Which of the following is the conjugate of the expression below when​

Answer:

Period ahhh

Step-by-step explanation:

Period uhhh

This program will calculate and print the numerical solution of the given ODE using the fourth-order Runge-Kutta method over the specified interval and step size. The result will be displayed as a list of {x, y} pairs.

Mathematica program that uses the fourth-order Runge-Kutta method to numerically solve the given ordinary differential equation (ODE) with the specified initial condition:

mathematica

Copy code

(* Define the ODE and initial condition *)

ode = Function[{x, y}, -2*x - M];

initialCondition = {x0, y0} = {0.0, 1.15573};

(* Define the interval and step size *)

interval = {0.0, 0.4};

stepSize = 0.1;

(* Define the Runge-Kutta method *)

rungeKuttaStep[{x_, y_}, h_] := Module[{k1, k2, k3, k4},

 k1 = h*ode[x, y];

 k2 = h*ode[x + h/2, y + k1/2];

 k3 = h*ode[x + h/2, y + k2/2];

 k4 = h*ode[x + h, y + k3];

 {x + h, y + (k1 + 2 k2 + 2 k3 + k4)/6}

];

(* Perform the Runge-Kutta method *)

solution = NestList[rungeKuttaStep[#, stepSize] &, initialCondition, Floor[(interval[[2]] - interval[[1]])/stepSize]];

(* Extract the x and y values from the solution *)

{xValues, yValues} = Transpose[solution];

(* Print the numerical solution *)

Print["Numerical Solution:"];

Print[Transpose[{xValues, yValues}]];

Make sure to replace M in the ode function with the desired value.

This program will calculate and print the numerical solution of the given ODE using the fourth-order Runge-Kutta method over the specified interval and step size. The result will be displayed as a list of {x, y} pairs.

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The system of equations given by x - 5y = 4 and -2x + 10y = k has no unique solution for any value of k. It has a solution for all real values of k and infinitely many solutions for all real numbers k.

To determine the values of k for which the system of equations has a unique solution, no solution, or infinitely many solutions, let's analyze the given equations:

x - 5y = 4

-2x + 10y = k

We can observe that equation 2 is a scalar multiple of equation 1. Multiplying equation 1 by -2, we obtain:

-2(x - 5y) = -2(4)

2x - 10y = -8

Comparing this with equation 2, we see that both equations represent the same line. This implies that the system of equations has infinitely many solutions for any value of k, as both equations are equivalent and represent the same line.

Therefore, for part (a), there is no value of k that gives the system a unique solution. The correct choice is C: There is no value of k that will give the system a unique solution.

For part (b), since the system has infinitely many solutions for all values of k, the correct choice is C: The given system has a solution for all real values k.

For part (c), we have already determined that the system has infinitely many solutions for all values of k. Therefore, the correct choice is C: The given system has infinitely many solutions for all real numbers k.

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Answer:

Step-by-step explanation:

Perpendicular lines have negative - reciprocal slopes

Given line:

Perpendicular line:

Use point Q(-2, 5) to complete the equation of the line:

The value of x is 7

The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°

Therefore ;

50+28+15x-3 = 180

78-3 +15x = 180

75 +15x = 180

collect like terms

15x = 180-75

15x = 105

divide both sides by 15

x = 105/15

x = 7

therefore the value of the missing variable (x) is 7

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Answer:n= 27

Sorry solved for 48 instead of 8 first time around.

Step-by-step explanation:

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

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From the proof of modular congruence below, it has been shown that;

41 ≡ 21 (mod 3).

We want to use the definition of modular congruence to prove that;

41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).

We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.

First, if we recall the definition of modular congruence:

For integers a, b and positive integer m,  

a ≡ b (mod m) if and only if m|a–b

Suppose 41 ≡ 21 (mod 3).

Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.

Thus;

–(41 – 21) = –3k

So

21 – 41 = 3(–k)

This shows that 3|21 – 41.

Thus;

21 ≡ 41 (mod 3) and the proof is complete

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The transitive closure of a relation R on a set X is the smallest relation on X that contains R and is transitive.

If X is a set of airports and x R y means "there is a direct flight from airport x to airport y" (for x and y in X), then the transitive closure of R on X is the relation R+ such that x R+ y means "it is possible to fly from x to y in one or more flights". Informally, the transitive closure gives you the set of all places you can get to from any starting place.

In mathematics, the transitive closure of a relation R on a set X is the smallest relation on X that contains R and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets it is the unique minimal transitive superset of R.

Thus,The transitive closure of a relation R on a set X is the smallest relation on X that contains R and is transitive.

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Answer: Number 1.

Step-by-step explanation: Given the information that is how I got it.

The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.

(a) Probability of getting a defective unit = P(D)Probability of getting a non-defective unit = P(N)P(D)

= P(N) (equal probabilities)P(D)

= 1/2P(N)

= 1/2Total number of units inspected

= 10(a)

Find the probability of getting at least 7 non-defective units

P(X = x) = nCx * P^x * q^(n-x)

Where nCx is the binomial coefficient

P is the probability of successq is the probability of failuren is the total number of trialsx is the number of successes

(a) The probability of getting at least 7 non-defective units

= P(X ≥ 7)P(X ≥ 7)

= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = x)

\(= nCx * P^x * q^{(n-x)}P(X = 7)\)

= 10C7 * (1/2)^7 * (1/2)^3 = 0.1172P(X = 8)

= 10C8 * (1/2)^8 * (1/2)^2 = 0.0439P(X = 9)

= 10C9 * (1/2)^9 * (1/2)^1 = 0.0098P(X = 10)

= 10C10 * (1/2)^10 * (1/2)^0 = 0.00098P(X ≥ 7)

= 0.1172 + 0.0439 + 0.0098 + 0.00098

= 0.1718

(b) Find the probability of getting at most 6 defective units

P(X = x) = \(nCx * P^x * q^{(n-x)}\)

Where nCx is the binomial coefficient P is the probability of success

q is the probability of failuren is the total number of trialsx is the number of successes

(b) The probability of getting at most 6 defective units

= P(X ≤ 6)P(X ≤ 6)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)P(X = x)

= \(nCx * P^x * q^{(n-x) }\times P(X = 0)\)

= 10C0 * (1/2)^0 * (1/2)^10

= 0.00098P(X = 1)

= 10C1 * (1/2)^1 * (1/2)^9 = 0.0098P(X = 2) = 10C2 * (1/2)^2 * (1/2)^8 = 0.044P(X = 3)

= 10C3 * (1/2)^3 * (1/2)^7 = 0.1172P(X = 4)

= 10C4 * (1/2)^4 * (1/2)^6 = 0.2051P(X = 5)

= 10C5 * (1/2)^5 * (1/2)^5 = 0.2461P(X = 6)

= 10C6 * (1/2)^6 * (1/2)^4 = 0.2051P(X ≤ 6)

= 0.00098 + 0.0098 + 0.044 + 0.1172 + 0.2051 + 0.2461 + 0.2051

= 1- P(X ≥ 7) = 1 - 0.1718= 0.8282

The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.

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It states that as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the underlying population distribution.

A numerical measure calculated from a sample is known as a statistic. A statistic is a summary measure that describes a characteristic of a sample. It is used to estimate the corresponding population parameter.

For example, the sample mean is a statistic that summarizes the average value of a variable in the sample. This value can be used to estimate the population mean, which is the parameter that describes the average value of the variable in the entire population.

In contrast, a parameter is a numerical measure that describes a characteristic of a population. It is typically unknown and must be estimated from a sample. Examples of parameters include the population mean, population standard deviation, population proportion, etc.

The central limit theorem is a statistical theory that describes the behavior of the mean of a large number of independent, identically distributed random variables. It states that as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the underlying population distribution.

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Answer:what

Step-by-step explanation:what does this mean

Answer:

800

hope this helps

we need to multiply this number by 100 to get the  as a percentage:

0.1806 * 100 = 18.06%

The probability of choosing a senior can be calculated using the formula:

P(senior) = (102/562) * 100

P(senior) = 18.06%

This means that there is an 18.06% chance of choosing a senior if a student is randomly selected from the school.

First, we need to calculate the total number of students in the school by adding together the number of students in each class:

Total = 165 + 145 + 114 + 102 = 562

Next, we need to calculate the probability of choosing a senior by taking the number of seniors enrolled in the school (102) and dividing it by the total number of students in the school (562).

102/562 = 0.1806

Finally, we need to multiply this number by 100 to get the probability as a percentage:

0.1806 * 100 = 18.06%

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Answer:

x = 13

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

x = \(\sqrt{169}\) = 13

Answer:

Answer:

the polygon name is decagon

Step-by-step explanation:

sum exterior angles is 360

10 sides

360÷10=36

Answer:

decagon

Step-by-step explanation:

\( \frac{360 \degree }{size \: \: of \: \: \: \: the \: \: exterior \: \: angle} = number \: \: of \: \: sides \\ \\ \frac{360}{36} = 10 \: \: sides \\ \)

Name of the polygon which has 10 sides is decagon

Answer:

a. The coordinates of the first train are (-12,6).  The coordinates of the second train are (20,35).

b. The slope of the line for the first train is \(-\frac{1}{2}\).  The slope is neither horizontal or vertical.  It slopes diagonally downward from left to write since the slope is negative.  In slope-interdept form, it is written as \(y=-\frac{1}{2} x\).  In standard form, it is written as \(x+2y=0\).   The slope of the line for the second train is \(\frac{7}{4}\).  The slope is neither vertical or horizontal.  It slopes diagonally upward from left to right since the slope is positive.  In slope-intercept form, it is written as \(y=\frac{7}{4}x\).  In standard form, it is written as \(-7x+4y=0\).

c. The equarion of a line in slope-intercept form of the new track would be \(y=-\frac{1}{2} x+2\).

Step-by-step explanation:

a.  The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual.  The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6).  On a coordinate plane, that would be marked as (-12,6).  The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35).  On a coordinate plane that would be marked as (20,35).  This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).

b. The way to find slope is to find \(\frac{delta "x"}{delta "y"}\).  "Delta" means "the change in".  The equation would be \(m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).  So, let's find the slope of the first train's travel path.  We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope.  \(\frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}\).  That makes the slope of the first train's travel path to be (-1/2).  Now, let's find the slope of the second train's travel path.  We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope.  \(\frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}\).  That makes the slope of the second train's travel path to be (7/4).  They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like.  To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path.  A horizontal line  would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either.  The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative.  The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing).  The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left.  Finally, the equations for this part of the question.  For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation.  The slope-intercept form of an equation of a line is \(y=mx+b\) where "m" is the slope and "b" is the y-intercept.  The "b" value is 0, so that will not be written.  The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x.  The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x.  As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0.  And for the second train, standard form would be -7x+4y=0.

c.  Parallel means having the same slope but a different y-intercept.  The second train station would be placed two miles north, or two units up, from the first train station.  The first train station is at (0,0), so the second train station would be placed at (0,2).  That makes 2 the y-intercept for if the first train had taken the second train station's travel route.  The slope for the intitial route was (-1/2), so that will stay the same.  Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.

Answer:

a must be 9

Step-by-step explanation:

Divide both sides of the given equation by 0.75, to isolate (a - 2):

a - 2 = 5.25/0.75 = 7

Then a - 2 = 7, and so a must be 9.

Answer:

4.9

Step-by-step explanation:

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Answer:

the bar charts not being shown properly

The equation 2 - 7/9x = 5/6, when rewritten without fractions, is x = 9/2.

To rewrite the equation 2 - 7/9x = 5/6 without fractions, we can eliminate the fractions by multiplying both sides of the equation by the least common denominator (LCD) of all the denominators involved.

The LCD in this case is the product of 9 and 6, which is 54.

Multiplying both sides of the equation by 54:

54 * (2 - 7/9x) = 54 * (5/6)

On the left side, we distribute the 54 to each term:

108 - (54 * 7/9)x = (54 * 5/6)

Now we simplify each side of the equation:

108 - (378/9)x = 270/6

108 - 42x/9 = 270/6

Now we can simplify the equation further:

108 - 14x = 45

To eliminate the constant term on the left side, we subtract 108 from both sides:

-14x = 45 - 108

-14x = -63

Finally, to isolate x, we divide both sides by -14:

x = (-63) / (-14)

Simplifying the division:

x = 9/2

Therefore, the equation 2 - 7/9x = 5/6, when rewritten without fractions, is x = 9/2.

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Answer:3−4x/7≤y≤−8+5x

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x - 9y = -9 x x - 3y = (5  + 9) - 6 - 9) + 9 - 5