y=-23/7;y=-19/7;y=-15/7

Step-by-step explanation:

when x is -2 then y is;

2(-2)-7y=19

-4-7y=19

-7y=23 divide both sides by -7

y=-23/7

when x=0 then y is;

2(0)-7y=19

-7y=19

y=-19/7

when x=2 then y is;

2(2)-7y=19

4-7y=19

-7y=15

y=-15/7

In AABC, mLA = 58° and mzB = 45°.
Select the triangle that is similar to AABC.
OA. AMNP, in which m/M = 58° and
m²N = 103°
B. AXYZ, in which mLX = 45° and
m²Y = 103°
C. AHIJ, in which mzH= 58° and
m2J = 77°
D. APQR, in which m4P = 58° and
m/R = 70°

In AABC, mLA = 58 and mzB = 45.Select the triangle that is similar to AABC.OA. AMNP, in which m/M = 58

Answers

The triangle that is similar to triangle ABC is triangle HIJ , in which <H is 58° , < J = 77°

What are similar triangles?

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.

Also the ratio of corresponding sides of similar triangles are equal.

Since in triangle ABC,

A = 58°, B = 45°

C = 180-( 58+45)

= 180- 103 = 77°

In triangle HIJ

the corresponding angles of H is A = 58°

the corresponding angles of J is C = 77°

Therefore the similar triangle to triangle ABC is triangle HIJ.

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find the indicated partial derivative. f(x, y) = y sin−1(xy); fy 4, 1 8

Answers

Therefore, the value of fy at (4, 1) is (sin⁻¹(4) + 4/√(-60)) / 8, or approximately -0.105 for given partial derivatives.

To find fy, we need to take the partial derivative of f with respect to y, treating x as a constant. Using the chain rule, we get:

f(x, y) = y sin⁻¹(xy)

∂f/∂y = sin⁻¹(xy) + y(1/√(1 - x²y²))(x)

Now we can substitute the given values of x and y to get:

∂f/∂y (4, 1) = sin⁻¹(4) + 1(1/√(1 - 16))(4)

= sin⁻¹(4) + 4/√(-60)

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on average, 30-minute television sitcoms have 22 minutes of programming. assume that the probability distribution for minutes of programming can be well approximated by an uniform distribution from 18 to 26 minutes. enter all your answers as a number between 0 and 1, rounded to three decimal places. what is the probability a sitcom will have 25 or more minutes of programming? what is the probability a sitcom will have between 21 and 25 minutes of programming? what is the probability a sitcom will have more than 10 minutes of commercials (or other non-programming interruptions)?

Answers

1) The probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) The probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) The probability that a sitcom will have more than 10 minutes of commercials (or other non-programming interruptions) is 0.250.

To solve this problem, we can use the probability density function of a uniform distribution

f(x) = 1/(b-a) for a <= x <= b

= 0 otherwise

where a and b are the endpoints of the interval.

Given that the programming time for sitcoms follows a uniform distribution from 18 to 26 minutes, we have

a = 18

b = 26

Therefore, the probability density function for the programming time is

f(x) = 1/8 for 18 <= x <= 26

= 0 otherwise

1) P(X >= 25) = ∫(25 to 26) f(x) dx

= ∫(25 to 26) 1/8 dx

= [x/8] from 25 to 26

= (26/8) - (25/8)

= 1/8

Therefore, the probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) P(21 <= X <= 25) = ∫(21 to 25) f(x) dx

= ∫(21 to 25) 1/8 dx

= [x/8] from 21 to 25

= (25/8) - (21/8)

= 1

Therefore, the probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) Since the total running time of a sitcom is 30 minutes and the programming time is uniformly distributed between 18 and 26 minutes, the time for commercials and interruptions is:

T = 30 - X

where X is the programming time.

Therefore, the probability of having more than 10 minutes of commercials and interruptions is

P(T > 10) = P(30 - X > 10)

= P(X < 20)

Using the cumulative distribution function (CDF) of the uniform distribution, we get

F(x) = (x - a)/(b - a) for a <= x <= b

= 0 for x < a

= 1 for x >= b

Therefore

P(X < 20) = F(20)

= (20 - 18)/(26 - 18)

= 2/8

= 0.250

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Which choice best supports the conclusion that
public transportation is compatible with the use of
personal electronic devices?
A) Lines 59-63 ("The . . . subways")
B) Lines 63-67 ("Part . . . annoyances")
C) Lines 68-70 ("Even . . . ago")
D) Lines 77-81 ("Already . . . homes")

Answers

Correct option is B. Lines 63-67 ("Part . . . annoyances")

Justifying lines are -

" Part of the reason is their ease with iPads, MP3 players, Kindles, and smartphones: you can get some serious texting done when you’re not

driving, and earbuds offer effective insulation from all but the most extreme commuting annoyances."

Below is the passage mentioned in the question which is from Taras Grescoe, Straphanger: Saving Our Cities and Ourselves from the Automobile by Taras Grescoe -

"Though there are 600 million cars on the planet,and counting,

there are also seven billion people,

which means that for the vast majority of us

gettingaround involves taking buses, ferryboats,

commutertrains, streetcars, and subways.

In other words,traveling to work,

school, or the market means

beinga straphanger: somebody who,

by choice or necessity,relies on public transport,

rather than a privatelyowned automobile.

Half the population of New York, Toronto,

andLondon do not own cars.

Public transport is howmost of the people of Asia and Africa,

the world’smost populous continents, travel.

Every day, subwaysystems carry 155 million passengers,

thirty-fourtimes the number carried by all the world’s airplanes,

.........................................

commanding enormous price premiums oversuburban homes.

The experience of European and

Asian cities shows that if you make buses, subways,and trains convenient, comfortable, fast, and safe,

asurprisingly large percentage of citizens will opt toride rather than drive."

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the length of a rectangle is four times its width. if the perimeter is at most 130 centimeters, what is the greatest possible value for the width? question 3 options: 2w + 2 • (4w) < 130 2w + 2 • (4w) > 130 2w + 2 • (4w) ≤ 130 2w + 2 • (4w) ≥ 130

Answers

Answer:

Step-by-step explanation:

Let L be the Length and W be the Width of a rectangle.

We are told that:    L = 4W   [the length of a rectangle is four times its width]

Perimeter = 2L + 2W

We learn that P ≤ 130 cm

2L + 2W ≤ 130 cm

Substitute L = 4W:  

2L + 2W ≤ 130 cm

2(4W) + 2W ≤ 130 cm

10W ≤ 130 cm

W ≤ 13 cm

Options:

2w + 2 • (4w) < 130     Not correct since the < sign does not allow for the "at most 130 cm.")

2w + 2 • (4w) > 130      Must be ≤, not >

2w + 2 • (4w) ≤ 130   This option works since the ≤ sign is correct.

A hot air balloon travels at a constant rate of 3 miles per hour. If the balloon traveled a total of 72 miles, how many hours would it take?

Answers

it would be 24 hours or 1 day long

Answer:

24 hours

Step-by-step explanation:

72 divided by 3

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