Step-by-step explanation:
Rearrange w = 3(2a + b) - 4 to make a the subject:
w = 3(2a + b) - 4
expand right side:
w = 6a + 3b - 4
add 4 to both sides:
w + 4 = 6a + 3b - 4 + 4
w + 4 = 6a + 3b
subtract 3b from both sides:
w + 4 - 3b = 6a + 3b - 3b
w + 4 - 3b = 6a
flip flop equation for readability ease:
w + 4 - 3b = 6a becomes:
6a = w + 4 - 3b
divide both sides by 6:
6a/6 = (w + 4 - 3b)/6
a = [tex]\frac{1}{6}w + \frac{4}{6} -\frac{3}{6}b[/tex]
reduce:
a = [tex]\frac{1}{6}w + \frac{2}{3} -\frac{1}{2}b[/tex]
Now, arrange right side of equation so variables are ordered alphabetically.
Answer: [tex]a = -\frac{1}{2}b +\frac{1}{6} w+\frac{2}{3}[/tex]
The perimeter of the front of an aquarium is 230m and its length is 85m. What is the width of the front of the aquarium?
The width of the front of the aquarium is 30m
How to determine the value of the widthThe formula for calculating the perimeter of a rectangle is expressed as;
P = 2( l + w)
Given that the parameters are;
P is the perimeter of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that the values are;
Perimeter = 230m
Length = 85m
Width = w
Substitute the values, we get
230 = 2(85) + 2w
expand the bracket
2w = 230 -170
subtract the values
2w = 60
Make 'w' the subject
w = 30m
Hence, the value is 30m
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9^-5*9^-3 Rewrite using a single positive exponent plssss
Answer:
[tex]\frac{1}{9^{8}}[/tex]
Step-by-step explanation:
When multiplying two numbers with exponents with the same base, you simply add the two exponents together, even if they're negative:
[tex]9^{-5}*9^{-3} =9^{-8}[/tex]
When a number has a negative exponent ([tex]x^{-2}[/tex]) it means that the number is equal to 1/that number ([tex]\frac{1}{x^{2}}[/tex])
[tex]9^{-8}=\frac{1}{9^{8}}[/tex]
The graph shows two functions, f(x) and g(x).
If the functions are combined using addition, which
statements describe the resulting graph h(x)? Check
two options
O domain: x 2 -2
O domain: x 22
O The point (2, 2) is on h(x).
O The point (-2, 0) is on h(x).
O The point (0, -3) is on h(x).
The graph shows two functions, f(x) and g(x). So, the statements that describe the resulting graph h(x) is point (-2,2) is on h(x)
What is graph?A graph is described as the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the question above, we have two functions f(x)=x²-2 and g(x)=x²+2 by adding the function we will get the combined function.
The graph that the function is varying from the coordinates (-2,2) is seen on the attached graph.
Therefore, we can conclude that the graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)
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The vertices of a figure are A(2,-2), B(4,-1),C(4,-3),and D(2,-4).
Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image.
Check the picture below.
Given that both p and p + 1 are prime, what is the smallest composite whole number
that is not divisible by p or p + 1?
Answer:
39
Step-by-step explanation:
circles of radii , and are mutually externally tangent, where and are relatively prime positive integers. find
The ratio of the areas of the two circles equals the square of the ratio of their radii: = 1/4
Let O1 be the center of the larger circle and O2 be the center of the smaller circle. T is the tangent point between the two circles.
The distance between their centers, O1O2, is equal to the sum of their radii, i.e., r1 + r2.
The Pythagorean theorem gives us:
(O1O2)^2 = r1^2 + r2^2
By substituting r1, r2, and O1O2 values, we obtain:
(r1 + r2)^2 = r1^2 + r2^2
By broadening and simplifying, we get:
2r1r2 = r2^2
When both sides are divided by r22, we get:
2r1/r2 = 1
So, r1/r2 = 1/2. r2 = 2r1.
The ratio of the areas of the two circles equals the square of the ratio of their radii:
A1/A2 = (r1/r2)^2 = 1/4
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Please help!!! I suck at algebra and this is middle school stuff:((
Answer:
77
Step-by-step explanation:
1. solve the first part by plugging in 7 for y.
14(7)+37/5
98+37/5
135/5
27
2. then solve the second part by plugging in 7 for y.
8(2(7)-1)
8(14-1)
104
3. then subtract 27 from 104
104-27=77
A club’s first meeting was attended by many people. The second meeting was attended by 6 times as many people as the first meeting. If 72 people attended the second meeting, what equation could you use to find how many people attended the first meeting, ? A) 72 x p = 6 B) 6 - p = 72 C) 6 ÷ p = 72 D) 6 x p = 72
Answer:
12
Step-by-step explanation:
6
×12=72
=72answer is=12
Answer:
Step-by-step explanation:
srry need the points
For the following exercise, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years: (46, 250), (48, 305), (50, 350), (52, 390), (54, 410). Use linear regression to determine a function y, where the profit in thousands of dollars depends on the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
To calculate the equation, we first need to calculate the slope and the y-intercept. Since we have 5 points, we can calculate the slope using the formula m=(y2-y1)/(x2-x1). For this problem, we'll use (46,250) and (54,410). Plugging the values into the formula, we get m = (410-250)/(54-46) = 4.5.
Next, we need to find the y-intercept, which is 200. The formula for this is b = y-mx. For our problem, we'll use (46,250). Plugging in the values, we get 200 = 250 - 4.5(46), so b = 200.
Therefore, the linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.
The length of the leg in the triangle is 4 units
How to find the length of the leg in the triangleFrom the question, we have the following parameters that can be used in our computation:
The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.The length of the other leg using Pythagorean Theorem is
Other Leg = √(Hypotenuse² - One Leg²)
So, we have
Orher Leg = √(5² - 3²)
Evaluate
Other leg = 4
Hence, the other leg is 4 units
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Using the region names in the image below, select all regions that represent:
A' ∩ B' ∪ C
3 group Venn Diagram with Roman numeral labeled regions
Not A intersection not B union C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
The Venn diagram shown to Region V: Items in A, B, and C are represent A' ∩ B' ∪ C
It is given that the diagram we need to find the regions represent the set.
What do you mean by Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.
So from the Venn diagram, the item represents the regions four, five, six and seven.
Therefore, it can be written us for Union Fight, Union Six, Union Seven. Therefore, we concluded that the regions represent see R. C.
Which is equal to for Union Fighting Union Six, Union Seven.
We have here, region represent A' ∩ B' ∪ C
Therefore, the Venn diagram shown to regions represent
A' ∩ B' ∪ C is Region V: Items in A, B, and C.
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6 x 1/3 _ 6
please explain or give and answer I beg of u
The complete expression is 6 * 1/3 = 1/3 * 6
How to complete the expressionFrom the question, we have the following parameters that can be used in our computation:
6 x 1/3 _ 6
Express properly
So, we have the following representation
6 * 1/3 = _6
Represent the blank with x
6 * 1/3 = x * 6
So, we have
2 = 6x
Divide by 6
x =1/3
Hence, solution to the expression is 1/3
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No entiendo nada de la fotografía
The numeric values of the graphed function are given as follows:
f(-2) = 2.f(0) = 3.f(4) = 1.How to obtain the numeric values from the graph?To obtain the numeric values from the graph, we must plot a vertical line at each x-coordinate, and then verify where the vertical line intersects the graph.
At x = -2, the vertical line would intersect the graph at y = 2, hence:
f(-2) = 2.
At x = -0, the vertical line would intersect the graph both at y = 1 and y = 3, however y = 3 has the closed circle, hence hence:
f(0) = 3.
At x = 4, the vertical line would intersect the graph at y = 1, hence:
f(4) = 1.
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Define units for the time that Marshall has the beans and the amount of coffee beans that Marshall has left.
After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.
How to calculate the amount of coffee left?The amount of ground coffee that Marshall bought for his office machine = 40 ounces
The quantity of coffee he uses per week in his office = 5 ounces.
Therefore for 4 weeks would be= ?
But, 1 week = 5 ounces
4 weeks = X
make X the subject of formula;
X = 5×4 = 20 ounces
The amount of ground coffee that will remain = 40-20 = 20 ounces.
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You are working with a hypothetical binary computer that stores integers as unsigned 4-bit words. What is the largest non-negative integer than can be represented on this computer?
The largest non-negative integer than can be represented on this computer is given as follows:
15.
How to obtain the largest number that can be represented with n bots?The largest non-negative integer that can be represented on an unsigned machine with n bits is given as follows:
N = 2^n - 1.
For this problem, the machine is of 4 bits, hence the parameter n is given as follows:
n = 4.
Hence the largest non-negative integer than can be represented on this computer is obtained as follows:
N = 2^4 - 1
N = 16 - 1
N = 15.
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Please help, I suck at algebra!
Answer: 3 1/5
Step-by-step explanation:
I nelieve fdhat the answer to thisxquestion is 3 1/5
At noon, the temperature in Hampstead, Virginia was 50℉
. By midnight, the temperature had fallen to 10℉
. What was the change in temperature over the 12-hour period?
The change in temperature over the 12-hour period was 50℉ - 10℉ = 40℉.
A gardener makes a new circular flower bed. The bed is twelve feet in diameter. Calculate the circumference and the
area of the circular flower bed.
circumference=12 feet, area = 12 square feet
circumference=12r feet, area = 144
square feet
circumference = 6 feet, area = 36
square feet
circumference 12 feet, area = 36 square feet
The circumference and the area of the circular flower bed are given as follows:
Circumference: 12π units.Area: 36π units squared.What are the area and the circumference of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The radius is half the diameter, hence it has the value given as follows:
r = 0.5d
r = 0.5 x 12
r = 6.
Then the area is obtained as follows:
A = π x 6²
A = 36π units squared.
The circumference is given by the multiplication of the diameter by π, hence:
C = 12π units.
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When a family has dental insurance, they are responsible for paying the deductible and any amount charged by their dentist that their insurance does not cover. A dental insurance policy states its family coverage as:
• $250 deductible (this means the family is responsible to pay for the first $250 of treatment)
•80% payment for charges that exceed $250 but do not exceed $1500
•50% payment for charges that exceed $1500
***The percent listed in the coverage is the amount the insurance company pays for (Hint: if the insurance company pays for 80% of the charges, then what percent does the family have to pay for?) ***
a) What is the family's payment if the dental charge is $680?
b) What is the family's payment if the dental charge is $4500?
c) Find a model that relates payments and charges.
The total payment of the family is given as $336
The family`s payment would be $2725
The model that elates payments and charges is Payment = $250 + (1 - insurance payment percentage) * (charge - $250)
How to solve for the paymenta) If the dental charge is $680, then the family's payment is:
Deductible: $250 (the family has to pay this first)
Remaining charges: $680 - $250 = $430
The insurance company pays for 80% of the remaining charges, which is 0.8 * $430 = $344
Therefore, the family has to pay for 100% - 80% = 20% of the remaining charges, which is 0.2 * $430 = $86
So, the total payment by the family is $250 + $86 = $336
b) If the dental charge is $4500, then the family's payment is:
Deductible: $250 (the family has to pay this first)
Remaining charges after deducting the deductible: $4500 - $250 = $4250
The insurance company pays for 80% of the remaining charges that do not exceed $1500, which is 0.8 * $1500 = $1200
So, the remaining charges for the family to pay after the insurance pays for the first $1500 of the remaining charges: $4250 - $1500 = $2750
The insurance company pays for 50% of the remaining charges that exceed $1500, which is 0.5 * $2750 = $1375
Therefore, the family has to pay for 100% - 50% = 50% of the remaining charges that exceed $1500, which is 0.5 * $2750 = $1375
So, the total payment by the family is $250 + $1200 + $1375 = $2725
c) The model that relates the payments and charges is:
Payment = $250 + (1 - insurance payment percentage) * (charge - $250)
where the insurance payment percentage is 80% if the charge is between $250 and $1500, and it is 50% if the charge exceeds $1500.
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Nikhil and Mae work at the same company. Nikhil has been at the company 6 times as long as Mae. Nikhil's time at the company is 8 more than 4 times Mae's. The following system of equations models the scenario:
x = 6y
x = 8 + 4y
How many years has each person been employed by the company?
Nikhil has been with the company for 36 years, while Mae has been there for 6 years.
Nikhil has been with the company for 30 years, while Mae has been there for 5 years.
Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
Nikhil has been with the company for 18 years, while Mae has been there for 3 years.
The number of years that each person would have been employed would be that Nikhil has been with the company for 24 years, while Mae has been there for 4 years. That is option C.
How to calculate the number of years each person has been employed?Nikhil has been at the company 6 times as long as Mae.
That is,
x = 6y-----> equation 1
where X= Nikhil
y = Mae
Nikhil's time at the company is 8 more than 4 times Mae's.
That is,
x = 8 + 4y----> equation 2
To solve for each years, substitute for X into equation 2;
6y = 8+4y
8 = 6y-4y
8 = 2y
y = 8/2 = 4
Substitute y into equation 1;
X= 6×4
X= 24
Therefore, Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
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Answer: Option C. Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
Step-by-step explanation:
find the following probabilities for the standard normal distribution in r or using the standard normal table. note i always recommend drawing the distribution. (round your answers to four decimal places.)
The probabilities for the standard normal distribution in r or using the standard normal table are
a) P(X<2.18) = 0.9854
b)P(X>2.18)= 0.0146
c) P(<-2.49) = 0.0064
The standard normal table is a mathematical table that allows us to know the percentage of values below the z-score (left) of the standard normal distribution. This is the "bell-shaped" curve of the standard normal distribution. It is a normal distribution with mean 0 and standard deviation 1. Using the Z-table:
Go to the row representing the ones place and the first decimal place (10's place) of the Z-score.Go to the column that represents the second decimal place (100ᵗʰ) of the z-score.Cross the rows and columns from steps 1 and 2. This result represents the probability that the random variable Z is less than the value Z, that is p(Z < z).Now, we have to determine the probability value for (a) , (b) and (c) .
a) P(X < 2.18) = P( Z< 2.18) = intersection point of row value 2.1 and column 0.08 = 0.9854
b) P(X >2.18) = P( Z> 2.18) = 1 - P( Z< 2.18)
= 1 - 0.9854 = 0.0146
c) P(X < -2.49) = P(Z < -2.49) = intersection point of row value -2.4 and column 0.09 = 0.0064.
Hence, we got all the required probability values.
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Complete question:
Find the following probabilities for the standard normal distribution in R or using the standard normal table. NoteI always recommend drawing the distribution. (Round your answers to four decimal places.) ### Example R code mu = 0; sigma = 1; x = x; # Note you will have to change the value of x. pnorm(x,mu,sigma)
(a) P(X < 2.18)
b) P(X >2.18)
(c) P(X < -2.49)
the park sprinkler can spray 1748 gallon of water on the grass in 38 minutes how many gallon can they spray in one minute
The spray rate of the park sprinkler is equal to 46 gallons per minute.
What is the spray rate of a park sprinkler?
In this problem we find that a park sprinkler that can spray a capacity of 1,748 gallon of water in a time of 38 minutes and we are asked to calculate the spray rate by the following fomula:
r = Q / t
Where:
Q - Capacity, in gallons.t - Time, in minutes. r - Spray rate, in gallons per minute.If we know that Q = 1748 gallon and t = 38 min, then the spray rate is:
r = (1748 gallon) / (38 min)
r = 46 gallons per minute
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The table shows the number of students graduating from a high school in selected years. Use a calculator to write a quartic model for the number of graduates in a given year since 1980. Then use the model to estimate the number of graduates in 1992.
P(x) ≈ 0.04x4 − 1.06x3 + 8.99x2 − 40.05x − 177.92
The estimated the number of graduates in 1992 is 367.
P(x) ≈ 0.14x3 + 1.95x2 − 20.17x − 191.86
The estimated the number of graduates in 1992 is 399.
P(x) ≈ −0.04x4 + 1.06x3 − 8.99x2 + 40.05x + 177.92
The estimated the number of graduates in 1992 is 367.
P(x) ≈ 0.14x3 − 1.95x2 + 20.17x + 191.86
The estimated the number of graduates in 1992 is 367.
The quartic regression equation is (a) y = -0.04x^4 + 1.06x^3 - 8.99x^2 + 40.05x + 177.92 and the estimated the number of graduates in 1992 is 367
How to determine the quartic regression equationFrom the question, we have the following parameters that can be used in our computation:
(-1,8), (5,-4), (7,8), (2,-6)
Using a graphing calculator, we have the following summary:
a0 = 177.9198a1 = 40.0522a2 = -8.9931a3 = 1.0627a4 = -0.0402Standard Error of Regression: 0.1001Coefficient of determination R²: 1The model from the above summary is
y = -0.0402x^4 + 1.0627x^3 - 8.9931x^2 + 40.0522x + 177.9198
Approximate
y = -0.04x^4 + 1.06x^3 - 8.99x^2 + 40.05x + 177.92
In the year 1992, we have
x = 12
So, we have
y = -0.04 * 12^4 + 1.06 * 12^3 - 8.99 * 12^2 + 40.05 * 12 + 177.92
Evaluate
y = 367
The estimated the number of graduates in 1992 is 367
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Find market value and preferred shares and common shares
Answer:
Step-by-step explanation:
eres un pendejo
Which segment of this graph shows a decreasing velocity?
Answer:
7
Step-by-step explanation: just do it
Calculate each quotient.
2 divided by 1.176
Answer:
Step-by-step explanation:
The quotient of 2 divided by 1.176 can be calculated as follows:
2 ÷ 1.176 = 1.70860927152318
Therefore, 2 divided by 1.176 is equal to 1.70860927152318.
suppose that in a year an american worker can produce 100 shirts or 20 computers and a chinese worker can produce 100 shirts or 10 computers
For each country, graph of computer the production possibilities frontier. Suppose that without trade the workers in each country spend half their time producing each good. Identify this point in your graphs.
Who has the comparative advantage in the production of shirts? What about for computers?
China has the comparative advantage in the production of shirts, while the US has the comparative advantage in the production of computers.
If these countries were open to trade, which country would export shirts? Give a specific numerical example and show it on your graphs. Which country would benefit from trade?
China would export 50 million shirts in exchange for 5 million computers (or more if they can). Trade would benefit the US since it will only need to trade 5 million computers in exchange for 50 million shirts, and it will still have 15 million computers that it can consume or trade with come other country.
Explain at what price of computers (in terms of shirts) the two countries might trade.
the minimum and maximum prices would be 5 to 10 shirts per computer. If the price of shirts per computer is 10 or near 10, then the US wins more. If the price of shirts per computer is 5 or near 5, then China wins more.
opportunity cost of producing 1 shirt in the US = 20/100 = 0.2 computers
opportunity cost of producing 1 computer in the US = 100/20 = 5 shirts
opportunity cost of producing 1 shirt in China = 10/100 = 0.1 computers
opportunity cost of producing 1 computer in China = 100/10 = 10 shirts
without trade:
total production of shirts in the US = 50 million
total production of computer in the US = 10 million
total production of shirts in China = 50 million
total production of computer in China = 5 million
with trade:
total production of computers in the US = 20 million
total production of shirts in China = 100 million
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A phone receives signals from a transmitter that is 13 km west and 21 km south of it.
What is the bearing from the phone to the transmitter?
Give your answer to the nearest degree.
To find the bearing from the phone to the transmitter, we can use the arctangent function.
The formula to find the bearing is:
θ = atan2(dy, dx)
where dx = difference in x-coordinates and dy = difference in y-coordinates.
Here, dx = -13 km and dy = -21 km, since the transmitter is located to the west and south of the phone.
Therefore, the bearing is:
θ = atan2(-21, -13) = atan2(21, 13) = 63.434948822922° (to the nearest degree)
So the bearing from the phone to the transmitter is approximately 63.4°.
find the values of x and y
The value of x is 10 and y is -5.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Three parallel lines.
From the diagram,
we have system of equations
6x + 2y + 130 = 180
2x - 4y + 140 = 180
Simplifying both equations,
3x + y = 25....(1)
x - 2y = 20,....(2)
Now, substituting the value of x from the equation 2 to equation 1,
7y = 25 - 60
y = -5.
And x = 10.
Therefore, the value of x is 10 and y is -5.
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complete solutions manual a first course in differential equations with modeling applications ninth edition differential equations with boundary-vary problems tenth edition
A first course in differential equations with modeling applications ninth edition is a textbook that covers the basics of differential equations and their applications in mathematical modeling.
It begins with an introduction to the concepts of differential equations, including the definition, solution methods, and the concept of modeling. It then covers topics such as first-order linear equations, higher-order linear equations, systems of linear differential equations, and nonlinear equations. It also has a chapter on boundary-value problems, which is a type of differential equation that involves a set of boundary conditions that must be satisfied for the solution to be valid.
In order to solve differential equations with boundary-value problems, we must first define the boundary conditions that must be satisfied for the solution to be valid. This involves setting up the boundary conditions in terms of the dependent and independent variables of the equation. We then solve the equation using the boundary conditions and the equation itself. The solution is then used to calculate values for the independent and dependent variables at the boundary points. Finally, we can verify the solution by substituting the calculated values into the equation and seeing if the solution is valid.
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