The average yearly salary of an individual with each of these final degrees is $22333 and $16666.6.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form
Ax + B = 0.
Given;
The average yearly salary of an individual whose final degree is a master's is $43000 less than twice that of an individual whose final degree is a bachelor's.
Combined, two people with each of these educational attainments earn $110 thousand.
Now, let the salary of bachelors be x
Then salary of masters= 2x-43000
x+2x-43000=110000
3x=67000
x=22333.33
2x-43000=16666.66
Therefore, by solving equations answer will be $22333 and $16666.6.
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A sewage treatment plant discharges a pollutant with a concentration of 23 mg/L. The plant's total discharge is 0.35 MGD (millions of gallons per day). Determine the rate of pollutant released in pounds per day. Give your answer accurate to at least two decimal places.
The rate of pollutant released is 67137 lbs/day.
How to determine the rate of pollutant releasedFirst, we need to convert the discharge from millions of gallons per day to gallons per day:
So, we have
0.35 MGD * 1,000,000 gallons/MGD = 350,000 gallons/day
Next, we need to convert the pollutant concentration from milligrams per liter to pounds per day:
Using the standard unit of conversion, we have
Rate = 23 mg/L * 350,000 gallons/day * 8.34 lbs/gallon * 1 gram/1000 mg
Evaluate
Rate = 67137 lbs/day
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Are 4x and 15 + x equivalent expressions? Explain why or why not
Answer:
Are equivalent
Step-by-step explanation:
4x=15+x
3x=15
x=5
4*5=15+5
Answer: No.
Step-by-step explanation: 15 +5 is 20,
and ,
4(5) is also 20,
so,
20=20
If n=250 and (p-hat) =0.41, find the margin of error at a 95% confidence level
Give your answer to three decimals
The margin of error of the 95% confidence interval is given as follows:
0.061.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is defined as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]\pi = 0.41, n = 250[/tex]
Hence the margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.41(0.59)}{250}}[/tex]
M = 0.061.
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Answer: M = 0.061.
Step-by-step explanation: The margin of error of the 95% confidence interval is given as follows:
0.061.
What is a confidence interval of proportions?
A confidence interval of proportions has the bounds given by the rule presented as follows:
In which the variables used to calculated these bounds are listed as follows:
is the sample proportion, which is also the estimate of the parameter.
z is the critical value.
n is the sample size.
The margin of error is defined as follows:
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of , so the critical value is z = 1.96.
The parameters for this problem are given as follows:
Hence the margin of error is given as follows:
bus arrival follow a poisson distribution with rate 2 bus in 30 minutes. (a) consider a random variable x that represents the number of arrived buses in 1 hour. what is the moment generating function of x and expected value of x? (b) consider a random variable y that represents the waiting time until the next bus arrival. what is the moment generating function of y and expected value of y
(a) The moment generating function of [tex]x = E[e^(tx)] = (1-e^(2t))^-1[/tex]and expected value of x = 4. (b) The moment generating function of[tex]y = E[e^(ty)] = 1/(1-2t) \\[/tex]and expected value of y = 30 minutes.
(a) The moment generating function of a random variable is defined as [tex]E[e^(tx)]\\[/tex], where t is a real number. In the given example, x is a random variable representing the number of arrived buses in 1 hour. Hence, the moment generating function of x is [tex]E[e^(tx)] = (1-e^(2t))^-1[/tex]. This is because the number of buses arriving in 1 hour follows a Poisson distribution with rate 2/30 minutes. Thus, the expected value of x is 4, which is the rate multiplied by the time period (2*2).
(b) The random variable y represents the waiting time until the next bus arrival. The moment generating function of y is [tex]E[e^(ty)] = 1/(1-2t)[/tex]. This is because the waiting time until the next bus arrival follows an exponential distribution with rate 2/30 minutes. Thus, the expected value of y is 30 minutes, which is the rate multiplied by the time period (2*30).
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The solution to 7(b-1)/b ≤0 is:
0
O 0
O 0>b≥1
O. 0≥b>1
The solution to the given inequality is b ≤ 1.
What are Inequalities?Inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥.
Given inequality expression is,
7 (b - 1) / b ≤ 0
(7b - 7) / b ≤ 0
(7b / b) - (7 / b) ≤ 0
7 - 7/b ≤ 0
Adding 7/b on both sides,
7 ≤ 7/b
Multiplying b on both sides,
7b ≤ 7
b ≤ 1
Hence the value of b is b ≤ 1.
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graph Y+1=-2/3(x+1)
how do i graph this line. I would need two points to graph the line.
Answer:
y = -2/3x + y
y = -2/3x + 1
Step-by-step explanation:
y = -2/3x + b
when x = 0,
y = -2/3 * 0 + b
y = b
b = y
Much of data analysis involves interpreting proportions lots and lots of related proportions. So let's recall the basics. It might help to start by reviewing the main rules from Data 8, with particular attention to what's being multiplied in the multiplication rule. (a) The Pew Research Foundation publishes the results of numerous surveys, one of which is about the trust that Americans have in groups such as the military, sci- entists, and elected officials to act in the public interest. A table in the article summarizes the results. Pick one of the options (1) or (2) to answer the question below; if you pick (1), tell us what p is. Then, explain your choice. The percent of surveyed U.S. adults who had a great deal of confidence in both scientists and religious leaders 1. is equal to p%. 2. cannot be found with the information in the article. Americans' trust in medical scientists, scientists, military relatively high; fewer trust journalists, business leaders, elected officials % of U.S. adults who say they have a (of) confidence in each of the following groups to act in the best interests of the public Great deal Fair amount Not too much None at all Medical scientists 43 46 9 2 Scientists 39 48 10 2 The military 38 45 13 4 Religious leaders 17 46 26 11 Journalists 9 39 33 19 Business leaders 5 43 41 11 Elected officials 3 33 49 14 Note: Respondents who did not give an answer are not shown. Source: Survey conducted April 20-26, 2020. PEW RESEARCH CENTER
The probability that an adult has a great deal of confidence in both scientists and religious leaders is equal to A x B = (43/100)(17/100) = 0.0721, or p = 7.21%.
I choose option 1. The percent of surveyed U.S. adults who had a great deal of confidence in both scientists and religious leaders is equal to p%.
To calculate p, we use the multiplication rule, which states that the probability of two independent events occurring together is equal to the product of their individual probabilities.
In this case, let A be the probability that an adult has a great deal of confidence in scientists, and let B be the probability that an adult has a great deal of confidence in religious leaders.
A = 43/100
B = 17/100
Therefore, the probability that an adult has a great deal of confidence in both scientists and religious leaders is equal to A x B = (43/100)(17/100) = 0.0721, or p = 7.21%.
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Please help need this before friday!!!
-(very important trying to get my grade up!!)
explanations, please!
The width of Polina's strategy =8¾
while the width of Jamie's strategy= 8 3/
How to calculate the width using the given table?The strategy that was used to calculate the width of the Hamza's bumper sticker would be to multiply the given height and widths with the values in ink.
For Polina;
Since 2×1¾ = 2× 7/4 =3½
5 × 1¾ = 5×7/4 = 35/4= 8¾
For Jamie;
since 2×2½= 2×5/2 = 5
= 3½ × 2½
= 7/2 × 5/2
= 35/4
= 8¾
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I want 5 halves of a cupcake for myself 6 halves for my friend and 3 half for our other friend
Answer:
I don't really understand what you mean, maybe is this?
Step-by-step explanation:
5 halves of 14 = 5/14
6 halves of 14 = 6/14
3 halves of 14 = 3/14
Answer:
5+6=11+1=12
Step-by-step explanation:
what is 12 halves? 6
Answer question number 22.
The measure of the angle ALP is 32 degrees
How to determine the measure of the angleFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
Also, we have
EA and LP are parallel lines
EAL = 32 degrees
Using the above as a guide, we have the following:
ALP = EAL
This is because theu are correspondng angles
Hence, ALP has a measure of 32 degrees
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Which of the following equations is an example of inverse variation between the variables x and y?
a. y = x+8
b. y = 8/x
c. y = 8x
d. y = x/8
Step-by-step explanation:
i think this. will help.
Answer:
The answer is: B. y = 8/x
Step-by-step explanation:
a golf ball is hit along a sloped surface. the objective is to determine time distance and speed when it lands.
To accurately determine the time, distance, and speed when a golf ball is hit along a sloped surface, you would need to measure the ball's initial velocity, the angle of the slope, and the acceleration due to gravity.
With these measurements, it would be possible to calculate the time and distance the ball traveled, as well as its speed at the moment it lands.
To calculate the time, distance, and speed when a golf ball is hit along a sloped surface, one must measure the ball's initial velocity, the angle of the slope, and the acceleration due to gravity. With these measurements, one can then calculate the ball's time, distance, and speed when it lands.
The complete question is :
A golfer is hitting a golf ball along a sloped surface. The ball is hit with an initial velocity of 50 m/s at an angle of 30 degrees to the horizontal. Determine the time, distance and speed when the ball lands.
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leonard mccoy is a manager at a coffee shop, and he has to decide how many workers to hire. one worker can make 30 drinks that sell for $2.50 on average in one hour. a second worker can make another 25 drinks in one hour.
McCoy should hire two workers if their total profit is greater than the total profit of one worker.
To calculate how many workers McCoy should hire to make the most profit, he must first calculate the total number of drinks that can be made in one hour. One worker can make 30 drinks in an hour, and a second worker can make 25 drinks in an hour. This means that with two workers, 55 drinks can be made in one hour.
The next step is to calculate the total profit that can be made in one hour. This can be done using the formula Profit = Price x Quantity. Since the drinks sell for $2.50 on average and the total number of drinks made in one hour is 55, the total profit from one hour of work is $137.50.
This means that hiring two workers can make McCoy $137.50 in profit in one hour. To decide if this is the best option, McCoy should compare the total profit of two workers to the total profit of one worker. If the total profit of two workers is greater than the total profit of one worker, then McCoy should hire two workers. If the total profit of one worker is greater than the total profit of two workers, then McCoy should hire one worker.
McCoy should hire two workers if their total profit is greater than the total profit of one worker.
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Add -12+7 = what is the answer ?
Answer:
-12 + 7 = -5
Step-by-step explanation:
An example of this equation could be if you owe someone $12 and then receive $7 from them, your debt to them would be reduced to $5. Another example could be if you have 12 apples and someone gives you 7 apples, you would have a total of 19 apples.
Mr. Kenmar has
28 peppers to sell. He packages the peppers into
equal groups of 4. How many packages can
Mr. Kenmar make? Explain how you solved.
Answer:
Kenmar can make 7 packages of peppers, since 28 divided by 4 is 7. To solve, I divided 28 by 4 and got the answer of 7.
Step-by-step explanation:
What is the excluded value from the domain? (Image below). I got x = -3 but it says it is x = -6, -3. I've also uploaded my work.
The excluded values from the domain of the function h(x) are given as follows:
x = -6 and x = -3.
What is the domain of a function?The domain of a function is the set that contains all the possible input values for the function.
The function in this problem is a rational function, meaning that all the values of x that make the denominator zero are excluded from the domain.
As you found out on the problem, the values that make the denominator zero are given as follows:
x = -6 and x = -3.
The value x = -6 is also a zero of the denominator, however this would be considered only to simplify and calculate the limit, it has no bearing on the domain of the function.
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For the following scores: 15,14,9,10,15,12,14,11,13. 14,13,14,12,14,13,13,12,11 Organize the scores in a frequency distribution table. If there are rows in the table below the minimum value of X , leave the unused rows at the bottom. Based on the frequencies, identify the shape of the distribution. The distribution is with of scores. Last question: The distribution is (negatively skewed, positively skewed, or roughly symmetrical) with (no distinct piles, two piles, or one pile) of scores.
At scores of 13 and 14, the two piles correspond to the two frequency local maxima.
Here's the frequency distribution table:
Score Frequency
9 1
10 1
11 3
12 4
13 5
14 5
15 2
The distribution has two piles of scores and is roughly symmetrical. This is due to the fact that the frequencies are concentrated in the center of the distribution and become less frequent as you move away from it.
The two piles correspond to the two frequency local maxima at scores of 13 and 14.
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The demand for pen decreased from 100 to 70
when the price of pen increased from Ghe2.00 to
Ghø5.00. What is the price elasticity of demand for
pen?
2.The quantity demanded of a commodity decreased
from 50kg to 30kg when the price of its related
product increased from Gh¢5.00 to Ghe8.00.
a.Calculate the cross price elasticity of demand for
the commodity and interpret your results.
b. If the price of the commodity rather decreased
from Gh¢5.00 to Gh¢2.50, calculate the cross price
elasticity of demand and interpret your results.
1. The price elasticity of demand for pen is 0.5
2. The cross price elasticity of demand for the commodity is 0.667
3. The cross price elasticity of demand is 0.8
What is Elasticity of Demand?The degree to which demand reacts to a change in an economic component is known as elasticity of demand. The most prevalent economic component considered when calculating elasticity is price. Income level and the accessibility of substitutes are further considerations. Elasticity gauges how demand changes in response to shifting economic conditions.
Given:
1. The demand for pen decreased from 100 to 70.
So, the percentage change in quantity
= (100 -70) / 100 = 0.3 = 30%
percentage change in the price
= (5 - 2) / 5
= 3/5
= 60 %
So, Cross price elasticity = 30% / 60% = 0.5
2. The quantity demanded of a commodity decreased from 50kg to 30kg.
So, the percentage change in quantity
= (50- 30)/50
= 40%
and, percentage change in price
= (8- 5)/5
= 60%
Then, cross price elasticity
= 40% / 60%
= 0.6667
Now, If the price of the commodity rather decreased from Gh¢5.00 to Gh¢2.50
So, the percentage change in price
= (5 - 2.5)/5
= 50%
Then, cross price elasticity
= 40% / 50%
= 0.8
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i bet you cant solve this...
After hip surgery, your physical therapist tells you to slowly return to walking. The therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter. How many weeks will it be before you are up to 45 minutes of walking per day?
10
11
9
13
Answer:
9
Step-by-step explanation:
figure it yourself...... .... ....
Solve the LP problem. If no optimal solution exists because there is no Solution Set, enter EMPTY. If no optimal solution exists because the region is unbounded, enter UNBOUNDED. Note that an unbounded region can still have an optimal solution while a bounded region is guaranteed to have optimal solutions. HINT [See Example 1.] Minimize c = x + 2y subject to x + 3y 2 28 5x + y 2 28 x > 0, y = 0. (X,Y)= ( ) +-/7.14 points My Notes Solve the LP problem. If no optimal solution exists because there is no Solution Set, enter EMPTY. If no optimal solution exists because the region is unbounded, enter UNBOUNDED. Note that an unbounded region can still have an optimal solution while a bounded region is guaranteed to have optimal solutions. HINT [See Example 1.] Maximize and minimize p = x + 2y subject to x + y28 x + y s 10 X-V58 x-y -8. Minimum: p = (x,y) =(
The optimal solution to the LP problem is (x,y) = (8,10). The objective function is minimized at this point, with a minimum value of 18.
We can solve this LP problem by using the graphical method.
First, we plot the constraints:
x + 3y <= 28 --> y <= -(1/3)x + 28/3
5x + y <= 28 --> y <= -5x + 28
x >= 0
y >= 0
Next, we find the feasible region formed by the intersection of these constraints. This region is a bounded polygon and is shown in blue in the figure below.
Finally, we find the point in the feasible region that minimizes the objective function c = x + 2y. We do this by plotting the objective function as a straight line with slope equal to 2 and y-intercept equal to 0. The line should pass through the feasible region and intersect it at the point with the minimum value of c.
From the figure, we can see that the line intersects the feasible region at the point (8, 10), which is the minimum value of c = x + 2y, with a minimum value of 18.
Therefore, the optimal solution to the LP problem is (x,y) = (8,10).
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The ratio of the number of boys to the number of girls in choir is 5 to 4. There are 63 students in the choir. How many boys are in the choir?
Based on the ratio of the number of boys to the number of girls in choir, 5:4, the number of boys is 35.
What is the ratio?The ratio refers to the relative size of a value, variable, or number to another.
Ratios are the quotients of a number or value and another value, which is the denominator.
As fractional values, ratios can be expressed in fractions, decimals, or percentages.
The ratio of boys to girls = 5:4
The sum of ratios = 9 (5 + 4)
The total number of students in the choir = 63
The number of boys = 35 (63 x 5/9)
The number of girls = 28 (63 x 4/9)
Thus, we can conclude that there are 35 boys and 28 girls in the choir.
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determine if the order pair (-1, -5) is a solution to inequality y < -3/4x - 1
No, because (-1, -5) is above the line.
Yes, because (-1, -5) is below the line.
No, because (-1, -5) is on the line.
Yes, because (-1, -5) is on the line.
Is the ordered pair (-1, -5) is a solution to inequality y < -3/4 x - 1
No, because (-1, -5) is above the line.
How to find if the ordered pair is a solutionThe inequality y < -3/4x - 1 represents a line on a coordinate plane.
The inequality symbol "<" means that the values of y that satisfy the inequality are those that are strictly less than the value of the right-hand side of the equation.
So, for any given x-value, all y-values that are less than the corresponding y-value on the line satisfy the inequality.
In this case, when x = -1, the corresponding y-value on the line is -3/4 * -1 - 1 = 1/4.
Since -5 is greater than 1/4, it means that (-1, -5) is above the line and does not satisfy the inequality y < -3/4x - 1.
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what is x if 3x+4=19
3x + 4 = 19
3x = 19-4
3x = 15
[tex]x = \frac{15}{3} \\ [/tex]
x = 5
What is the area of the triangle?
Write your answer as a fraction or as a whole or mixed number.
10 3/4 mm height
10 2/3 mm base
Answer: 57 1/3
Step-by-step explanation:
Area = (height * base) divided by 2
A = (b*h)/2
10 3/4 times 10 2/3 = 114 2/3
114 2/3 divided by 2 is 57 1/3
Answer: 57 1/3
Area of a triangle= 1/2*base*height
A=1/2* 10 3/4* 10 2/3
1/2* 10 3/4= 5 3/8
5 3/8 * 10 2/3 =57 1/3
Step-by-step explanation: Hope this helps!! :)) Mark me brainliest ! :))
off the production line, there is a 3.7% chance that a candle is defective. if the company selected 45 candles off the line, what is the standard deviation of the number of defective candles in the group? homework help: 3vd. mean, variance, and standard deviation for binomial experiments links to an external site.(1:28) 3dh. mean, variance, and standard deviation of a binomial variable links to an external site. (docx) group of answer choices 1.60 0.25 1.67 1.27
The standard deviation of the number of defective candles in a group of 45 candles selected off the production line would be 1.67.
This can be calculated using the formula for the standard deviation of a binomial distribution:
sqrt(np(1-p))
where:
n = 45 (the sample size)
p = 0.037 (the probability of a defective candle)
Plugging in the values:
sqrt(45 * 0.037 * (1 - 0.037)) = sqrt(45 * 0.037 * 0.963) = sqrt(1.67) = 1.67
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PLEASE HELP NOW! GRADPOINT
WHICH SYSTEM IS THE SOLUTION OF THE GRAPH?
Option B is correct, y≥-4 and y≤-x+4 is the system of solutions of the given graph.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the given graph a line is passing at y=-4
and the shading is towards the origin so the inequality will be y≥-4.
The other line is passing through points (4,0) and (0,4)
Slope=4/-4=-1
So equation of line is y=-x+4
and the shading is y≤-x+4
Hence, option B is correct, y≥-4 and y≤-x+4 is the system of solutions of the given graph.
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which of the following is not true of the u.s. rule?multiple choicecan involve more than one payment before maturity datecan use 365 days in its calculationsallows borrower to receive proper interest creditscalculate interest on principal from date of loan to date of first payment
None of the above is the correct answer. There is no answer in the given choices.
The U.S. Rule produces no compounding of interest in that any unpaid accrued interest is accumulated separately and is not added to the principal.
At maturity, using the U.S. rule, the interest calculated from the last partial payment is subtracted from the beginning balance and added to the adjusted balance.
Under U.S. Rule, unpaid accrued interest is accumulated separately and is not added to the principal. In addition, interest is not calculated until payment is made.
It also allows the borrower to receive proper interest credits. This rule defines that any partial loan payment first covers any interest that has built up, and the remainder of the partial payment will decrease the loan principal.
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The sum of 21 and 4, doubled
21
The terminal side of angle θ intersects the unit circle in the first quadrant at x=8/21. What is the value of secθ?
The value of the secθ for the unit circle in the first quadrant is 21/8.
What are terminal angles?The terminal sides coincide at the same angle whether the angles are rotated clockwise or anticlockwise. A ray's rotation around its starting point is quantified by an angle. The starting side of that angle refers to the original beam, and the terminal side denotes the ray's final position following its rotation.
Given The terminal side of the angle, θ intersects the unit circle in the first quadrant at x=8/21
which means cosθ = 8/21
and we know secθ is the inverse of cosθ
so secθ = 1/cosθ
and the unit circle in the first quadrant so the value of secθ will be positive.
secθ = 1/(8/21)
secθ = 21/8
Hence the value of secθ is 21/8.
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You are designing an obstacle course along a straight path. The distance between obstacle
three and obstacle seven is the same as the distance between obstacle four and obstacle nine. Show that the
distance between obstacle three and obstacle four is the same as the distance between obstacle seven and obstacle
nine.
d = 2d/3 = 4d/3, which implies that the distance between obstacle three and obstacle four is the same as the distance between obstacle seven and obstacle nine.
What do you mean by Distance?In mathematics, distance refers to a metric of the separation between two points or objects. It is often thought of as a measure of the length of the shortest path between two points. Distance can be represented in various forms such as Euclidean distance, Manhattan distance, and others. In Euclidean distance, the distance between two points is calculated using the Pythagorean theorem, while Manhattan distance is calculated as the sum of the absolute differences of their coordinates. Distance is widely used in various fields such as physics, geography, computer science, and engineering.
Let's call the distance between obstacle three and obstacle four as "d". Similarly, we can call the distance between obstacle seven and obstacle nine as "d".
The distance between obstacle three and obstacle seven is also "d".
So, the total distance between obstacle three and obstacle nine is 2d + d = 3d.
And the total distance between obstacle four and obstacle seven is d + d = 2d.
Since the distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine, we have 3d = 2d.
Therefore, d = 2d/3.
Dividing both sides of the equation by d, we get 3 = 2(2/3) = 4/3.
So, d = 2d/3 = 4d/3, which implies that the distance between obstacle three and obstacle four is the same as the distance between obstacle seven and obstacle nine.
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