the straight-line distance from capital city to little village is miles. from capital city to mytown is miles, from mytown to yourtown is miles, and from yourtown to little village is miles. how far is it from mytown to little village?

Answers

Answer 1

The distance from Mytown to Little Village is z + w miles.

To find the distance from Mytown to Little Village, we need to add the distances between Mytown and Yourtown, and between Yourtown and Little Village. Let's assume the distances are as follows:

Distance from Capital City to Little Village: x miles

Distance from Capital City to Mytown: y miles

Distance from Mytown to Yourtown: z miles

Distance from Yourtown to Little Village: w miles

Given this information, we can determine the distance from Mytown to Little Village by summing the two distances:

Distance from Mytown to Little Village = Distance from Mytown to Yourtown + Distance from Yourtown to Little Village

= z + w miles

So, the distance from Mytown to Little Village is z + w miles.

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Related Questions

Estimate the flow rate at t=9s.
Time (s) 0,1,5,8,11,15
Volume cm3 0,2,13.08,24.23,36.04,153.28

Answers

The estimated flow rate is approximately 3.94 cm3/s.

To estimate the flow rate at t=9s, we can use the formula:

flow rate = change in volume / change in time.

Using the data given, we can calculate the change in volume and change in time for the interval between t = 8s and t = 11s.

Change in volume = 36.04 - 24.23 = 11.81 cm³

Change in time = 11 - 8 = 3s

Now, we can plug these values into the formula to find the flow rate:

flow rate = change in volume / change in time = 11.81 cm3 / 3s ≈ 3.94 cm3/s

Therefore, the estimated flow rate at t=9s is approximately 3.94 cm3/s.

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Write two sentences to explain what taxes are.

Answers

Answer:

Taxes are money paid to the government, you need to pay these for the army , teachers, and it forms a better economy etc.!:) Have a nice day friend.

Step-by-step explanation:

rylee1015, it does matter because you are copying answers just to get points, and it might be wrong which is not fair, so stop it!!!:(

2) A 95% confidence interval estimate for a population mean u is (23, 45). Which of the following is a true statement?
(A) There is 0.95 probability that μ is between 23 and 45.
(B) If 95% confidence intervals are calculated from all possible samples of the given size, μ will be in 95% of these intervals.
(C) If 95% confidence intervals are calculated from all possible samples of the given size, 95% of them will be
(23, 45).
(D) We are 95% confidence that the interval from (23, 45) contains the sample mean x
(E) The margin of error of this confidence interval is 22.

Answers

The correct statement for the 95% confidence interval is given by

option (B) If 95% confidence intervals are calculated from all possible samples of the given size, μ will be in 95% of these intervals.

Confidence interval = 95%

Population mean μ

A confidence interval is an estimate of a population parameter  the population mean μ based on sample data.

The interpretation of a 95% confidence interval is that ,

Sample from the population and construct 95% confidence intervals,

Approximately 95% of these intervals would contain the true population parameter.

Therefore, statement (B) accurately reflects the concept of confidence intervals.

It states that if we calculate 95% confidence intervals from all possible samples of the given size,

The true population mean μ will be within 95% of these intervals.

This aligns with the interpretation of a confidence interval as a measure of the precision or reliability of our estimate.

The other statements which are not accurate,

(A) There is no probability associated with a specific confidence interval.

Confidence intervals provide a range of plausible values, but they do not represent probabilities of the parameter being within that range.

(C) Calculating confidence intervals from all possible samples will not guarantee that 95% of them will be (23, 45).

The specific values of the confidence intervals will vary across samples.

(D) Confidence intervals provide a range in which we are confident the true parameter lies.

But it does not imply that the sample mean x falls within that range with 95% certainty.

(E) The margin of error is the half-width of the confidence interval, which represents the maximum amount of error we expect in our estimate.

Here, the margin of error would be (45 - 23) / 2 = 11, not 22.

Therefore , for the confidence interval 95% option B is correct.

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What is the range of the absolute value function shown in the graph?
A. 3 ≤ y < ∞
B. -∞ < y ≤ 3
C. -6 ≤ y < ∞
D. -∞ < y < ∞

Answers

Answer:

C. -6 ≤ y < ∞

C is correct

Step-by-step explanation:

edmentum

Use the following function rule to find f(6).
f(x)=6x+11

Answers

f(6)=6(6)+11
answer:47

Answer:

X=-11/6

Steps

f(x)=6x+11

simplify,

0=6x+11

-6x+11

Divide both sides,

Answer is x = -¹¹/6

Scuba tanks arrive at a pressure test station for testing prior to shipment. The arrival rate is 16mins and the station test time averages 8 minutes per tank. Poisson distributions are assumed
A. What is the utilization of the test station?
B. What is the probability that a tank have to wait in the queue prior to testing?
C. What is the mean time a tank will spend in queue?
D. What is the mean time that a tank will spend in the system ?
E. What is the mean number of tanks that might be expected to be in queue at any time?
F. What is the mean number of tanks that might be expected to be in the system at any time ?
G. What is the probability of finding four or more tanks in the system at any time ?
H. Find the probability of 6 or more in the system

Answers

The probability of finding four or more tanks in the system at any time is approximately 0.95. The probability of having 6 or more tanks in the system is approximately 0.77.

A. The utilization of the test station is calculated by dividing the average service rate (1 tank per 8 minutes) by the arrival rate (1 tank every 16 minutes). Utilization = Service rate / Arrival rate = 1/2 = 0.5 or 50%.

B. The probability that a tank has to wait in the queue prior to testing can be calculated using the queuing theory formula for the M/M/1 queue. In this case, the utilization (ρ) is 0.5. The formula for the probability of waiting in the queue (Pw) is Pw = ρ^2 / (1 - ρ) = 0.5^2 / (1 - 0.5) = 0.25 / 0.5 = 0.5 or 50%.

C. The mean time a tank spends in the queue can be calculated using Little's Law, which states that the mean number of customers in a stable system (L) is equal to the arrival rate (λ) multiplied by the mean time spent in the system (W). In this case, L = λ * W. The mean number of tanks in the queue (Lq) can be calculated using Lq = λ * Wq, where Wq is the mean time spent in the queue. Given λ = 1/16 tanks per minute and Lq = 8 tanks, we can rearrange the equation to solve for Wq: Wq = Lq / λ = 8 / (1/16) = 128 minutes / 16 = 8 minutes.

D. The mean time a tank spends in the system (queue + test) is equal to the mean time spent in the queue (Wq) plus the mean service time (1/8 tanks per minute). Therefore, the mean time in the system (Ws) is Ws = Wq + 1/μ = 8 + 1/8 = 8.125 minutes.

E. The mean number of tanks expected to be in the queue at any time can be calculated using Little's Law: Lq = λ * Wq. Given λ = 1/16 tanks per minute and Wq = 8 minutes, we can calculate Lq: Lq = (1/16) * 8 = 0.5 tanks.

F. The mean number of tanks expected to be in the system at any time can be calculated using Little's Law: L = λ * Ws. Given λ = 1/16 tanks per minute and Ws = 8.125 minutes, we can calculate L: L = (1/16) * 8.125 = 0.507 tanks.

G. The probability of finding four or more tanks in the system at any time can be calculated using the Poisson distribution formula. By summing the probabilities for four, five, and more tanks, we get 0.043.

H. The probability of having 6 or more tanks in the system can also be calculated using the Poisson distribution formula, which results in a probability of 0.002.

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Bridget has captured many purple-footed bog frogs. She weighs each one
and then counts the number of yellow spots on its back. This trend line is a
fit for these data.
$
Number of spots
NA DONN
1 2 3 4 5 6 7 8 9 10 11 12
Weight (g)
A. strong
B. parabolic
c. negative
D. weak

Answers

Answer:

A. Strong

Step-by-step explanation:

I took the test

Have a great day! ;)

This trend line is a strong fit for these data. Then the correct option is A.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Bridget has captured many purple-footed bog frogs.

She weighs each one and then counts the number of yellow spots on its back.

This trend line is a strong fit for these data.

Because all the points are closer to the line.

Then the correct option is A.

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Daniel has 280 baseball cards. 15% of there are rare collector's items. How
many baseball cards does Daniel possess that are rare? *

Answers

Answer:

the answer is 42. hope this helped

First turn 15% into a decimal.

You get .15

Then multiply .15 by 280

You get 42

Find the center and radius of the circle: x^2 + y^2 + 4x + 14y +52 = 0​

Answers

The center of the circle is point: C=(−2,−7).

Fill in the blanks below in order to justify whether or not the mapping shown
represents a function.
Set A
Set B
4.
5
9
→ 2
-1
-3

Answers

Answer:

Step-by-step explanation:

How to write numbers in standard form:

Write the first number 8.

Add a decimal point after it: 8.

Now count the number of digits after 8. There are 13 digits.

So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³

Emily played softball all weekend. She was wondering the difference in time between the shortest game and the longest game. Can you help her figure it out?

Answers

Answer:

hh

Step-by-step explanation:

I need help with this 2 questions can someone help me pls I need it !!!!!

Answers

Answer:

8. center: (-7,5)

radius: 9

Step-by-step explanation:

8. to find the center, you need to get the equation in the form of (x-h)^2+(y-k)^2=r^2

you can do this by completing the square:

x^2+y^2+14x-10y-7=0

x^2+14x+49+y^2-10y+25=7+49+25

(x+7)^2+(y-5)^2=81

so, the center is (-7,5) and the radius is 9

Maxie spent 15 hours doing her homework last week this week she spent 18 hours doing her homework she says that she spent 120% more time doing homework this week is she correct

Answers

Answer: She's wrong.

Step-by-step explanation:

Numbers of hours used in solving homework last week = 15

Numbers of hours used in solving homework this week = 18

Percentage increase = (18 - 15) / 15 × 100

= 3/15 × 100

= 1/5 × 100

= 20%

Since Maxie said that she spent 120% more time doing homework this week, she's wrong. She only spent 20% more.

Mrs. Habib has 46.25 feet of border for a bulletin board for her classroom. the board is 37.5 feet tall and 8.3 feet wide. how many feet of border will Mrs habib have left after she puts border around the board?

It’s not 22.15 I’ve tried.

Answers

Answer:

Mrs. Habib will have 22.25 feet of border left after she puts border around the board.

Step-by-step explanation:

You must find the perimeter of the board and subtract it from the amount of border she has to find how much she will have left after she uses it. The formula for perimeter is [tex]P=2(l+w)[/tex], where [tex]l=[/tex] the length of the board, and [tex]w=[/tex] the width of the board. You will add those together and multiply them by 2 because there are 4 sides to a rectangle. That means this equation will look like:

[tex]P=2(8.25+3.75)[/tex]

Now you can just solve for the perimeter.

[tex]P=2(12)[/tex]

[tex]P=24[/tex]

The perimeter is 24 feet. That means it will take 24 feet of border to cover her board. In order to find out how much she'll have left over, just subtract 24 from the total amount of border she has.

[tex]46.25-24=22.25[/tex]

Therefore Mrs. Habib will have 22.25 feet of border left over after she covers the bulletin board.

According to a recent survey, the probability that the driver in a fatal vehicle accident is female (ovont F) is 0.2907 The probability that the driver is 24 years old or less (event A) is 0.1849. The probability that the driver is female and is 24 years old or less is 0.0542.

a. Find the probability of FUA
b. Find the probability of F'UA

Answers

The probability of F'UA is 0.9458.

According to the given data; the probability of ovont F is 0.2907, the probability of event A is 0.1849 and the probability of the driver is female and is 24 years old or less is 0.0542.

Here are the required probabilities;

a. The probability of FUA:F: Female U: 24 years old or less A: Fatal vehicle accident We can find the probability of FUA using the formula; P(FUA) = P(F ∩ U ∩ A)

We know that the probability of the driver in a fatal vehicle accident is female is 0.2907P(F) = 0.2907 Also, we know that the probability that the driver is 24 years old or less is 0.1849.P(U) = 0.1849

We also know that the probability that the driver is female and is 24 years old or less is 0.0542.P(F ∩ U) = 0.0542Now we can use the formula; P(FUA) = P(F ∩ U ∩ A)= P(F) x P(U) x P(A|FU)= 0.2907 × 0.1849 × (0.0542 / 0.2907)= 0.0542

So, the probability of FUA is 0.0542.

b. The probability of F'UA: It can be calculated by using the complement of FUA.P(F'UA) = 1 - P(FUA)= 1 - 0.0542= 0.9458

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Answer:

Step-by-step explanation:

Given data: The probability that the driver in a fatal vehicle accident is female (event F) is 0.2907. The probability that the driver is 24 years old or less (event A) is 0.1849. The probability that the driver is female and is 24 years old or less is 0.0542.

a) The probability of FUA is 0.4214.

b) The probability of F'UA is 0.5786.

a) The probability of FUA can be calculated as follows:

P(FUA) = P(F) + P(A) - P(F ∩ A) [By Addition Law], Where P(F) = 0.2907, P(A) = 0.1849, P(F ∩ A) = 0.0542.

By putting these values in the above equation we get:

P(FUA) = P(F) + P(A) - P(F ∩ A)

= 0.2907 + 0.1849 - 0.0542

= 0.4214

Therefore, the probability of FUA is 0.4214.

b) The probability of F'UA can be calculated as follows:

P(F'UA) = P(F' ∩ A') [By Complement Law], Where

P(F' ∩ A') = 1 - P(FUA)

= 1 - 0.4214

= 0.5786

Therefore, the probability of F'UA is 0.5786.

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Please answer the question in the picture

Answers

Answer:

Hey kid stop cheating XDDDDDDDDDDDDDDDDDDD

Step-by-step explanation:

Budget planners for a certain community have determined that $3,000,000 wel be required to provide a povernment service rester. The total property value in the communty 120,000,000 wat tax rate is required to meet the budgetary demands?

Answers

The tax rate required to meet the budgetary demands is 2.5%.

According to the given information;

Total property value in the community = $120,000,000

Total amount required to provide a government service = $3,000,000

Now, to find the tax rate required to meet the budgetary demands we will use the formula;

Tax Rate = (Total amount required to provide a government service / Total property value in the community) × 100

Substitute the given values in the above formula;

Tax Rate = ($3,000,000 / $120,000,000) × 100= 2.5%

Thus, the tax rate required to meet the budgetary demands for a community is 2.5 percent.

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Jordan runs to the end of his street and back home every day. The total distance of a trip to the end of the street and back home is 7/8 mile.
How many miles has Jordan run after 6 days?

Answers

Jordan has run 21/4 miles after 6 days.

Jordan runs to the end of his street and back home every day and the total distance of a trip to the end of the street and back home is 7/8 mile.

Since Jordan runs to the end of the street and back home every day, the distance he runs in one day is given by;

2 × (distance to the end of the street)

= 7/8 mile (distance to the end of the street)

= 7/16 mile

The distance Jordan runs in 6 days is;

6 × (distance to the end of the street and back home)

= 6 × 7/8 miles

= 42/8 miles

= 21/4 miles

Therefore, Jordan has run 21/4 miles after 6 days.

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if you use a level of significance in a two-tail hypothesis test, what decision will you make if zstat -1.58?

Answers

In a two-tail hypothesis test, if the calculated test statistic (z-statistic) is -1.58 and the level of significance is used, the decision will depend on comparing the z-statistic to the critical values of the standard normal distribution corresponding to the desired level of significance.

Explanation: In a two-tail hypothesis test, the null hypothesis assumes that there is no significant difference between the sample and population parameters. The alternative hypothesis, on the other hand, suggests a significant difference. The level of significance, denoted as α, determines the critical values that divide the rejection and non-rejection regions.

If the calculated test statistic, in this case -1.58, falls within the rejection region, which is determined by the critical values, we reject the null hypothesis. If the test statistic falls outside the rejection region, we fail to reject the null hypothesis.

To make a decision, we compare the z-statistic to the critical values corresponding to the level of significance. If the z-statistic of -1.58 falls outside the critical values, it means it is not extreme enough to reject the null hypothesis, and we fail to reject it. However, if the z-statistic falls within the critical values, we reject the null hypothesis in favor of the alternative hypothesis.

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Please help! I know its a lot and I'm sorry but I REALLY NEED HELP!!! I just don't understand this and I don't want to fail my brain just is not smart with math. Even if you answer just ONE question it would mean the WORLD TO ME thanks!

Answers

Answer:16

Step-by-step explanation:

Help me please ahhhh...Simplify the expression below.
2.5x. 4

Answers

Just multiply, it’s 40x.

Answer:

Maybe multiply 2 and 4 then multiply 5x  of product of 2 and 4  

Step-by-step explanation:

Let f, g and h be the functions from the set of integers to the set of integers defined by f(x) = 2x +3, g(x) = 3x + 2 and h(x) = x3 +1.

(a) Find (fºg)(x) (b) Find (gof)(x) (c) l'ind (f)(x) (d) Find (h+h)(x) (e) Find h-1(x)

Answers

Let f, g and h be the functions from the set of integers to the set of integers defined by f(x) = 2x +3, g(x) = 3x + 2 and h(x) = x3 +1.

(a) To find (f º g)(x), we substitute g(x) into f(x) as follows:

  (f º g)(x) = f(g(x)) = f(3x + 2) = 2(3x + 2) + 3 = 6x + 4 + 3 = 6x + 9.

(b) To find (g º f)(x), we substitute f(x) into g(x) as follows:

  (g º f)(x) = g(f(x)) = g(2x + 3) = 3(2x + 3) + 2 = 6x + 9 + 2 = 6x + 11.

(c) To find the inverse of f(x), denoted as l'ind (f)(x), we solve for x in terms of f(x):

  x = (f(x) - 3) / 2.

  Rearranging the equation, we get f^(-1)(x) = 1/2x - 3/2.

(d) To find (h + h)(x), we add h(x) to itself:

  (h + h)(x) = h(x) + h(x) = ([tex]x^3[/tex] + 1) + (x^3 + 1) = 2[tex]x^3[/tex] + 2.

(e) To find the inverse of h(x), denoted as h^(-1)(x), we solve for x in terms of h(x):

  x = (h(x) - 1)^(1/3).

  Rearranging the equation, we get h^(-1)(x) = (x - 1)^(1/3).

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Could someone plz help and show work? Thanks

Answers

Answer:

3 cm

Step-by-step explanation:

The answer is 3.......

y=-3 - x, how to draw the graph​

Answers

Answer: See attachment below (graphing)

Step-by-step explanation:

INFORMATION:

The slope-intercept is when y=mx+b

mx=the slope

b=y-intercept

REPHRASE EQUATION:

y=mx+b

y=-3-x

y=(-1)x-3

CONCLUSION:

Slope=-1

Y-intercept=-3

Hope this helps!! :)

Please let me know if you have any questions

Answer:

the graph​: y = -3 - x

Tammy read for 1/3 hour today. She read for 1/6 hour yesterday. How many hours did Tammy read in all?

Answers

Answer is 1/3+1/6= 1/2 hours

On a blueprint lets say that every 1/4 inch is equal to 1 foot in real life.
What is the actual length of the room if it measures 3 3/4 inches on the blue print?
Write the fractions as decimals 1/4 = 0.25 and 3 3/4 = 3.75
15 ft
O 0.9375 ft
4 ft
7 ft

Answers

Answer:

15 ft

Step-by-step explanation:

If every 1/4 of an inch is a foot, than every inch is 4 feet.

1 inch = 4ft

3 inches = 12ft

1/4 + 1/4 + 1/4 = 3/4

3/4=3 ft

12+3=15ft

HELLPP WORTH 20 POINTS ✨

Answers

Answer:

it's radius is 9 and diameter is 18

Answer:

diameter=18cm

radius =diameter/2=18/2=9cm

Estimate the derivative using forward finite divided difference applying both truncated and more accurate formula using 0.5 and step sizes of ht=0.25 and tu=0.125 4x12x2 + x3 -1 #x) = 5 + 3sinu = 2x1 + x2 + x3 = 4 2xy + 2x2 + x3 = 3

Answers

The more accurate forward finite divided difference estimates for the derivatives are

f₁'(x₁) = 0

f₂'(x₂) = 0

f₃'(x₃) = 0

To make it easier to work with, let's rearrange the equations in terms of the variables:

4x₁ + 2x₂ + x₃ = 1

2x₁ + x₂ + x₃ = 4

2x₁ + 2x₂ + x₃ = 3

The truncated formula for estimating the derivative using the forward finite divided difference is given by:

f'(x) ≈ (f(x + ht) - f(x)) / ht

Here, f(x) represents the function we want to differentiate, and ht is the step size.

Let's calculate the derivatives using the truncated formula for the given equations:

For x₁:

f₁'(x₁) ≈ (f₁(x₁ + ht) - f₁(x₁)) / ht

= (4(x₁ + ht) + 2x₂ + x₃ - 4x₁ - 2x₂ - x₃) / ht

= (4x₁ + 4ht + 2x₂ + x₃ - 4x₁ - 2x₂ - x₃) / ht

= (4ht) / ht

= 4

Similarly, we can calculate the derivatives for x₂ and x₃.

For x₂:

f₂'(x₂) ≈ (f₂(x₂ + ht) - f₂(x₂)) / ht

= (2x₁ + (x₂ + ht) + x₃ - 2x₁ - x₂ - x₃) / ht

= (x₂ + ht - x₂) / ht

= ht / ht

= 1

For x₃:

f₃'(x₃) ≈ (f₃(x₃ + ht) - f₃(x₃)) / ht

= (2x₁ + 2x₂ + (x₃ + ht) - 2x₁ - 2x₂ - x₃) / ht

= (x₃ + ht - x₃) / ht

= ht / ht

= 1

So, the truncated forward finite divided difference estimates for the derivatives are:

f₁'(x₁) = 4

f₂'(x₂) = 1

f₃'(x₃) = 1

The more accurate formula for estimating the derivative using the forward finite divided difference is given by:

f'(x) ≈ (-3f(x) + 4f(x + ht) - f(x + 2ht)) / (2ht)

Let's calculate the derivatives using the more accurate formula for the given equations:

For x₁:

f₁'(x₁) ≈ (-3f₁(x₁) + 4f₁(x₁ + ht) - f₁(x₁ + 2ht)) / (2ht)

= (-3(4x₁ + 2x₂ + x₃) + 4(4(x₁ + ht) + 2x₂ + x₃) - (4(x₁ + 2ht) + 2x₂ + x₃)) / (2ht)

= (-12x₁ - 6x₂ - 3x₃ + 16x₁ + 8ht + 4x₂ + 2x₃ - 4x₁ - 8ht - 2x₂ - x₃) / (2ht)

= (-12x₁ + 16x₁ - 4x₁ + 8ht - 8ht) / (2ht)

= 0

Similarly, we can calculate the derivatives for x₂ and x₃.

For x₂:

f₂'(x₂) ≈ (-3f₂(x₂) + 4f₂(x₂ + ht) - f₂(x₂ + 2ht)) / (2ht)

= (-3(2x₁ + x₂ + x₃) + 4(2x₁ + (x₂ + ht) + x₃) - (2x₁ + (x₂ + 2ht) + x₃)) / (2ht)

= (-6x₁ - 3x₂ - 3x₃ + 8x₁ + 4x₂ + 4ht + 4x₃ - 2x₁ - x₂ - x₃) / (2ht)

= (-6x₁ + 8x₁ - 2x₁ - 3x₂ + 4x₂ - x₂ - 3x₃ + 4x₃ - x₃ + 4ht) / (2ht)

= 0

For x₃:

f₃'(x₃) ≈ (-3f₃(x₃) + 4f₃(x₃ + ht) - f₃(x₃ + 2ht)) / (2ht)

= (-3(2x₁ + 2x₂ + x₃) + 4(2x₁ + 2x₂ + (x₃ + ht)) - (2x₁ + 2x₂ + (x₃ + 2ht))) / (2ht)

= (-6x₁ - 6x₂ - 3x₃ + 8x₁ + 8x₂ + 4x₃ + 4ht - 2x₁ - 2x₂ - x₃) / (2ht)

= (-6x₁ + 8x₁ - 2x₁ - 6x₂ + 8x₂ - 2x₂ - 3x₃ + 4x₃ - x₃ + 4ht) / (2ht)

= 0

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please soon aaaaaaaaaaaaaaaaaaaaaaa

Answers

Answer:

3

Step-by-step explanation:

the answer is 3!!!!!!!

The partial sum - 2 + ( − 6) + ( − 18) + ...... + (-486) =__________

Answers

The partial sum of the given sequence, -2 + (-6) + (-18) + ... + (-486), can be found using the formula Sₙ = a(1 - rₙ)/(1 - r), where a is the first term, r is the common ratio, and n is the number of terms. The value of the partial sum is 728.

To find the partial sum of the given sequence, we can use the formula for the sum of a geometric series, which is Sₙ = a(1 - rₙ)/(1 - r). In this case, the first term a is -2, and the common ratio r is -3. We need to determine the number of terms, n.

By examining the sequence, we can see that each term is obtained by multiplying the previous term by -3. This indicates that the common ratio is -3, as each term is multiplied by -3 to obtain the next term.

To find the number of terms, we can determine the value of n using the formula rₙ = a * r^(n-1). In this case, we have -486 = -2 * (-3)^(n-1).

By solving this equation, we find n = 6.

Substituting the values into the formula for the partial sum, we have:

S₆ = -2(1 - (-3)^6)/(1 - (-3)),

= -2(1 - 729)/(1 + 3),

= -2(-728)/4,

= 728.

Therefore, the partial sum of the given sequence is 728.

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