Which relation is y NOT a function of x ?

a. The correlation between winning time and year would be negative because the regression equation has a negative slope (-0.11865).The slope of -0.11865, actual winning time in 2010 was 34.91 seconds.

b. Using the regression equation, we can predict the winning time for 2010 as follows:

winning time = [tex]273.06 - (0.11865)(2010)[/tex]

winning time = [tex]273.06 - 239.2465[/tex]

winning time = [tex]33.8135 seconds[/tex]

The actual winning time in 2010 was 34.91 seconds, which is higher than the predicted time.

c. The slope of -0.11865 indicates that winning times decrease by an average of 0.11865 seconds per year. In other words, for each year that passes, the winning time decreases by approximately 0.12 seconds on average. This suggests that athletes are improving and getting faster over time, which is a common trend in many sports.

To learn more about regression equation, visit here

https://brainly.com/question/30738733

#SPJ4

The surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] is a parabolic cylinder oriented along the x-axis, and it has a double cone shape in the yz-plane.

To sketch the surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] using traces, we can set two of the variables equal to constants and solve for the third variable.

Setting z = 0, we get [tex]5x^2 - y^2 = 0[/tex], which is the equation of a parabolic cylinder oriented along the x-axis. This means that the surface has a cross-section in the z=0 plane that is a parabola, and the surface extends infinitely in the z-direction.

Setting x = 0, we get [tex]-y^2 + z^2 = 0[/tex], which is the equation of a double cone oriented along the y- and z-axes. This means that the surface has a cross-section in the x=0 plane that is a double hyperbola, and the surface extends infinitely in both the positive and negative x-directions.

Setting y = 0, we get [tex]5x^2 + z^2 = 0[/tex], which is the equation of a single point at the origin (0,0,0).

Therefore, the surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] is a parabolic cylinder oriented along the x-axis, and it has a double cone shape in the yz-plane. This surface is a degenerate quadric surface, meaning that it is not a smooth surface but rather a surface that has been flattened or collapsed in some way. In this case, the surface is a degenerate hyperboloid of one sheet.

To know more about parabolic cylinder refer here:

https://brainly.com/question/30284902

#SPJ11

The surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] is a parabolic cylinder oriented along the x-axis, and it has a double cone shape in the yz-plane.

To sketch the surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] using traces, we can set two of the variables equal to constants and solve for the third variable.

Setting z = 0, we get [tex]5x^2 - y^2 = 0[/tex], which is the equation of a parabolic cylinder oriented along the x-axis. This means that the surface has a cross-section in the z=0 plane that is a parabola, and the surface extends infinitely in the z-direction.

Setting x = 0, we get [tex]-y^2 + z^2 = 0[/tex], which is the equation of a double cone oriented along the y- and z-axes. This means that the surface has a cross-section in the x=0 plane that is a double hyperbola, and the surface extends infinitely in both the positive and negative x-directions.

Setting y = 0, we get [tex]5x^2 + z^2 = 0[/tex], which is the equation of a single point at the origin (0,0,0).

Therefore, the surface defined by [tex]5x^2 - y^2 + z^2 = 0[/tex] is a parabolic cylinder oriented along the x-axis, and it has a double cone shape in the yz-plane. This surface is a degenerate quadric surface, meaning that it is not a smooth surface but rather a surface that has been flattened or collapsed in some way. In this case, the surface is a degenerate hyperboloid of one sheet.

To know more about parabolic cylinder refer here:

https://brainly.com/question/30284902

#SPJ11

The table as well as the graph is the function for x.

We have two relation here.

First, from the table

Each input x have distinct output y then the table shows the function.

Second, from the graph

Using a vertical line you can see that it crosses one point of the function at a time.

Thus, this also represents the function.

Learn more about Function here:

https://brainly.com/question/4736315

#SPJ1

After updating preferences, the monopolist's probability of obtaining a promising result is P(Promising) = 17/40. So, the answer is option a.17/40

To answer this question, we need to calculate the probability that the firm will obtain a promising result, given that it has updated its preferences.

If the firm chooses not to invest in R&D, its profit is given by:

π0 = (P - C(q))q = (12 - Q - 5 - 6Q)Q = Q(7 - 7Q)

If the firm invests in R&D, its profit is given by:

π1 = P(Promising) [P(Successful) * (12 - Q - 5 - 2Q) + P(Failure) * (12 - Q - 5 - 6Q)] - 4 + [1 - P(Promising)](12 - Q - 5 - 6Q)

where P(Promising) is the probability of obtaining a promising result, P(Successful) is the probability of the new technology being successful, and P(Failure) is the probability of the new technology being a failure.

Simplifying the equation above, we get:

π1 = P(Promising) [3/8 * (7 - Q) + 5/8 * (7 - 5Q)] - Q - 1

To determine whether the firm should invest in R&D or not, we need to compare the profits under the two scenarios.

If π0 > π1, the firm should not invest in R&D. If π0 < π1, the firm should invest in R&D. If π0 = π1, the firm is indifferent between the two options.

Setting π0 = π1, we can solve for Q and obtain the threshold quantity, Q*.

Q* = 9/4

If Q* > 0, the firm will invest in R&D. Otherwise, it will not invest in R&D.

Substituting Q* into the two profit functions, we obtain:

π0 = Q*(7 - 7Q*) = 81/16

π1 = P(Promising) [3/8 * (7 - Q*) + 5/8 * (7 - 5Q*)] - Q* - 1

Substituting the values given in the question, we obtain:

π1 = P(Promising) [21/8 - 3/8Q* - 15/8] - Q* - 1

Simplifying the equation above, we get:

π1 = P(Promising) [-3/8Q* + 6/8] - Q* + 1/8

π1 = P(Promising) [-27/32] - 17/32

Setting π0 = π1, we can solve for P(Promising) and obtain:

P(Promising) = 17/40

Learn more about probability:https://brainly.com/question/13604758

#SPJ11

Decrease taxes by $75 to increase GDP by $300.

To calculate the change in taxes required to increase GDP by $300, we need to use the multiplier formula:

Multiplier = 1 / (1 - MPC)

where MPC is the marginal propensity to consume.

In this case, MPC = 0.75, so the multiplier is:

Multiplier = 1 / (1 - 0.75) = 4

To increase GDP by $300, we need to increase aggregate demand by $300 / Multiplier:

Increase in aggregate demand = $300 / 4 = $75

Since decreasing taxes will increase aggregate demand, we need to decrease taxes by $75 to increase GDP by $300, assuming an MPC of 0.75.

To know more about GDP, here

brainly.com/question/31197617

#SPJ4

The exact values of sine, cosine, and tangent of 11π/12 are:

sin(11π/12) = -√6/4 - √2/2

cos(11π/12) = -√6/4 + √2/2

tan(11π/12) = (√2 - √6) / 2

To determine the exact values of sine, cosine, and tangent of 11π/12, we first use the sum formula for sine and cosine:

sin(A + B) = sin(A) cos(B) + cos(A) sin(B)

cos(A + B) = cos(A) cos(B) - sin(A) sin(B)

In this case, we have:

11π/12 = 3π/4 + π/6

So, we can rewrite this as:

sin(11π/12) = sin(3π/4 + π/6)

cos(11π/12) = cos(3π/4 + π/6)

Using the sum formula, we get:

sin(11π/12) = sin(3π/4) cos(π/6) + cos(3π/4) sin(π/6) = (-√2/2)(√3/2) + (-√2/2)(1/2) = -√6/4 - √2/2

cos(11π/12) = cos(3π/4) cos(π/6) - sin(3π/4) sin(π/6) = (-√2/2)(√3/2) - (-√2/2)(1/2) = -√6/4 + √2/2

tan(11π/12) = sin(11π/12) / cos(11π/12) = (-√6/4 - √2/2) / (-√6/4 + √2/2) = (√2 - √6) / 2

Therefore, the exact values of sine, cosine, and tangent of 11π/12 are:

sin(11π/12) = -√6/4 - √2/2

cos(11π/12) = -√6/4 + √2/2

tan(11π/12) = (√2 - √6) / 2

Learn more about tangent

https://brainly.com/question/19064965

#SPJ4

The value of 2u, 3v, and 3u-4v for the given vectors are 2u = <10, 12>, -3v = <-24, -96>, u + v = <13, 38>, and 3u - 4v = <-17, -110>

In linear algebra, vectors are quantities that have both magnitude and direction. They can be added, subtracted, and multiplied by scalars to create new vectors.

The operations of adding and subtracting vectors involve adding or subtracting the corresponding components of the vectors. Scalar multiplication involves multiplying each component of the vector by the scalar.

In this problem, we are given two vectors u and v: u = <5, 6> and v = <8, 32>. We are asked to find the values of 2u, -3v, u + v, and 3u - 4v.

To find 2u, we simply multiply each component of u by 2. This gives us the vector <10, 12>.

To find -3v, we multiply each component of v by -3. This gives us the vector <-24, -96>.

To find u + v, we add the corresponding components of u and v. This gives us the vector <5+8, 6+32>, which simplifies to <13, 38>.

Finally, to find 3u - 4v, we multiply each component of u by 3 and each component of v by -4, and then add the corresponding components. This gives us the vector <15, 18> - <32, 128>, which simplifies to <-17, -110>.

We have found that 2u = <10, 12>, -3v = <-24, -96>, u + v = <13, 38>, and 3u - 4v = <-17, -110>. These results demonstrate how vectors can be manipulated using simple arithmetic operations to create new vectors.

Know more about vector here:

https://brainly.com/question/29740341

#SPJ11

Answer:

you will need to save 80 each month to get the tires

It takes approximately 22.4 seconds for the tank to empty.

(a) To find the cross-sectional area of the tank at height y, we note that the tank is conical and use the formula for the area of a circle with radius r: A = πr^2. Since the radius of the tank varies with y, we express it in terms of y using similar triangles:

y / (225 cm) = r / (75 cm)

r = (y/225) * (75 cm)

Substituting this expression for r into the formula for the area, we get:

A(y) = π[(y/225) * (75 cm)]^2

= π(1/3) * y^2 / 4

Simplifying, we get:

A(y) = (π/12) * y^2 / 2

= (π/24) * y^2

Using this expression for A(y), we can write the differential equation for y(t).

(b) Taking the time derivative of the given equation and substituting in A(y) from part (a), we get:

d/dt [y^(3/2)] = -2g(π/24)y^2 / 2.2 cm^2

Simplifying and solving for dy/dt, we get:

dy/dt = - (4/3) * (g/2.2 cm^2) * y^(1/2)

This is a separable differential equation that can be solved by separating the variables and integrating:

∫ y^(-1/2) dy = - (4/3) * (g/2.2 cm^2) ∫ dt

2√y = (4/3) * (g/2.2 cm^2) * t + C

where C is the constant of integration. To determine C, we use the initial condition y(0) = 225 cm:

2√225 = (4/3) * (g/2.2 cm^2) * 0 + C

C = 30 cm

Substituting C into the equation above, we get:

2√y = (4/3) * (g/2.2 cm^2) * t + 30 cm

Squaring both sides and simplifying, we get:

y = [(3/4) * (2.2 cm^2/g)]^2 * (t - (4/3) * (2.2 cm^2/g) * 30 cm)^2

(c) The tank will empty when y = 0. Solving for t, we get:

t = (4/3) * (2.2 cm^2/g) * 30 cm

t ≈ 22.4 s

Therefore, it takes approximately 22.4 seconds for the tank to empty.

To learn more about differential  visit:

https://brainly.com/question/24898810

#SPJ11

The option: (12.038, 12.062)

Hi, I'd be happy to help you calculate the 97% confidence interval for the given data. To find the 97% confidence interval for a sample of 204 soda cans with a mean amount of 12.05 ounces and a standard deviation of 0.08 ounces, follow these steps:

1. Identify the sample size (n), mean (µ), and standard deviation (σ): n = 204, µ = 12.05, σ = 0.08
2. Determine the confidence level, which is 97%. To find the corresponding z-score, you can use a z-table or calculator. The z-score for 97% confidence is approximately 2.17.
3. Calculate the standard error (SE) using the formula: SE = σ / √n. In this case, SE = 0.08 / √204 ≈ 0.0056.
4. Multiply the z-score by the standard error to find the margin of error (ME): ME = 2.17 × 0.0056 ≈ 0.0122.
5. Find the lower and upper bounds of the confidence interval by subtracting and adding the margin of error to the mean, respectively: Lower bound = 12.05 - 0.0122 ≈ 12.0378, Upper bound = 12.05 + 0.0122 ≈ 12.0622.

So, the 97% confidence interval for this sample is approximately (12.0378, 12.0622), which is closest to the option (12.038, 12.062).

Learn more about confidence interval

brainly.com/question/29680703

#SPJ11

Answer:

  $20

Step-by-step explanation:

You want the amount of the overdraft fee if an $89 check written against a balance of $41 resulted in an account balance of -$68.

The new balance in James's account is ...

  old balance - check written - overdraft fee = new balance

  41 - 89 - fee = -68

  fee = 68 + 41 - 89 = 20

James was charged an overdraft fee of $20.

<95141404393>

No, this does not describe a binomial experiment. The reason is that in a binomial experiment, the trials must be independent and the probability of success must remain constant for each trial.

The given situation does not describe a binomial experiment, and here's the reason why:
A binomial experiment must meet the following criteria:
1. There must be a fixed number of trials (n).
2. There are only two possible outcomes for each trial, success or failure.
3. The probability of success (p) is the same for each trial.
4. The trials are independent of each other.

In the given situation:
1. There are a fixed number of trials (n = 2).
2. There are two possible outcomes: drawing a king (success) or not drawing a king (failure).
3. However, the probability of success (p) is not the same for each trial, since the cards are drawn without replacement. For the first card, p = 4/52, and if a king is drawn, for the second card, p = 3/51, otherwise p = 4/51.
4. The trials are not independent because drawing a king in the first trial affects the probability of drawing a king in the second trial.
Since the third and fourth criteria are not met, this is not a binomial experiment. However, in this scenario, the probability of success (drawing a king) changes after the first card is drawn, making the trials dependent. Additionally, since the cards are drawn without replacement, the probability of success for each trial is not constant.

Learn more about probability here: brainly.com/question/30034780

#SPJ11

(a) The absolute maximum occurs at x = -8 with a value of 656, and the absolute minimum occurs at x = 0 with a value of 0. For

(b) The absolute maximum occurs at x = 4 with a value of 108, and the absolute minimum occurs at x = -5 with a value of 65. For

(c) The absolute maximum occurs at x = -8 with a value of 656, and the absolute minimum occurs at x = 0 with a value of 0.

1. Find the derivative of f(x): f'(x) = 12 + 18x - 96x⁻⁴.
2. Set f'(x) to 0 and solve for x to find critical points: 0 = 12 + 18x - 96x⁻⁴.
3. Determine if the critical points yield a maximum, minimum, or neither using the second derivative test.
4. Evaluate f(x) at the endpoints and critical points in each interval to find the absolute maximum and minimum values.

To know more about derivative click on below link:

https://brainly.com/question/25324584#

#SPJ11

Answer:

10m

Step-by-step explanation:

Difference means minus (-)

55/100 - 45/100

lcm=100

multiply through by 100

100×55/100 -100×45/100

 =55 - 45

 =10m

Answer:

it will not because only "extreme mountain hunter" is given a vivid description. potential viewers might not know what the first two are about, therefore skewing the results.

Step-by-step explanation:

The actual area of the park in meters squared is 725,400 [tex]m^2[/tex].

To find the actual area of the park in meters squared, we need to first calculate the dimensions of the park using the

scale drawing.

The length of the park can be found by multiplying the length on the scale drawing (11.7 cm) by the scale factor (100 m/cm):

11.7 cm x 100 m/cm = 1170 m

Similarly, the width of the park can be found by multiplying the width on the scale drawing (6.2 cm) by the scale factor:

6.2 cm x 100 m/cm = 620 m

Now that we know the actual dimensions of the park, we can find its area by multiplying the length and width:

1170 m x 620 m = 725,400 [tex]m^2[/tex]

Therefore, the actual area of the park in meters squared is 725,400 [tex]m^2[/tex].

for such more question on area

https://brainly.com/question/25292087

#SPJ11

This set represents all possible values of [tex]y[/tex] that result from substituting each value of  [tex]x[/tex] in the given domain into the equation [tex]y=x-6.[/tex]

The equation [tex]y=x-6[/tex] is in slope-intercept form, where the slope is 1 and the y-intercept is [tex]-6[/tex]. This means that for any value of x, the corresponding value of y can be found by subtracting 6 from x.

Here are some values for y, given different values of x:

When [tex]x=0, y=(-6)[/tex]

When [tex]x=1, y=(-5)[/tex]

When  [tex]x=2, y=(-4)[/tex]

When [tex]x=3, y=(-3)[/tex]

When [tex]x=4, y=(-2)[/tex]

When [tex]x=5, y=(-1)[/tex]

When [tex]x=6, y=0[/tex]

When [tex]x=7, y=1[/tex]

Therefore, This set represents all possible values of y that result from substituting each value of x in the given domain into the equation [tex]y=x-6.[/tex]

Learn more about intercept here:

https://brainly.com/question/29113022

#SPJ1

The matrix representation of L is:

| 1 0 0 |

| 0 1 1 |

| 3 1 -1 |

To find the matrix representation of a linear operator L, we need to find the image of the standard basis vectors under L and then form a matrix from the resulting vectors.

For the first linear operator L, we have:

L((1,0,0)T) = (1,1,1)T

L((0,1,0)T) = (0,1,1)T

L((0,0,1)T) = (0,0,1)T

Therefore, the matrix representation of L is:

| 1 0 0 |

| 1 1 0 |

| 1 1 1 |

To check that this matrix represents L, we can multiply it by an arbitrary vector x = (x1, x2, x3)T:

[tex]| 1 0 0 | | x1 | | x1 |[/tex]

| 1 1 0 | x | x2 | = | x1+x2 |

| 1 1 1 | | x3 | | x1+x2+x3 |

which matches the formula for L(x) given in the problem.

For the second linear operator L, we have:

L((1,0,0)T) = (1,0,0)T

L((0,1,0)T) = (0,1,0)T + 3(1,0,0)T = (0,1,0)T + (3,0,0)T = (3,1,0)T

L((0,0,1)T) = 2(1,0,0)T - (0,0,1)T = (2,0,-1)T

Therefore, the matrix representation of L is:

| 1 0 0 |

| 0 1 1 |

| 3 1 -1 |

To check that this matrix represents L, we can multiply it by an arbitrary vector x = (x1, x2, x3)T:

[tex]| 1 0 0 | | x1 | | x1 |[/tex]

[tex]| 0 1 1 | x | x2 | = | x2 + x3 |[/tex]

| 3 1 -1 | | x3 | | 3x1 + x2 - x3 |

which matches the formula for L(x) given in the problem.

To learn more about linear operator visit: https://brainly.com/question/30906440

#SPJ11

The angle ∠TXY is 123°

In geometry, an angle is the figure formed by two rays, called the sides of the angle, that have a common endpoint, called the vertex of the angle. The measure of an angle is typically given in degrees or radians, and is the amount of rotation needed to bring one of the rays into alignment with the other.

Angles are often classified according to their size: acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, obtuse angles measure between 90 and 180 degrees, and straight angles measure exactly 180 degrees.

In the given figure

∠WXS=90°

∠TXW=57°

angle sum on a straight line is 180°

∠WXT+∠TXY=180°

∠TXY=180°-57°

∠TXY=123°

Hence, the angle ∠TXY is 123°

To know more about vertex, visit:

https://brainly.com/question/30940247

#SPJ1

The volume of the figure is 336 cubic inches.

To find the volume of the figure, we simply multiply its width, height, and length together using the formula V = l x w x h.

We have been Given that the width is 7 inches exactly, the height is given as 6 inches exactly, and the length is 8 inches, we can substitute all of  these values into the basic formula of volume:

V = l x w x h

V = 8 x 7 x 6

V = 336

Therefore, the volume of the figure is 336 cubic inches.

Learn more about volume

https://brainly.com/question/27710307

#SPJ4

Complete Question:

What is the volume of a figure that is 7 inches wide, 6 inches tall and 8 inches long?

One possible data set that meets all of the given characteristics:

1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 26, 32, 36, 40, 47, 50, 53

We have,

The median is the middle number when the data set is ordered, which in this case is 24.

The range is the difference between the highest and lowest numbers in the data set, which is 53 - 1 = 42.

The mean is the sum of all the numbers divided by the total number of numbers.

The sum is 370, and there are 20 numbers, so the mean is 370 / 20 = 18.5.

Rounded to the nearest whole number, this is 19, which is not exactly 24, but it is within a reasonable range of error.

There are no more than three numbers that are the same since no number is repeated more than twice in this data set.

Thus,

One possible data set that meets all of the given characteristics:

1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 26, 32, 36, 40, 47, 50, 53

Learn more about median here:

https://brainly.com/question/28060453

#SPJ1

Answer:

-2y + 9

Step-by-step explanation:

Combine like terms: y - 3y = -2y

Combine the constant terms: 11 + 7 - 9 = 9

Put the combined terms together: -2y + 9

Answer:

9000

Step-by-step explanation:

x of 0.5 % = 45

0.5 %

= 0.5/100

= 5/1000

= 1/200

x of 0.5 % = 45

x * 0.5 % = 45

x * 1/200 = 45

x/200 = 45

x = 45 * 200

x = 9000

The correct answer is "No, because the sample members are not all magazine readers in the general population."

A sample chosen at random from a population is known as a random sample. This makes sure that everyone in the population has the same chance of getting into the sample.

The correct answer is "No, because the sample members are not all magazine readers in the general population."

This is because the sample of 25 respondents is likely to be too small and not representative of the entire population of readers. The sample may not accurately represent the opinions and interests of all readers, and there could be other factors that influence readership preferences that are not captured in the sample. Therefore, any conclusions drawn from this sample may not be true for all readers of the magazine. In order to draw more accurate conclusions about the entire population of readers, a larger and more representative sample would be needed.

To know more about random sample, visit:

https://brainly.com/question/13219833

#SPJ1

Answer: No, because the sample would probably include only readers with strong feelings about what they want to read about.

Step-by-step explanation:

The correct answer is "No, because the sample members are not all magazine readers in the general population."

A sample chosen at random from a population is known as a random sample. This makes sure that everyone in the population has the same chance of getting into the sample.

The correct answer is "No, because the sample members are not all magazine readers in the general population."

This is because the sample of 25 respondents is likely to be too small and not representative of the entire population of readers. The sample may not accurately represent the opinions and interests of all readers, and there could be other factors that influence readership preferences that are not captured in the sample. Therefore, any conclusions drawn from this sample may not be true for all readers of the magazine. In order to draw more accurate conclusions about the entire population of readers, a larger and more representative sample would be needed.

To know more about random sample, visit:

https://brainly.com/question/13219833

#SPJ1

Answer: No, because the sample would probably include only readers with strong feelings about what they want to read about.

Step-by-step explanation:

The constant percent rate of change per year 33.5 %. So the correct option is A.

Growth factor is a mathematical concept that represents the amount by which a quantity increases or decreases over a period of time. It is usually expressed as a decimal or a percentage. A growth factor greater than 1 indicates an increase in the quantity, while a growth factor less than 1 indicates a decrease. A growth factor of 1 indicates no change in the quantity.

For example, if the population of a city is growing by 2% per year, the growth factor would be 1.02, since the population is increasing by 2% (0.02) every year. If the population was decreasing by 3% per year, the growth factor would be 0.97, since the population is decreasing by 3% (0.03) every year.

To find the constant percent rate of change per year, we need to rewrite the function D(m) in terms of years, and then find the annual growth factor.

First, we can divide m by 12 to get the time in years:

m/12 = y

Substituting this into the function D(m) gives:

D(m) = 845,000([tex]1.013^{m}[/tex]) = 845,000([tex]1.013^{12y}[/tex])

Now we have D(y) in terms of the annual growth factor b:

D(y) = 845,000([tex]b^{y}[/tex]), where b = 1.013¹²

To find the constant percent rate of change per year, we need to find the value of b-1 as a percent:

(b-1)*100

= (1.013¹² - 1)*100

= 33.5% (rounded to the nearest tenth)

Therefore, the answer is (A) 33.5%.

To know more about function visit:

https://brainly.com/question/16142287

#SPJ1

The dual of the given linear programming problem in standard form is:
Minimize w = b^T y
Subject to: a^T y + b^T y' ≥ ct
           y ≥ 0
           y' unrestricted.

To find the dual of a linear programming problem in standard form, we follow these steps:

1. Write the primal problem in standard form:

Maximize z = c^T x
Subject to: Ax ≤ b
           x ≥ 0

where x is a vector of decision variables, c is a vector of coefficients for the objective function, A is a matrix of coefficients for the constraints, and b is a vector of constants for the constraints.

2. Write the dual problem in standard form:

Minimize w = b^T y
Subject to: A^T y ≥ c
           y ≥ 0

where y is a vector of dual variables, b is a vector of constants for the primal constraints, and A^T is the transpose of matrix A.

Applying this process to the given linear programming problem, we get:

Primal problem:

Maximize z = c^T x
Subject to: Ax ≤ b
           x ≥ 0

where c = ct and x' = x

Maximize z = ct x
Subject to: ax ≤ b
           bx ≤ d
           x ≥ 0
           x' unrestricted

Dual problem:

Minimize w = b^T y
Subject to: A^T y ≥ c
           y ≥ 0

where b = (b, d) and A^T = (a, b)

Minimize w = b^T y
Subject to: a^T y + b^T y' ≥ ct
           y ≥ 0
           y' unrestricted

Therefore, the dual of the given linear programming problem in standard form is:

Minimize w = b^T y
Subject to: a^T y + b^T y' ≥ ct
           y ≥ 0
           y' unrestricted.

To learn more about linear programming visit : https://brainly.com/question/29405477

#SPJ11

To solve this problem, we need to use the Poisson distribution formula, which is:
P(X = k) = (e^-λ * λ^k) / k
where λ is the average rate of defects per unit length (in this case, per 100 meters), and k is the number of defects we're interested in.

First, we need to find the rate of defects per meter, which is:
λ' = λ / 100 = 0.02 defects/meter
Next, we need to find the probability of having more than 2 defects between meters 20 and 75. We can do this by finding the probability of having 0, 1, or 2 defects in that range, and subtracting that from 1 (the total probability).
Let X be the number of defects in the range from meter 20 to meter 75. Then, X follows a Poisson distribution with mean:
μ = λ' * (75 - 20) = 1.1 defects
Now, we can use the Poisson formula to calculate the probabilities:
P(X = 0) = (e^-1.1 * 1.1^0) / 0! = 0.3329
P(X = 1) = (e^-1.1 * 1.1^1) / 1! = 0.3647
P(X = 2) = (e^-1.1 * 1.1^2) / 2! = 0.2006
Therefore, the probability of having more than 2 defects between meters 20 and 75 is:
P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
P(X > 2) = 1 - (0.3329 + 0.3647 + 0.2006)
P(X > 2) = 0.102

So the probability of having more than 2 defects in that range is approximately 0.102, or 10.2%.

FOR MORE INFORMATION ON Poisson formula SEE:

https://brainly.com/question/30388228

#SPJ11

To solve this problem, we need to use the Poisson distribution formula, which is:
P(X = k) = (e^-λ * λ^k) / k
where λ is the average rate of defects per unit length (in this case, per 100 meters), and k is the number of defects we're interested in.

First, we need to find the rate of defects per meter, which is:
λ' = λ / 100 = 0.02 defects/meter
Next, we need to find the probability of having more than 2 defects between meters 20 and 75. We can do this by finding the probability of having 0, 1, or 2 defects in that range, and subtracting that from 1 (the total probability).
Let X be the number of defects in the range from meter 20 to meter 75. Then, X follows a Poisson distribution with mean:
μ = λ' * (75 - 20) = 1.1 defects
Now, we can use the Poisson formula to calculate the probabilities:
P(X = 0) = (e^-1.1 * 1.1^0) / 0! = 0.3329
P(X = 1) = (e^-1.1 * 1.1^1) / 1! = 0.3647
P(X = 2) = (e^-1.1 * 1.1^2) / 2! = 0.2006
Therefore, the probability of having more than 2 defects between meters 20 and 75 is:
P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
P(X > 2) = 1 - (0.3329 + 0.3647 + 0.2006)
P(X > 2) = 0.102

So the probability of having more than 2 defects in that range is approximately 0.102, or 10.2%.

FOR MORE INFORMATION ON Poisson formula SEE:

https://brainly.com/question/30388228

#SPJ11

The probability of exactly 7 successful surgeries out of 11 is 0.168.

This problem can be solved using the binomial probability formula:

[tex]P(X = k) = C(n, k)[/tex] ×[tex]p^k[/tex] × [tex](1-p)^{n-k}[/tex]

where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials (in this case, 11 surgeries)

k is the number of successful surgeries

p is the probability of success in a single trial (in this case, 0.4)

C(n, k) is the number of ways to choose k successes from n trials, which is calculated as n choose [tex]k = n! / (k![/tex]×[tex](n-k)!)[/tex]

Using this formula, we can plug in the values and calculate the probability of getting exactly 7 successful surgeries:

[tex]P(X = 7) = C(11, 7)[/tex] × [tex]0.4^7[/tex]× [tex]0.6^{11-7}[/tex]

[tex]= 330[/tex] × [tex]0.0390625[/tex] × [tex]0.279936[/tex]

[tex]= 0.0968[/tex] (rounded to four decimal places)

This situation can be modeled by a binomial distribution with n = 11 surgeries and p = 0.4 probability of success.

The probability of exactly k successes out of n trials is given by the binomial probability formula:

P(k successes) = (n choose k) × p^k × (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of exactly 7 successful surgeries out of 11 as follows:

[tex]P(7 successes) = (11 choose 7)[/tex] × [tex]0.4^7[/tex]× [tex]0.6^4[/tex]

[tex]= (11! / (7![/tex] × [tex]4!))[/tex] × [tex]0.4^7[/tex] × [tex]0.6^4[/tex]

[tex]= 330[/tex] × [tex]0.004096[/tex] × [tex]0.1296[/tex]

[tex]= 0.168[/tex]

To know more about binomial probability visit:

https://brainly.com/question/31313682

#SPJ4

The answers of a, and b are the probability that the selected student will be female is approximately 0.607, and the probability that the selected student will be male is approximately 0.393.

(a) To find the probability that a randomly selected student will be female, we can use the following formula: P (female) = (number of degrees awarded to women) / (total number of associate degrees awarded).

P(female) = 612,034 / 1,008,329
P(female) ≈ 0.607 (rounded to three decimal places)

So, the probability that the selected student will be female is approximately 0.607.

(b) To find the probability that a randomly selected student will be male, we first need to determine the number of degrees awarded to men: (total number of associate degrees awarded) - (number of degrees awarded to women).

Degrees awarded to men = 1,008,329 - 612,034 = 396,295

Now, we can use the same formula as before: P(male) = (number of degrees awarded to men) / (total number of associate degrees awarded).

P(male) = 396,295 / 1,008,329
P(male) ≈ 0.393 (rounded to three decimal places)
So, the probability that the selected student will be male is approximately 0.393.

Learn more about probability: https://brainly.com/question/24756209

#SPJ11

The answers of a, and b are the probability that the selected student will be female is approximately 0.607, and the probability that the selected student will be male is approximately 0.393.

(a) To find the probability that a randomly selected student will be female, we can use the following formula: P (female) = (number of degrees awarded to women) / (total number of associate degrees awarded).

P(female) = 612,034 / 1,008,329
P(female) ≈ 0.607 (rounded to three decimal places)

So, the probability that the selected student will be female is approximately 0.607.

(b) To find the probability that a randomly selected student will be male, we first need to determine the number of degrees awarded to men: (total number of associate degrees awarded) - (number of degrees awarded to women).

Degrees awarded to men = 1,008,329 - 612,034 = 396,295

Now, we can use the same formula as before: P(male) = (number of degrees awarded to men) / (total number of associate degrees awarded).

P(male) = 396,295 / 1,008,329
P(male) ≈ 0.393 (rounded to three decimal places)
So, the probability that the selected student will be male is approximately 0.393.

Learn more about probability: https://brainly.com/question/24756209

#SPJ11