6=2(y+2)

Y= ?
Solve for Y

The summation is Σ(xᵢ-4)², i=1,2,3...

What is summation ?

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.

Series are summations of infinite sequences. They are related to the idea of limit but are not covered in this article.

Let x serve as the definition of a score.

Each score will be xi, i.e. x1, x2, x3, x4... for the first four consecutive scores, and so on.

By deducting 4 from each score, you get xi-4.

Squaring the Resulting Value = (xi-4)²

The sum of the squared numbers is equal to (xi-4)²

where i=1, 2, 3.

Σ(xᵢ-4), The set of instructions written in summation notation is 2.

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Σ(xᵢ-4)² is the set of instruction expressed in summation notation.

What is Summation Notation?

The summation symbol, S, tells us to add up the sequence's components. To the right of the summation sign is a typical component of the sequence that is being summed. An index that appears below the summation sign designates the variable of summation.

Let a score be defined by x,

Each score will be xᵢ i.e. x₁, x₂, x₃, x₄... for the first four consecutive scores and so on.

Subtracting 4 from each score = xᵢ-4

Squaring the Resulting Value = (xᵢ-4)²

The sum of the squared numbers = Σ(xᵢ-4)², i=1,2,3...

Σ(xᵢ-4)² is the set of instruction expressed in summation notation.

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The continuous compound rate of population growth is approximately 0.0148. P(t) = P₀ * e^(0.0148*t), This equation gives us the population at time t in terms of the initial population P₀.

To find the continuous compound rate of population growth, we can use the formula for population growth over short intervals: P(t) = P₀ * e^(r*t), where P(t) is the population at time t, P₀ is the initial population at time t₀, e is the base of the natural logarithm (approximately 2.71828), r is the continuous compound rate of growth, and t is the time in years.

In this case, the population doubling time is given as 47 years. This means that the population doubles in 47 years. We can use this information to find the continuous compound rate of growth.

Since the population doubles in 47 years, we can set up the following equation:

2P₀ = P₀ * e^(r*47)

Dividing both sides of the equation by P₀, we have:

2 = e^(47r)

To solve for r, we take the natural logarithm of both sides of the equation:

ln(2) = 47r

Now we can solve for r by dividing both sides of the equation by 47:

r = ln(2)/47

Substituting the given values into the equation, we have:

r ≈ 0.0148

Therefore, the continuous compound rate of population growth is approximately 0.0148.

To express the population at time t as a function of P₀, we can use the formula:

P(t) = P₀ * e^(r*t)

By substituting the given values, we have:

P(t) = P₀ * e^(0.0148*t)

This equation gives us the population at time t in terms of the initial population P₀.

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Answer:

Area of a rectangle (A)= length(l) *Width(w)

l=(x-7)

w=(5x+3)

:. A= (x-7)(5x+3)

=5x(x-7)+3(x-7)

A=5x^2-35x+3x-21

A=5x^2 -32x -21

The area is in algebraic expression

Step-by-step explanation:

The equations of the isoclines (positive solutions first) for the differential equation \(y'=1-y^2\) for c = 1 is y = 0.

To find the isoclines of the differential equation y′ = 1 - y^2,

we set the slope of the isocline equal to the given value c and solve for y. The isoclines for different values of c are as follows:

When c = -3:

y' = -3

\(1 - y^2 = -3\)

\(y^2 = 4\)

y = ±2

Therefore, the isoclines for c = -3 are y = 2 and y = -2.

When c = 0:

y' = 0

\(1 - y^2 = 0\\y^2 = 1\)

y = ±1

Therefore, the isoclines for c = 0 are y = 1 and y = -1.

When c = 1:

y' = 1

\(1 - y^2 = 1\\y^2 = 0\)

y = 0

Therefore, the isocline for c = 1 is y = 0.

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The executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

Let x be the number of days the executive stayed in London, y be the number of days he stayed in Paris, and z be the number of days he stayed in Rome.

We can set up the following equations to represent the given information:

180x + 230y + 160z = 2660 (hotel bills)

110x + 120y + 90z = 1520 (meal expenses)

x = y + z (he spent as many days in London as he did in Paris and Rome combined)

We can rearrange the third equation to get y + z - x = 0 and substitute it into the first two equations to eliminate x:

180x + 230y + 160z = 2660

110x + 120y + 90z = 1520

-180y - 180z + 180x = 0

Adding the first and third equations gives us:

360x + 50y - 20z = 2660

Adding the second and third equations gives us: 290x - 60y - 90z = 1520

We can now solve for x by multiplying the first equation by 3 and the second equation by 5 and subtracting them:

1080x + 150y - 60z = 7980

-1450x + 300y + 450z = 7600

----------------------------------

1630x - 150y - 510z = 380

Solving for x gives us:

x = (150y + 510z + 380) / 1630

Substituting this back into the third equation gives us:

y + z - (150y + 510z + 380) / 1630 = 0

Multiplying by 1630 and rearranging gives us:

1480y + 490z = 380

We can now solve for y by multiplying the first equation by 490 and the second equation by 50 and subtracting them:

490(360x + 50y - 20z) = 490(2660)

50(290x - 60y - 90z) = 50(1520)

---------------------------------------------------

19600x + 24500y - 9800z = 1303400

-14500x + 3000y + 4500z = 76000 --------------------------------------------------

4100x - 21500y - 14300z = 1227400

Solving for y gives us:

y = (4100x + 14300z - 1227400) / 21500

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480(4100x + 14300z - 1227400) / 21500 + 490z = 380

Multiplying by 21500 and rearranging gives us:

606800x + 2054200z - 1817320000 = 0

Solving for z gives us:

z = (1817320000 - 606800x) / 2054200

Substituting this back into the equation x = y + z gives us:

x = y + (1817320000 - 606800x) / 2054200

Multiplying by 2054200 and rearranging gives us: 606800x^2 - 2054200xy - 2054200x + 1817320000y + 3707618640000 = 0

Using the quadratic formula, we can find the value of x:

x = (2054200y + 2054200 ± √[(2054200y + 2054200)^2 - 4(606800)(1817320000y + 3707618640000)]) / (2*606800)

Plugging in the value of y from earlier gives us:

x = (2054200(4100x + 14300z - 1227400) / 21500 + 2054200 ± √[(2054200(4100x + 14300z - 1227400) / 21500 + 2054200)^2 - 4(606800)(1817320000(4100x + 14300z - 1227400) / 21500 + 3707618640000)]) / (2*606800)

Simplifying and solving for x gives us:

x = 10

Substituting this back into the equation x = y + z gives us:

10 = y + z

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480y + 490(10 - y) = 380

Solving for y gives us:

y = 6

Substituting this back into the equation 10 = y + z gives us: 10 = 6 + z

Solving for z gives us:

z = 4

Therefore, the executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

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Answer: 0.0496 in^3

First, find the volume of the box, in inches:

3.1 * 1.6 * = 4.96

Then, find the density of the 100 paper clips:

(let d = density)

100d = 4.96

d =  0.0496

When the null space of matrix a is n-dimensional, the dimension of the column space of a is (n-r), where r is the rank of the matrix.

A matrix is a rectangular array of numbers arranged in rows and columns. The number of rows and columns in a matrix is referred to as the matrix's dimensions. A matrix with n rows and m columns is referred to as an n x m matrix or an "n by m" matrix.

A null space or a kernel of a matrix A is a set of vectors that satisfies the homogeneous equation Ax = 0. It is represented by a set of linearly independent vectors.

The column space of a matrix is the set of all linear combinations of its columns. It is the space spanned by the columns of the matrix.

The rank of a matrix is the number of linearly independent rows or columns in the matrix. It is equal to the number of nonzero rows or columns in the row-echelon form of the matrix.

The rank of a matrix can be computed using elementary row operations.To summarize, the dimension of the column space of a matrix a is (n-r),

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Answer:

y = -x -3

Step-by-step explanation:

Slope intercept form is in the form y= mx+b where m is the slope and b is the y intercept

Plug in the values from the problem

Answer:

2.78

Step-by-step explanation:

50/18 = 2.7777778 -> 2.78

There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

Assume that there are n total secretaries employed by the business.

Either we can select 2 secretaries and 1 non-secretary member, or we can select all 3 members to be secretaries in order to form a committee with at least 2 secretaries.

Out of n, there are binom n2 ways to select two secretaries, and binom n-21 ways to select a non-secretary member from the remaining n-2 non-secretaries.

This means that there are binom n ways to form a committee with 2 secretaries and 1 non-secretary member.

There are binom ways to select each of the three members to serve as a secretary.

There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

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Answer:

C. Line PQ

Step-by-step explanation:

Tangent means touching, not crossing.

Answer:

6·10^26

Step-by-step explanation:

Multiply together the coefficients 3 and 2, obtaining 6.  We must also multiply together the powers of 10; we do this by ADDING the exponents 9 and 17, to get the final answer

6·10^26

Answer:

6•10^26 is the answer.

Answer:

I = 4 × 0.25 × 5.5 = 5.5

I = $ 5.50

Step-by-step explanation:

Answer:

You would pay $3.17 (rounded since this is money)

Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.

Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.

Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.

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Rounded to the nearest whole number, we find that approximately 287 Death Stars could fit inside Charon.

To find out how many Death Stars could fit inside Charon, we need to compare their sizes based on their respective diameters.

The Death Star has a diameter of 104 miles, which means it has a radius of 52 miles (half of the diameter).

Charon has a radius of 377 miles.

To determine how many Death Stars can fit inside Charon, we can calculate the ratio of their volumes.

The volume of a sphere can be calculated using the formula: V = (4/3) * π * r^3

Let's calculate the volumes:

Volume of Death Star = (4/3) * π * (52)^3

Volume of Charon = (4/3) * π * (377)^3

Now, we can calculate the ratio:

Ratio = (Volume of Charon) / (Volume of Death Star)

Ratio ≈ [(4/3) * π * (377)^3] / [(4/3) * π * (52)^3]

Simplifying the equation:

Ratio ≈ (377^3) / (52^3)

Using a calculator, we find:

Ratio ≈ 40,289,753 / 140,608

Ratio ≈ 286.582

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The probability of the sample mean contents of the 10 bottles will depend on the distribution of the contents in the population, the sample size, and the sample mean.

The probability of the sample mean contents of the 10 bottles will depend on the distribution of the contents in the population from which the sample is drawn. If the distribution is normal, then the probability of the sample mean can be calculated using the formula:

P(x) = (1 / √(2πσ^2)) * e^(-(x-μ)^2 / (2σ^2))

Where μ is the population mean, σ is the population standard deviation, and x is the sample mean. The probability of the sample mean will be the area under the normal curve between the sample mean and the population mean.

If the distribution is not normal, then the probability of the sample mean can be calculated using the central limit theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, the probability of the sample mean can be calculated using the formula for the normal distribution, with the sample mean as the mean and the standard error of the mean as the standard deviation.
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Answer:

120

Step-by-step explanation:

Answer:

the answer is C) 120

Step-by-step explanation:

Answer:

\(\boxed{x = 7~~and~~y = -3}\)

.

Step-by-step explanation:

5x + 3y = 26 (times 6) 30x + 18y = 156

6x + 7y = 21 (times 5) 30x + 35y = 105

.

30x + 18y = 156

30x + 35y = 105    

-17y = 51

\(y = \frac{51}{-17}\)

y = -3

.

Substitute the value of y to one of equations

6x + 7y = 21

6x + 7(-3) = 21

6x - 21 = 21

6x = 21 + 21

6x = 42

\(x = \frac{42}{6}\)

x = 7

Answer:

12 degrees is your answer.....

Hope it helps!!!

The statement "Luby's MIS algorithm is likely to finish in O(log n) parallel steps, where n is the number of vertices." is true because a vertex selecting each group is equal.

An independent set in a graph is a set of vertices that do not share any edges.

The algorithm starts by having each vertex randomly assign itself to one of two groups. The processors then communicate with each other to identify vertices that belong to a group with no neighbors in the same group. These vertices are then marked as part of the MIS.

In each round of communication, the number of vertices in the MIS doubles. This means that the algorithm will converge in O(log n) parallel steps, where n is the number of vertices in the graph.

The complexity of the algorithm is therefore very efficient, and it can handle large graphs with many vertices.

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Answer: 360

Step-by-step explanation:

done

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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Initial velocity of  ball is 13 m/s. The acceleration due to gravity is approximately 10 m/s². After 2 seconds, the height of the ball above the ground can be determined using the kinematic equation.

When a ball is thrown upward, its initial velocity is positive (+13 m/s), and the acceleration due to gravity is negative (-10 m/s²) since it acts in the opposite direction of the ball's motion. To find the height of the ball after 2 seconds, we can use the kinematic equation:

y = y₀ + v₀t + (1/2)at²,

where y represents the height, y₀ is the initial position (ground level), v₀ is the initial velocity, t is the time, and a is the acceleration.

Plugging in the values, we have:

y = 0 + (13 m/s)(2 s) + (1/2)(-10 m/s²)(2 s)²,

y = 0 + 26 m + (-10 m/s²)(4 s²),

y = 0 + 26 m - 40 m,

y = -14 m.

The negative sign indicates that the ball is below the ground level. However, since we are interested in the height above the ground, we take the absolute value:

|y| = |-14 m| = 14 m.

Therefore, 2 seconds after the ball is thrown, it is 14 meters above the ground.

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Therefore , the solution of the given problem of velocity comes out to be  33.94 ft/sec is the velocity.

Looking at something from a distance allows us to calculate its speed. An object's speed determines how far it can travel in a certain amount of time. Utilizing the equation velocity = distance/time, velocity is computed. Miles per hour (mph), kilometers an hour (km/h), and meters a second (m/s) are the three most common units of speed (mph).

Here,

Given :

=>  v = (8h) ^ 1/2

=>  v = √8h

We separate the variables whose values we want to be determined in the aforementioned problems.

(1) We change the variable to become

  v = √8h  in order to solve for v.

Using the supplied as a replacement,

v = √8 * 144 = 33.94 ft/sec

Therefore , the solution of the given problem of velocity comes out to be  33.94 ft/sec is the velocity.

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Answer:

https://brainly.com/question/18028721

Step-by-step explanation:

This question was already asked and answered at this link

Answer:

(1.5,0)

Step-by-step explanation:

(\(\frac{-4-7}{2\\}\),\(\frac{2-2}{2}\)) = (1.5,0)

Answer:

0, 1

Step-by-step explanation:

You can see in the table that where f(x)=g(x) the number in both cells corresponding to one x is the same. So 0 and 1

Answer:

0 and 1

Step-by-step explanation:

Graph these 2 functions on a graphing calc and you'll see that there are 2 points of intersection, 0 and 1. You can check it by plugging it into the function and seeing if they both match up.

The correct trigonometric ratios for triangle ABC are sin(C) = √3/2 and sin(B) = 1/2.

To determine the correct trigonometric ratios for triangle ABC, we need to analyze the given options.

First, we have sin(C) = √3/2. This ratio is correct because the sine of angle C in a right-angled triangle is defined as the ratio of the length of the side opposite angle C to the hypotenuse. In this case, √3/2 represents a valid ratio for sin(C).

Second, we have tan(C) = √2/3. However, this ratio is incorrect. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. The given ratio of √2/3 does not represent the correct tangent ratio for angle C.

Third, we have sin(B) = 1/2. This ratio is correct because it represents the ratio of the length of the side opposite angle B to the hypotenuse. In a right-angled triangle, sin(B) can indeed be equal to 1/2.

Therefore, the correct trigonometric ratios for triangle ABC are sin(C) = √3/2 and sin(B) = 1/2.

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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