The Joint Pruf of bivariete (x, y) is given by Pxy (x₁, y₁) = P(X=²
Answers
The joint probability of bivariate (x, y) is given by Pxy (x₁, y₁) = P(X= x₁, Y=y₁). This probability is used to compute the probability of multiple events. It is a statistical tool used to calculate the likelihood of two events occurring together.
The joint probability is often used in statistical modeling and machine learning to predict the likelihood of multiple events occurring at the same time.
For example, suppose we wanted to determine the likelihood of a particular stock price increasing and the economy experiencing a recession. We could use the joint probability of these two events to estimate the likelihood of them occurring together.
The formula for joint probability is P x y (x₁, y₁) = P(X=x₁, Y=y₁), where P x y represents the joint probability, X and Y are the random variables, and x₁ and y₁ represent specific values of those variables.
Joint probability can be calculated using a contingency table, which shows the possible combinations of values for two or more variables and their corresponding probabilities.
The joint probability of two events A and B can be calculated by multiplying their individual probabilities and the probability of their intersection. P x y (x₁, y₁) = P(X=x₁, Y=y₁) ≥ 0
The sum of all the possible joint probabilities of x and y is equal to one.
This means that all possible outcomes for x and y have been taken into account. It is important to note that the joint probability of two events is only valid if the events are independent.
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Related Questions
Please help I need to turn this in
Answers
Answer:
14x
Step-by-step explanation:
State if the two triangles are congruent. If they are, state how you know.
(look at the picture)
Answers
Answer:
Step-by-step explanation:
yes congruent, by AAS
the angles are stating , w/ the little red lines that they are the same.. so we know two angles of the triangles are the same, and we also know that one side touching is the same. so yes.. AAS.
21. A scuba diver dives to a depth of 50 feet,
then rises 15 feet, then rises 20 feet. Write an
addition expression to describe this situation.
Then determine the sum and explain its
meaning.
Answers
Answer:
73
Step-by-step explanation:
Based on the given conditions, formulate: 20+50+15-12
Calculate the sum or difference:70+15-12
Calculate the sum or difference:85-12
Calculate the sum or difference:73
get the result:73
Answer:
50 - 15 = 35
35 + 20 = 55
Total amount of feet diven : 55 feet
Brainlist!
Show all steps and I will make you Brainlist.
Answers
Answer:
The height of the tree to the nearest foot is 75.
Step-by-step explanation:
The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.
tangent = opposite/adjacent
\(\frac{tan(59)}{1} = \frac{h}{45}\)
h = tan(59) * 45
h ≈ 74.89
To the nearest foot, 74.89 is 75 ft.
a researcher calculated that the total sum of squares for a regression equation was 153.7, and the error sum of squares was 82.6. what is the proportionate reduction in error for knowing the value of the independent variable?
Answers
The proportionate reduction in error for knowing the value of the independent variable is 0.54.
What is independent variable ?The variable which does not depend on any variable and hence independent are known as independent variable.
Given that,
sum of squares for a regression equation was 153.7 = SST
error sum of squares was 82.6 = SSE
SS (reg) = SST - SSE
153.7 - 82.6
SS(reg) = 71.1
The proportionate reduction in error for knowing the value of the independent.
= 1 - \(\frac{(SS)reg}{SST}\)
= 1 - \(\frac{71.1}{153.7}\)
= 1 - 0.46
= 0.54
The proportionate reduction in error for knowing the value of the independent variable is 0.54.
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write an equation in
Slope Intercept
from of the line that passes through
the
Give in Points
(-5,19) (5,3)
Answers
Step-by-step explanation:
3-19/5--5 = -16/10 = -8/5
y- 3 = -8/5(x-5)
y = -8/5x +11
Answer:
y=-8/5x+11
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-19)/(5-(-5))
m=-16/(5+5)
m=-16/10
simplify
m=-8/5
y-y1=m(x-x1)
y-19=-8/5(x-(-5))
y-19=-8/5(x+5)
y=-8/5x-40/5+19
y=-8/5x-8+19
y=-8/5x+11
The measure of an angle is 119.4°. What is the measure of its supplementary angle?
Answers
Answer:
180 - 119.4 = 60.6
So the answer is 60.6
Answer:
60.6°
Step-by-step explanation:
Supplementary angles equal 180 degrees. So we can show this with the following equation:
119.4 + x = 180
where x is the measure of the other supplementary angle.
If we subtract 119.4 from both sides, we get the the value of x, which is 60.6.
Zoe is driving on a long road trip. She currently has 13 gallons of gas in her car. Each
hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in
the tank after driving for 2 hours? How much gas would be left after t hours?
Gas left after 2 hours:
Gas left after t hours:
Answers
Gas left after 2 hours is 1.5 gallons and the function that represent the gas which is left in the tank after driving for t hours is 13 - 0.75t gallons.
Zoe is driving on a long road trip.
The amount of gas she has in her car = 13 gallons.
It is given that each hour that she drives, functions her car uses up 0.75 gallons of gas.
So, Gas used in the car for one hour = 0.75 gallons
Gas used in the car for two hours = 0.75*2 = 1.5 gallons
Hence, Gas left in the tank after driving for 2 hours = 13 - 1.5 = 11.5 gallons.
Now,functions
Gas used in the car for t hours = 0.75*t = 0.75t gallons
Gas left in the tank after driving for t hours = 13 - 0.75t gallons.
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Check each true statement, and only the true statements. The domain for all variables is the set of integers.
Group of answer choices
∀x ∃y (x+2y=1)
∃y ∀x (x+2y=1)
∃x ∀y (x+2y=1)
∀y ∃x (x+2y=1
Answers
The domain for all variables is the set of integers.The correct answer is: ∀y ∃x (x+2y=1).
This statement is true because for any integer value of y, there exists an integer value of x that satisfies the equation x+2y=1. For example, if y=0, then x=1; if y=1, then x=-1; if y=2, then x=-3, and so on.
The other statements are not true for all integer values of x and y. For example, ∀x ∃y (x+2y=1) is not true because there are integer values of x for which there is no integer value of y that satisfies the equation (e.g. if x=2, then y= -0.5, which is not an integer). Similarly, ∃y ∀x (x+2y=1) and ∃x ∀y (x+2y=1) are not true because there is no single integer value of y or x that satisfies the equation for all integer values of x or y, respectively.
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CC has the following beginning balances in its stockholders' equity accounts on January 1, 2012: Common Stock, $100,000; Additional Paid-in Capital, $4,100,000; and Retained Earnings, $3,000,000. Net income for the year ended December 31, 2012, is $800,000. Court Casuals has the following transactions affecting stockholders' equity in 2012:
May 18 Issues 25,000 additional shares of $1 par value common stock for $40 per share.
May 31 Repurchases 5,000 shares of treasury stock for $45 per share.
July 1 Declares a cash dividend of $1 per share to all stockholders of record on July 15. Hint: Dividends are not paid on treasury stock.
July 31 Pays the cash dividend declared on July 1.
August 10 Reissues 2,500 shares of treasury stock purchased on May 31 for $48 per share.
Taking into consideration all the entries described above, prepare the statement of stockholders' equity for the year ended December 31, 2012.
Answers
Total stockholders’ equity 7,800,000
Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000
Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000
Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000
To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.
The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.
Calculations:Opening balance of common stock = $100,000
Opening balance of additional paid-in capital = $4,100,000
Opening balance of retained earnings = $3,000,000
Net Income for the year ended December 31, 2012 = $800,000
Retained earnings (Opening Balance) = $3,000,000
Add: Net Income for the year ended December 31, 2012 = $800,000
Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000
Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000
Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Validation of the model and answering the question "what are my options" occur in the ___ phase of the IDC.
A. choice
B. design
C. intelligence
D. implantation
Answers
Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.
The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.
In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.
In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.
Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.
The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.
Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.
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A compacted clay liner is to be constructed for the expansion of a landfill. The claywill be taken from a location ("borrow pit") where the in-place dry unit weight is
105 pcf and the water content is 9%. The soil will be excavated from the borrow
pit, moistened to increase the water content to 13.5% and then compacted to a final
dry unit weight of 118 pcf. The total final volume of the compacted fill will be
300,000 yd3. (note: 1 yd3 = 27 ft3)
a) How many cubic yards of soil must be excavated from the borrow pit?
b) How many gallons of water must be added to the excavated soil to raise
the water content to the final value (note: 1 ft3 = 7.48 gallons)?
Answers
Therefore, 1,502 gallons of water must be added to the excavated soil to raise the water content to the final value.
a) Given information: Total final volume of compacted fill = 300,000 yd3Final dry unit weight = 118 pcf
In-place dry unit weight = 105 pcf
Water content = 9%
Final water content = 13.5%1 y
d3 = 27 ft3
Let's calculate the volume of soil in cubic feet and then convert it to cubic yards.
Volume of soil in cubic feet= Total final volume of compacted fill/ (1 + (Final dry unit weight/ In-place dry unit weight) × (1 - Final water content/ Water content))
= 300,000 / (1 + (118/105) × (1 - 13.5/9))
= 300,000 / 1.104
= 271,447 ft3
So, the amount of soil to be excavated in cubic yards= 271,447 / 27
= 10,064.33 yd3
Therefore, about 10,065 cubic yards of soil must be excavated from the borrow pit.
b) Given information: Water content = 9%
Final water content = 13.5%
Volume of soil = 10,065 yd31 ft3
= 7.48 gallons
First, let's find out the volume of excavated soil in cubic feet and then calculate the amount of water to be added.
Volume of excavated soil in cubic feet= Volume of soil in cubic yards × 27
= 10,065 × 27= 271,455 ft3
Initial weight of excavated soil = Volume × Dry unit weight
= 271,455 × 105/ 144
= 197,951.25 pounds
Initial amount of water in the excavated soil= Initial weight of soil × Initial water content/ 100
= 197,951.25 × 9/ 100
= 17,818.6175 pounds or 2,378.381 gallons
To raise the water content from 9% to 13.5%, the amount of water to be added is= Final weight of soil × Final water content/ 100 - Initial amount of water
= (Initial weight of soil + Weight of water to be added) × 13.5/ 100 - 2,378.381
= (197,951.25 + Weight of water to be added) × 13.5/ 100 - 2,378.381
Weight of water to be added = 11,238.5279 pounds or 1,501.96 gallons
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I just need level two and three solved please
Answers
Answer:
intercepts: (0, 5/2) or (-5, 0)arbitrary point: (7, 6)Step-by-step explanation:
You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).
InterceptsWriting the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -2 = 1/2(x -(-1)) . . . . . using given slope and point
2y -4 = x +1 . . . . . . . . . . multiply by 2
x -2y = -5 . . . . . . . . . . . . add -1 -2y
Setting x=0 tells us the y-intercept is ...
0 -2y = -5
y = -5/-2 = 5/2
So, the y-intercept is (0, 5/2).
Setting y=0 tells us the x-intercept is ...
x -2(0) = -5
x = -5
So, the x-intercept is (-5, 0).
Arbitrary pointIt will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...
x -2y = -5
x = -5 +2y = -5 +2(6) = 7
Another point on the line is (7, 6).
__
Additional comment
If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.
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I really need help on this question, thank you!
Answers
Answer:
Your answer is D
Step-by-step explanation:
When we reflect the point which is at the coordinates (-2,4) we count how far it is from the Y line, it is 2 units away thus we must put our point on the Y line and count 2 to the other side giving us (2,4)
Hope this helps!
SOMEONE, PLEASE HELP ME!
Answers
Answer:
Find the heigh if a=550cm and r=7cm
C) 92.65%
To find the percent decrease in customers, we first need to find the difference in the number of customers between the two given hours.
Number of customers on Saturday from 6:00 p.m. to 7:00 p.m. = 68
Number of customers on Wednesday from 5:00 p.m. to 6:00 p.m. = 5
Difference in number of customers = 68 - 5 = 63
Next, we need to find the percent decrease in customers, which is given by:
(percent decrease) = (difference / original) x 100%
where "original" refers to the number of customers on Saturday from 6:00 p.m. to 7:00 p.m.
Plugging in the values, we get:
(percent decrease) = (63 / 68) x 100% ≈ 92.65%
Therefore, the percent decrease in customers from the given hour on Saturday to the given hour on Wednesday is approximately 92.65%.
What is the rate of change between the two given points? ..... help
Answers
If Judy uses 400 chocolate chips to make x cookies, write an expression that represents the number of chocolate chips in each cookie.
Answers
Answer:
y=\(\frac{400}{x}\)
Step-by-step explanation:
Answer: 400/x (over x} = Y {amount on each cookie}
Step-by-step explanation:
i need help pleaseeeeeee
Answers
By using the definition of inverse functions we can see that:
a) g(7) = -10
b)(-10,7) is a point on h(x).
c)(7, -10) is a point on j(x)
How to evaluate the functions?Remember that if two functions f(x) and g(x) are inverses, then:
f(y) = x
g(x) = y
And also g(f(x)) = x = g(f(x)).
Here we know that functions h(x) and j(x) are inverses, and we also know that:
h(-10) = 7
So for the input -10, we have the output 7.
Then, by using the relation written above, we know that for the inverse function we must have:
j(7) = -10
That is the answer for a.
And for b and c the notation is (input, output), then:
(-10, 7) is a point on h.(7, -10)is a point on jThese are the answers of points B and C of the question.
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Is it possible to have triangle whose sides have length 10.2 cm 5 8 cm and 4.5 cm give reason?
Answers
A triangle is a closed shape in geometry with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices P, Q, and R is represented as triangle △PQR. The most commonly seen examples of triangles are the signboards and sandwiches that are in the shape of a triangle.
Given Lengths of the ∆ -
10.2 cm
5.8 cm
4.5 cm
We know that by triangle formula,
The sum of any two sides of a triangle is always greater than the third side.
So, according to the given sides of the triangle that are 10.2, 5.8, 4.5.
(10.2 + 5.8) cm = 16 cm > 4.5 cm
(10.2 + 4.5) cm = 14.7 cm > 5.8 cm
(5.8 + 4.5) cm = 10.3 cm > 10.2 cm
Yet, it is also possible to have a triangle having sides 10.2 cm, 4.5 cm & 5.8 cm.
A triangle is just a simple polygon with three sides and three interior angles.
It is one of the basic structures in geometry in which the three vertices are joined with each other and it is denoted by the symbol △.
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Find the area of the rhombus
Answers
Answer:
A=27
Step-by-step explanation:
find the range of the function f(x)=2x+4
Answers
Answer:
(0,4)
Step-by-step explanation:
this is highest and only Y intercept. the range of a graph is all of the Y intercepts. and the domain of a graph is all of the x-intercepts
Solve w2 + 2 w - 24 = 0.
Answers
Answer:
w= -6
w= 4
Step-by-step explanation:
w= -b sqrt(b^2-4ac)
2a
let
a=1
b=2
c= -24
substitute values~
\(==========================================\)
In order to solve this equation for w, we need to factor it.
First, let's think of 2 numbers that multiply to -24 and add to 2.
These numbers are -4 and 6.
Check:
6×(-4)=-24 ✓
6+(-4)=6-4=2✓
Now, factor:
( ) ( )
That's how it should look like:
(w+ )( w- )
Now, instead of the blanks, plug in -4 & 6:
(w-4)(w+6)
Now, set each factor equal to 0:
w-4=0
w=4
w+6=0
w=-6
\(====================================\)
Notes:-Hope everything is clear.Let me know if you have any questions!Enjoy your day!Always remember: Knowledge is power!Answered by:-Nickname:-
\(\rule{1}{1}~\rule{2}{2}\mathbb{DiAmOnD}\)Elsie starts a food blog. In the first month, there are 46 new subscribers. Each month after that, the number of new subscribers
increases by 15 more than the number of new subscribers in the previous month. At this rate, what will be the total number of
subscribers after 8 months?
788
394
151
848
Answers
Answer:C 151
Step-by-step explanation:
7 * 15=105 + 46=151
Answer: 788
Step-by-step explanation:
(L3) A segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side is called the _____ of the triangle.
Answers
(L3) A segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side is called the incenter of the triangle.
The incenter of a triangle is an important point that can be constructed by drawing a perpendicular line from each vertex of the triangle to the opposite side, and then finding the intersection of these lines. This intersection point is equidistant from the three sides of the triangle, and is therefore the center of the circle that can be inscribed within the triangle.
The incenter also has the property that it is the point of concurrency of the angle bisectors of the triangle, meaning that it is equidistant from the three angles of the triangle as well. The incenter is used in a variety of geometric constructions and proofs, including the construction of the inscribed circle and the solution of problems involving the ratio of the sides of a triangle.
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two cylinders have the same size base but one is twice as tall. explain why the tallest cylinder does not have double the surface area
Answers
Answer: Since a cylinder has a circular base which is counted when measuring the surface area and is unchanged with a doubled height the surface area will increase but won't be doubled. It will only be doubled if the circle's radius is doubled aswell.
Step-by-step explanation: ^^ please mark 5 star and give thanks.
At age 45 when the deferred payments from his current contract ends, all-star shortstop Alex Rodriguez plans to have $230 million in savings from his baseball playing days. He wants two things from his savings: a 40-year ordinary annuity and $500 million at age 60 in order to purchase majority ownership in his native Miami's Florida Marlins. How large can his annual annuity payment be based on this information and assuming his savings can earn 8% annually after age 45 ? $6,069,727 $5,620,118 $6,906,832 $6,395,215
Answers
Therefore, the annual annuity payment can be approximately $6,069,727.
To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:
PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]
Where:
PMT = Annual annuity payment
PV = Present value of the annuity
r = Annual interest rate
n = Number of periods
Given:
PV = $230 million
r = 8% = 0.08
n = 40 years
Using the formula, we can calculate the annual annuity payment:
PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]
PMT ≈ $6,069,727
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In ΔGHI, g = 3.4 cm, i = 8.2 cm and ∠I=29°. Find all possible values of ∠G, to the nearest 10th of a degree.
Answers
Answer:
11.6°
Step-by-step explanation:
In ΔGHI, g = 3.4 cm, i = 8.2 cm and ∠I=29°. Find all possible values of ∠G, to the nearest 10th of a degree.
We solve the above question using Law of Sines
= g/sin G = I / sin I
Substituting
= 3.4/ sin G= 8.2/ sin 29
Cross Multiply
3.4 × sin 29 = sin G × 8.2
sin G = 3.4 × sin 29/ 8.2
G = arc sin[3.4 × sin 29/ 8.2]
G = arcsin [0.2]
G = 11.59653°
Approximately = 11.6°
∠G = 11.6°
obtain the deviance residuals (14.83) and plot them against the estimated model probabilities with a lowess smooth superimposed. what does the plot suggest about the adequacy of the fit of the logistic regression model?
Answers
The plot suggests that the logistic regression model is not adequately fitting the data.
The deviance residuals plot against the estimated model probabilities with a lowess smooth indicates how well the logistic regression model fits the data. A plot with residuals around zero suggests that the model is adequately fitting the data. In this case, the deviance residuals are around 14.83 which indicates a poor fit of the model. Therefore, the plot suggests that the logistic regression model is not adequately fitting the data.
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Answers
A custotuer requires during the next four months respectively 50,65,100, and 70 units of a commodity (no backlogs wllowed). Productions costs are $5,$8,$4, and $7 per unit during these months. The storage cost from one month to the next are $2 per unit (assessed on the end of the month inventory). Each unit at the end of the month 4 could be sold for $15 /unit. The production capacities for each month are 90, 75, 80 , and 50 units respectively. Currently, there are 15 units in inventory. Formulate a Linear Program that will minimize the objective function (sum of the production and inventory costs - revenue from selling end of period inventory at month 4). Note, inventory cost is assessed only for the first 3 periods. Model and solve the problem in AMPL and answer the quiz.
Answers
The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.
In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:
Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.
Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.
The objective function we want to minimize is:
Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)
Subject to the following constraints:
1. Initial inventory: y1 = 15 (given)
2. Production capacity constraints:
x1 <= 90 (month 1 capacity)
x2 <= 75 (month 2 capacity)
x3 <= 80 (month 3 capacity)
x4 <= 50 (month 4 capacity)
3. Inventory balance equations:
y1 + x1 - 50 = y2 (month 1)
y2 + x2 - 65 = y3 (month 2)
y3 + x3 - 100 = y4 (month 3)
y4 + x4 - 70 = 0 (month 4, no carryover inventory)
4. Non-negativity constraints:
x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0
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