The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, satisfies the KKT condition.
To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).
The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.
We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.
To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.
The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.
KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.
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Write an equation for a parabola with x-intercepts (-4,0) and (3,0) which passes through the point (2,-24).
Answer:
good job
Step-by-step explanation:
is it possible to use the law of cosines to solve for one angle in a triangle?
Yes, it is possible to use the law of cosines to solve for one angle in a triangle.
The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):
c^2 = a^2 + b^2 - 2ab * cos(C)
If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.
For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:
c = sqrt(a^2 + b^2 - 2ab * cos(C))
Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:
b = sqrt(c^2 - a^2 - 2ac * cos(B))
In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.
Sharon wants to make keychains with different colored beads as shown below.
Each key-chain will look the same Sharon will use a total of 20 green beads to make all her keychains. What is the number of red Beads and the number of blue Beads she will need to make all of the keychains
The numbers of each beads that Sharon will need to make all of the key chains is given as follows:
Red beads: 15.Blue beads: 30.How to obtain the amounts needed of each bead?The amounts for each bead are obtained applying the proportions built from the image given at the end of the answer.
From the images, for a single key chain, the amounts needed are given as follows:
4 green beads.3 red beads. 6 blue beads.Hence, for each 4 green beads, 3 red beads are needed. For 20 green beads, the number of red beads needed is given as follows:
3/4 x 20 = 60/4 = 15 red beads.
For each 4 green beads, 6 blue bears are needed. For 20 green beads, the number of blue beads needed is given as follows:
6/4 x 20 = 120/4 = 30 blue beads.
Missing InformationThe image is given at the end of the answer.
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PLS HELP I’m struggling with this question and could use some help to answer it.
The required inverse function of the given function is given as f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and the range of the inverse function is all real numbers.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
f(x) = -x + 9 / [8 + 9x]
Now,
y = f(x)
y = -x + 9 / [8 + 9x]
x = 9 - 8y / [1 + y]
Now,
x ⇄ y
y = 9 - 8x / 1 + x
Now y = f⁻¹[x]
f⁻¹(x) = [9 - 8y] / [1 + y],
Thus, the required inverse function is f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and its range is all real numbers.
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Sam wanted to graph the equation
y = 2x -7. She plotted her y-intercept
point and started to count the slope.
Which of the following should she do?
A. count up 2, and left 1
B. count down 2, over 0
C. count down 2, and right 1
D. count up 2, and right 1
We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
How can we find the intercepts and slope of the equations?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.
y=mx+b is the slope intercept formula
CalculationThe given equation is y=2x-7.
By comparing to slope intercept formula y=mx+b,
m=2 and b=-7.
So the slope of the given equation is 2 and y-intercept is (0,-7).
we know that,
m=rise/run
so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.
We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.
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The distance between P and T on the coordinate grid is
units. (Input whole numbers only.)
Image of a coordinate grid with point P located at negative 10, 15 and point T located at 15, 15.
Answer:
25
Step-by-step explanation:
Select ALL solutions
Answer:
in the picture
Step-by-step explanation:
in the picture
θ =120°
θ =240°
θ =270°
θ =0°
θ =210°
θ =180°
θ =90°
02410.0 points
The charge on an electron is 1.60218 x 10⁻¹⁹C and its mass is 9.10939 x 10⁻³¹ kg.
What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1mT ?
Answer in units of eV.
The kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
In the given question, the charge on an electron is 1.60218 x 10^(-19) C and its mass is 9.10939 x 10^(-31) kg.
We have to find the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT.
E = 0.18 kV/m
B = 1.1 mT
mass m = 9.10939*10^(-31) kg
Then force on a moving charge in electric and magnetic field = Lorentz force
F = qE+ q*VB
So,
F = qE+ q*VB = 0
E = V*B
Find V , so
V = E/B
V = 0.18*10^3 /( 1.1*10^-3)
V =163637 m/s
so KE = 1/2*m*v^2
Then put values..
KE = 0.5*9.11*10^(-31)*163637^(2)
KE = 1.2197*10^(-20) J
in eV = 1.2197*10^-20 / ( 1.6*10^-19 )
eV = 0.07623125 eV
Hence, the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.
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ASAP PLEASEEE!!!
Suppose that the function g is defined, for all real numbers, as follows. Find g(-2), g(1), and g(2).
Answer:
for g(-2)
we wil take -1/4 x -1
so g(-2) = - 1/2
for g(1)
we will take (x+1)²
so g(1) = (1+1)² = 4
for g(2)
we will take (x+1)²
so g(2)= ,(2+1)² = 9
Judy purchased a home in 1956. The
function represents y, the value of the home
x years since 1956.
f(x) = 11,500(1.09)^x
A. Judy purchased the home for
$109,000.
B. The value of the home increases by 9%
each year.
C. In 1986, Judy's home had a value over
$150,000.
After 26 years Judy purchased the home for $109,000.
What is function?
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.
A function is a relationship between a set of inputs and a set of potential outputs, where each input is related to exactly one output.
Given:
Judy purchased a home in 1956.
The function represents y, the value of the home x years since 1956.
f(x) = 11,500(1.09)^x
Let Judy purchased the home for $109,000.
We have to find the the number of years when Judy purchased the home for $109,000.
Plug f(x) = 109,000 in the above equation.
109,000 = 11,500(1.09)^x
218/23 = (1.09)^x
Taking log on both sides,
ln(218/23) = ln(1.09)^x
ln(218/23) = x ln(1.09)
x = ln(218/23)/ln(1.09)
x = 26.097
⇒ x ≈ 26
Hence, after 26 years Judy purchased the home for $109,000.
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a die is rolled until the first time t that a six turns up, what is the probability distribution for t
The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
What is a probability distribution?
A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.
In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.
The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.
The probability distribution for t in this case can be represented by the following table:
t Probability
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
... ...
This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.
Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.
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Help as soon as possible
The value of /BD/ in the quadrilateral is 16.9m
How to determine length in a triangle?A quadrilateral is polygon with four sides, four angles, four vertices, two diagonals whose sum of angles is 360 degrees
The diagonal of the quadrilateral forms a triangle.
From the triangle ΔABD, two sides are given with an included angle.
/AB/=16m
/AD/=19m
/BD/=?
To find the length /BD/
let it be a.
Using cosine rule, we have
a²=b²+d²-2bdcosA
a²=19²+16²-2*19*16*cos57⁰
Simplifying the formula
a²=361+256-608*0.5446
a²=617-311.1168
a²=285.8832
taking the square of both sides we have
a=√285.8832
a=16.9m
Therefore the length of the side /BD/ = 16.9m
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Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. If AB and FG are corresponding sides, and the length of AB is 4x + 4, what is the length of FG?
Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. the length of FG is x + 1.
What is the length of FG?Generally, A distance may be measured in terms of its length. A quantity that has the dimension distance in the International System of Units is referred to as length. In the vast majority of measuring systems, a length base unit is selected, and it is from this unit that all other units are derived.
The meter serves as the fundamental measuring device for length in accordance with the International System of Units.
Since the ratio of the sides of the two pentagons is 4:1, the length of FG is 1/4 of the length of AB.
Therefore, the length of FG is
(1/4)(4x + 4) = x + 1.
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Complete Question not found
Image not found
Answer:
its 1/4
Step-by-step explanation:
Step 1: Calculate the ratio of the side lengths for the original image to the corresponding side lengths of the transformed image using side FG and its corresponding side in
I need help please ANYONE???!!!!!
Identify the slope and y-intercept of each linear function's equation.
x-3=y
-x + 3 = y
y=1-3x
y=3x-1
Intro
slope = 3, y-intercept at -1
slope =-3, y-intercept at 1
slope = 1 y-intercept at -3
slope-1-y-intercept at 3
Done
A. y = 3x-1; slope is 3 and y-intercept is -1
B. -x+3 = y; slope is -1 and y-intercept is 3
C. x-3 = y; slope is 1 and y-intercept is -3
D. y = 1-3x; slope is -3 and y-intercept is 1
What is slope-intercept form?In math, slope interceptor form is the method of writing an equation for a line in the form y = mx + b.
Slope-Intercept form
The slope - intercept form equation with slope m and y intercept c is given by, y = mx+c
Option A:
y = 3x-1
slope m = 3
y-intercept c = -1
Option B:
-x+3 = y
slope m = -1
y-intercept c = 3
Option C:
x-3 = y
slope m = 1
y-intercept c = -3
Option D:
y = 1-3x
slope m = -3
y-intercept c = 1
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At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n. The weight of the i th person in the elevator Is a continuous random variable Y, with mean E(Yi)=w. The random variable N and the random variables Yi are independent. Let W be the total weight of all people in the elevator at a given time. Prove that E(w)=w. (Hint: This is very simple to prove if you use properties of conditional expectation).
At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n, then E(Y1) = w
Let W be the total weight of all people in the elevator at a given time and N be the number of people in the elevator at a given time.
E(W) = E[E(W|N)]
Since N and Y are independent, we can also write with mean:
E(W|N) = E[E(W|N,Y)]
Since the weight of each person is independent of the others, we can write:
E(W|N,Y) = E[E(W|N,Y1)]
Since Y is a continuous random variable and the weights of each person are independent, we can further write:
E(W|N,Y1) = E(Y1) = w
Therefore, we can conclude that:
E(W) = E[E(W|N)] = E[E(W|N,Y)] = E[E(W|N,Y1)] = E(Y1) = w
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Algebra
A line has a slope of 0 and passes through the point (13, 2). What is its equation in
slope-intercept form?
Answer:
y = 2 (This equation is in slope intercept form.)
Step-by-step explanation:
y = 0x + b
2 = 0(13) + b
2 = 0 + b
b = 2
y = 2
which measures do not represent the length of 3 sides of a triangel
Answer: correct answer is A
Step-by-step explanation:The numbers of sets which cannot represent the lengths of the sides of a triangle are 8, 9, 11.We have to determineWhich set of numbers cannot represent the lengths of the sides of a triangle?According to the questionThe length of sides which can not form a triangle is determined in the following steps given below.
Answer:
The correct answer is A.
Step-by-step explanation:
You have to look at the triangle inequality theorem where a + b ≥ c. Any two sides of a triangle must be greater than or equal to the third, in this case, 1 ft + 3 ft only = 4. Therefore A does not represent the length of 3 sides of a triangle.
Hope this helps, Have an amazing day!
Help please fast!! What is the measure of angle C? I’m confused please help!
Answer:
[tex]61.8^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are congruent
Answer:
61.8
Step-by-step explanation:
The measure of angle C is 61.8 degrees.
Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. They are called "vertical" because they are opposite each other and share the same vertex (the point at which the two lines intersect). Because vertical angles share the same vertex, they are always congruent, which means that they have the same measure.
In this case, angles C and E are a pair of vertical angles, so they are congruent. Since the measure of angle E is 61.8 degrees, the measure of angle C must also be 61.8 degrees. Therefore, the answer is 61.8 degrees.
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PLEASE ANSWER FAST
If your velocity is 20 m/s south and you traveled for 10 MINUTES, how far have you gone?
The telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05
per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part
a.
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a telephone company offers two billing plans for local calls. Plan 1 charges $25 per month for unlimited calls and Plan 2 charges $18 per month plus $0.05 per call.
For the part [1] -
25 < 18 + 0.05x
25 < 18 + 0.05x
25 - 18 < 0.05x
7 < 0.05x
x > (7/0.05)
x > 140
For part [2] -
For the number of calls greater than 140, the plan [1] is more economical than plan [2].
Therefore, for the number of calls greater than 140, the plan [1] is more economical than plan [2].
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5. A table of values and the plot of the residuals for the line of best fit are shown.
x
The point that the line estimate best fits is the point x = 6 with a residual of 0.18
How to interpret the residuals of the line of best fit?
We are given a table which displays the point and then their residual values are also added from the graph to get;
The table is as follows:
x y Residual Absolute Residual value
1 10 0.4 0.4
2 8 -1.125 1.125
2.5 9.5 0.625 0.625
4 8 -0.25 0.25
5 8 0.2 0.2
6 7.5 0.18 0.18
7.2 7 0.19 0.19
8.5 6 -0.25 0.25
The residual value is negative if the point on the scatter plot lies below the regression line and it is positive if the point on the scatter plot lies above the regression line.
Formula for the residual value is;
Residual value = Actual y-value(i.e. on scatter plot) - Observed y-value
Now, the residual value is farthest from the line if the absolute value of the residual value is highest.
Hence, the highest absolute residual value is: 1.125
The point that it best fits is the lowest absolute value which is 0.18
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A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm) , and the foot length, in cm , for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown.
The figure presents a scatterplot in a coordinate plane. The horizontal axis is labeled Foot Length, in centimeters, and the numbers 18 through 34, in increments of 2, are indicated. The vertical axis is labeled Height, in centimeters, and the numbers 150 through 190, in increments of 10, are indicated. There are 65 data points in the scatterplot, and a trend line is given as follows. Note that all values are approximate. The data points begin in the lower left part of the plane at the point with coordinates 19 comma 160. The data points trend upward and to the right and end with the coordinates 33 comma 190. The least-squares regression line begins at the point 18 comma 153, and slants upward and to the right at a constant rate to end at the point 35 comma 197.
Term Coef (SE) Coef T -Value P -Value
Constant 105.08 6.00 17.51 0.000
Foot length 2.599 0.238 10.92 0.000
S=5.90181 R–sq=65.42%
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm .
(b) The standard deviation of the residuals is s=5.9 . Interpret the value in context.
Unit 2 Progress Check: FRQ
Aubree Flores
As per the least-squares regression,
a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94
b) As per the given standard deviation, the value of the context 5.9
The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.
Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.
And we need to find following.
While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,
=> y = 2.599x + 105.08
Now, we have to apply the value of x as 20, then we get,
=> y = 2.599(20) + 105.08
=> y = 157.06
Therefore, the residual is calculated as,
=> 160 − 157.06 = 2.94
b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.
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HELP ME PLEASE ASAP!!!
Maya has 360 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing. As shown below, one of the sides has length x (in meters).
Answer:
a) [tex]A(x)=360x-2x^2[/tex]
b) [tex]90m[/tex]
c) [tex]16200m^2[/tex]
Step-by-step explanation:
This is related to a differential topic called optimisation.
We here have two sides of the field that are equal to [tex]x[/tex], and another unknown (that we will call [tex]y[/tex]). Maya has 360m of fencing, so we will say that [tex]2x+y=360[/tex], and this means that [tex]y=360-2x[/tex].
Our first task is to find a function for the area of the field. We know that the area of a field is length × width. We know we have a length of [tex]y[/tex] which is [tex]360-2x[/tex] and a width of [tex]x[/tex], therefore:
[tex]A(x)=x(360-2x)=360x-2x^2[/tex]
To find the maximum value of [tex]x[/tex], we must first differentiate the function:
[tex]A'(x)=360-4x[/tex]
We must then set the equation equal to 0 and solve for [tex]x[/tex], where the line/curve would be stationary.
[tex]360-4x=0[/tex]
[tex]4x=360[/tex]
[tex]x=90[/tex]
Finally, to find the maximum area, we would substitute this value of [tex]x[/tex] back into the original equation:
[tex]A(x)=360x-2x^2\\\\A(90)=360(90)-2(90)^2\\\\A(90)=16200[/tex]
For the following:
(a) The area is A(x) = x × (180 - x)(b) The side length x that gives the maximum area is 90 meters.(c) Maximum area that the field can have is 8100 square meters.How to find area and length?(a) To find a function A(x) that gives the area of the field in terms of x, use the information given about the fencing and the shape of the field.
Let the length of the other two sides (perpendicular to the side with length x) be y (in meters).
The perimeter of the rectangle is given by the sum of all four sides:
Perimeter = 2x + 2y
According to the problem, the perimeter is 360 meters, set up an equation:
2x + 2y = 360
Now, solve this equation for y in terms of x:
2y = 360 - 2x
y = (360 - 2x) / 2
y = 180 - x
The area A(x) of the rectangle is given by the product of its length (x) and width (y):
A(x) = x × y
A(x) = x × (180 - x)
(b) To find the side length x that gives the maximum area for the field, maximize the function A(x) from part (a). To do that, take the derivative of A(x) with respect to x, set it equal to zero, and solve for x:
A(x) = x × (180 - x)
dA/dx = (180 - x) - x
dA/dx = 180 - 2x
Now, set dA/dx = 0 and solve for x:
180 - 2x = 0
2x = 180
x = 90
So, the side length x that gives the maximum area is 90 meters.
(c) Now there is the value of x, find the maximum area by substituting x = 90 into the area function A(x) from part (a):
A(x) = x × (180 - x)
A(90) = 90 × (180 - 90)
A(90) = 90 × 90
A(90) = 8100
The maximum area that the field can have is 8100 square meters.
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the positive integers are arranged in the patterm illustrated below: if this pattern continues indifinetely, what is the number immediately above 39863
Answer:
Step-by-step explanation:
986
ryland is creating an article about commonly used compression algorithms for an online educational site. he's debating whether to express each algorithm in natural language, flow charts, pseudocode, or c , a general-purpose programming language. which of these is a good argument for expressing the algorithm in pseudocode? choose 1 answer:
Pseudocode doesn't depend on the syntax and subtitles of a particular programming language, so his readers will be able to understand it as long as they know at least one language.
In computer science, pseudocode is a undeniable language description of the stairs in an set of rules or any other system. Pseudocode frequently makes use of structural conventions of a regular programming language, however is supposed for human studying as opposed to gadget studying. Pseudocode is known via way of means of the programmers of all types. it allows the programmer to pay attention most effective at the set of rules a part of the code development. It can't be compiled into an executable program.
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Complete question:
Ryland is creating an article about commonly used compression algorithms for an online educational site.
He's debating whether to express each algorithm in natural language, flow charts, pseudocode, or C++, a general-purpose programming language.
Which of these is a good argument for expressing the algorithm in pseudocode?
34. selecting from urns an urn contains four red marbles and three green marbles. one marble is removed, its color noted, and the marble is not replaced. a second marble is removed and its color noted.
The probability states that- (r+w+b+g)min =21,
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
r−3=4w,r−2=3b,r−1=2g
r=4w+3,r=3b+2,r=2g+1
rmin=11⇒w min=2⇒bmin=3⇒g min =5
Hence, (r+w+b+g)min =21,
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Ajay and deepak can do an allocated work in 15 days and 10days respectively. They stated the work together but Deepak left after sometimes and ajay finished the remaining work in 5 days. After how many days (from the start)did Deepak leave
Answer:
Deepak have taken 5 days leave from the start of the work.
Calculate the difference and enter below. 5-(-5)
Answer: 10
Step-by-step explanation: As I said in your previous question, we can make this an addition problem, to make it easy, and make more sense. S0, it would be 5+5, which is our answer; 10. I hoped this helped
. in addition to limit theorems that deal with sums, there are limit theorems that deal with extreme values such as maxima or minima. here is an example. let u1,..., un be independent uniform random variables on [0, 1], and let u(n) be the maximum. find the cdf of u(n) and a standardized u(n), and show that the cdf of the standardized variable tends to a limiting value.
As per the limit theorem, the CDF of the standardized variable tends to a limiting value.
The term limit theorem states that the average of a large number of id and the random variables converges to the expected value.
Here we have given that let u1,..., un be independent uniform random variables on [0, 1], and let u(n) be the maximum. find the CDF of u(n) and a standardized u(n).
And we need to prove that the the cdf of the standardized variable tends to a limiting value.
Let us consider the density function of a uniform random variable on [0,1] is f(x)=1 and the cdf is F(x)=x for x∈[0,1], so for U(n), the density function is
fₙ(x) = nxⁿ⁻¹
Whereas the CDF is written as,
fₙ(x) = xⁿ
When we equate both then we get
fₙ(x) = nx²ⁿ⁻¹
Therefore, the given statement is proved.
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