Suppose a cluster M at a certain iteration of the k-means
algorithm contains the observations x1 = (2, 3), x2 = (−1, −3), x3
= (−2, 3). If M only cluster, what would be the sum of squared
errors

Answer:

M = 18

Step-by-step explanation:

Answer: 54.29%

Step-by-step explanation:

Given: The probability that they  will win both games is 38%.

i.e. P( both games will win) =0.38

The probability that they will win just the first game is  70%.

P(first game will win) = 0.70

To find : P(second game will win| first game will win)

Using formula: \(P(B|A)=\dfrac{P(\text{both A and B})}{P(A)}\)

So, P(second game will win| first game will win) = \(\dfrac{\text{ P( both games will win)}}{\text{P(first game will win)}}\)

\(=\frac{0.38}{0.70}\approx0.5429=54.29\%\)

Hence, the required probability = 54.29%

Answer:

$12.50

Step-by-step explanation:

Answer:

x = 132°

Just add the opposite interior angles

The linearly independent solutions of the differential equation Y"' + 2xy = 0, in the given form, are y1 = 1 - (1/18)x⁶ + ... and y2 = x + (1/210)x⁷ + ... The coefficients a₃ = 0, a₆ = -1/18, b₄ = 0, and b₇ = 1/210.

To find two linearly independent solutions of the differential equation Y"' + 2xy = 0 in the given form, we can assume power series solutions of the form:

y1 = 1 + a₃x³ + a₆x⁶ + ...

y2 = x + b₄x⁴ + b₇x⁷ + ...

We will substitute these series into the differential equation and equate the coefficients of corresponding powers of x to find the values of the coefficients.

Substituting y1 and y2 into the differential equation, we have:

(1 + a₃x³ + a₆x⁶ + ...)''' + 2x(x + b₄x⁴ + b₇x⁷ + ...) = 0

Expanding the derivatives and collecting like terms, we can set the coefficients of corresponding powers of x to zero.

The first few coefficients are:

a₃ = 0

a₆ = -1/18

b₄ = 0

b₇ = 1/210

Therefore, the linearly independent solutions of the differential equation are

y1 = 1 - (1/18)x⁶ + ...

y2 = x + (1/210)x⁷ + ...

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--The given question is incomplete, the complete question is given below " (25 points) Find two linearly independent solutions of Y"' + 2xy = 0 of the form y1 = 1 + a₃ x³ + a₆ x⁶ + ...,

y2 = x + b₄x⁴ + b₇x⁷ + ...

Enter the first few coefficients: а₃=

a₆ =

b₄ =

b₇ ="--

The upper class represents approximately 1-2% of the population. The upper class is composed primarily of CEOs, government officials, celebrities, and very successful professionals.

This class is the smallest among the five social classes, comprising only a tiny percentage of the population (1-2 percent).Individuals in the upper class are often referred to as the "social elite," as they are frequently born into money, live in luxurious estates, and are members of exclusive clubs. Upper-class individuals usually have excellent education and a variety of skills that have helped them accumulate wealth and power. Therefore, the upper class represents approximately 1-2% of the population.

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Answer:

Option A ( -3/2 , \(\frac{-3\sqrt{3} }{2}\) )

Step-by-step explanation:

(For Diagram, Please Find in attachment)

Now In Triangle OAB

        1/2 = -X / 3 Thus X= -3/2

        \(\sqrt{3}\)/2 = -Y / 3 Thus Y = -\(\sqrt{3}\) * 3 /2

Answer:

Step-by-step explanation:

Covert 21 out of 175 into percentage:

We need percentage

\(\\ \bull\sf\dashrightarrow \dfrac{21}{175}\times 100\)

\(\\ \bull\sf\dashrightarrow \dfrac{21}{7}\times 4\)

\(\\ \bull\sf\dashrightarrow 3(4)\)

\(\\ \bull\sf\dashrightarrow 12\%\)

Answer:

6fc5dx7 8tfl 8tf . 8tfl 8tf tfd4 4 Ltd Ltd PM. tfl t

Each piece of furniture used 4/25 gallons of paint. The answer lies between 0 and 1, and each piece of furniture used 0.16 gallons of paint.

A full number plus a legal fraction are combined to form a mixed number. It is expressed in the form of "a b/c", where "a" is the whole number, "b" is the constant term of the correct fraction, and "c" is the denominator of the proper fraction. For instance, the mixed number 3 1/4, which equals three and one-fourth, is a mixed number. The entire integer can also be expressed as an improper fraction by multiplying it by the fraction's denominator, adding the numerator, and then putting the resulting sum over the denominator.

Let us suppose the amount of paint used = x.

Thus,

20x + 5x = 4

25x = 4

x = 4/25

Therefore, each piece of furniture used 4/25 gallons of paint.

To find between what two whole numbers the answer lies, we can convert 4/25 to a mixed number:

4/25 = 0.16

Hence, the answer lies between 0 and 1, and each piece of furniture used 0.16 gallons of paint.

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The two positive real numbers with a product of 11 that have the smallest possible sum are √11 and √11. In decimal form, these numbers are approximately 3.3166 and 3.3166.

To determine two positive real numbers whose product is 11 and have the smallest possible sum, we can use the concept of the arithmetic mean-geometric mean inequality.

Let the two numbers be x and y.

We have the following conditions:

1. xy = 11 (product of the two numbers is 11)

2. x > 0, y > 0 (both numbers are positive)

According to the AM-GM inequality, the arithmetic mean of two numbers is always greater than or equal to the geometric mean of those numbers.

Using this inequality, we have:

(x + y)/2 ≥ √(xy)

Substituting the value of xy as 11, we get:

(x + y)/2 ≥ √11

To minimize the sum (x + y), we need to make it as close as possible to the right side of the inequality.

This occurs when equality holds, that is, when:

x = y = √11

So, the answer is approximately (3.3166, 3.3166).

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Answer:

4

Step-by-step explanation:

Simplifying

5a + -4 = 2a + 8

Reorder the terms:

-4 + 5a = 2a + 8

Reorder the terms:

-4 + 5a = 8 + 2a

Solving

-4 + 5a = 8 + 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

-4 + 5a + -2a = 8 + 2a + -2a

Combine like terms: 5a + -2a = 3a

-4 + 3a = 8 + 2a + -2a

Combine like terms: 2a + -2a = 0

-4 + 3a = 8 + 0

-4 + 3a = 8

Add '4' to each side of the equation.

-4 + 4 + 3a = 8 + 4

Combine like terms: -4 + 4 = 0

0 + 3a = 8 + 4

3a = 8 + 4

Combine like terms: 8 + 4 = 12

3a = 12

Divide each side by '3'.

a = 4

Simplifying

a = 4

Answer:

Step-by-step explanation:

to make 3255 a perfect square subtract 6 from 3255

3255 - 6 = 3249

3249 is a perfect square

The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.

The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.

Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.

1. y = x² + 8x + 18

To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.

The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2

. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.

The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.

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The given data set is:

It is required to find the mode.

Recall that the mode is the value in a set of data that has the most occurrences.

Note that the mode is not unique and a data set may have no mode.

The value that has the most occurrences in the set is not unique.

Hence, the data set has no mode score

The minimum height of the ladder needed to change the lightbulb is 29 feet.

To determine the minimum height of the ladder, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this problem, the ladder acts as the hypotenuse of a right triangle, and we know the height of the lightbulb (27 feet), the reach of the ladder (3 feet), and the distance between the ladder and the wall of the house (7 feet).

Let h be the minimum height of the ladder. Then, using the Pythagorean theorem, we have:

h^2 = 27^2 + 7^2 + 3^2

h^2 = 729 + 49 + 9

h^2 = 787

h ≈ 28.06

Since we need to round up to the nearest whole number (since ladders come in discrete sizes), the minimum height of the ladder needed is 29 feet.

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The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

Answer:

y = (2/5)x + 2

Step-by-step explanation:

The given equation y = (2/5)x - 2​ is already in slope-intercept form.  The equation of the new line has precisely that form, except that the constant is different.  To find the new constant (which is the y-intercept), replace x with 5 and y with 4 in y = (2/5)x + C:

4 = (2/5)(5) + C, or

4 = 2 + C.  Therefore, C = 2 and the equation of the new line is y = (2/5)x + 2.

The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)

Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.

They are also described as expressions composed of arithmetic operations, such as;

It is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.

From the information given, we have the expression;

27 g^7 k^3 z^4 - 9 g^2 K^5 z

Subtract the coefficient

18(g⁷k³z⁴ - g²k⁵z)

Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)

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The probabilities that the defective bolt was manufactured by machines A, B, and C are approximately 0.3623, 0.4058, and 0.2319, respectively.

To solve this problem, we can use Bayes' theorem.

Let's denote the events as follows:

A: Bolt is manufactured by machine A

B: Bolt is manufactured by machine B

C: Bolt is manufactured by machine C

D: Bolt is defective

We need to find the conditional probabilities P(A|D), P(B|D), and P(C|D). According to Bayes' theorem:

P(A|D) = (P(D|A) x P(A)) / P(D)

P(B|D) = (P(D|B) x P(B)) / P(D)

P(C|D) = (P(D|C) x P(C)) / P(D)

We are given the following information:

P(A) = 0.25 (machine A manufactures 25% of the total output)

P(B) = 0.35 (machine B manufactures 35% of the total output)

P(C) = 0.40 (machine C manufactures 40% of the total output)

P(D|A) = 0.05 (5% of machine A's output is defective)

P(D|B) = 0.04 (4% of machine B's output is defective)

P(D|C) = 0.02 (2% of machine C's output is defective)

To calculate P(D), we can use the law of total probability:

P(D) = P(D|A) x P(A) + P(D|B) x P(B) + P(D|C) x P(C)

Let's substitute the given values into the equations:

P(D) = (0.05 x 0.25) + (0.04 x 0.35) + (0.02 x 0.40)

= 0.0125 + 0.014 + 0.008

= 0.0345

Now, we can calculate the conditional probabilities:

P(A|D) = (0.05 x 0.25) / 0.0345

= 0.0125 / 0.0345

≈ 0.3623

P(B|D) = (0.04 x 0.35) / 0.0345

= 0.014 / 0.0345

≈ 0.4058

P(C|D) = (0.02 x 0.40) / 0.0345

= 0.008 / 0.0345

≈ 0.2319

Therefore, the probabilities that the defective bolt was manufactured by machines A, B, and C are approximately 0.3623, 0.4058, and 0.2319, respectively.

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Answer:

22,260

Step-by-step explanation:

Answer:

i just took the answer thing and it would be 22,260 sorry i am so late with the answer but yea hope this helps

Answer:

1) 5 & 9

5=Corresponding Angle

9=Alternate Exterior Angle

2) 7 & 8

We know 4 is supplementary to 8.  Since that is true, 7 & 8 are also.

8=Corresponing angle to 4

7=Verticle angle to 8

3) We know 1 and 3 equal 180

x-20+x+40=180

2x+20=180

2x=180-20

2x=160

x=80

<2=X+20

=80+20

=100

Angle 2 is the same as angles 5 and 6 added together.

We know angle 5 is the same as angle 1 (corresponding angles).

<1=X-20

=80-20

=60

Now that we know <2=100 and <5=60, we can figure out <6

100-60=40

<6=40°

Step-by-step explanation:

1) 5 & 9

5=Corresponding Angle

9=Alternate Exterior Angle

2) 7 & 8

We know 4 is supplementary to 8.  Since that is true, 7 & 8 are also.

8=Corresponing angle to 4

7=Verticle angle to 8

3) We know 1 and 3 equal 180

x-20+x+40=180

2x+20=180

2x=180-20

2x=160

x=80

<2=X+20

=80+20

=100

Angle 2 is the same as angles 5 and 6 added together.

We know angle 5 is the same as angle 1 (corresponding angles).

<1=X-20

=80-20

=60

Now that we know <2=100 and <5=60, we can figure out <6

100-60=40

<6=40°

The value of chi-square statistic (\(X^{2}\)) is 11.26

As per the given question

the sample space of all the four cases are 30

the proportions that land upright are the same when the dropping height is 3, 5, 10, and 20 cm.

the formula of chi-squared test is

\(X^2=\sum\frac{(O_i-E_i)^2}{E}\)

where

\(X^{2}\) is chi-square

\(O_i\) is the observed value

\(E_i\) is the expected value

the upright observed value are 20,23,27,29

the upright expected values are 24.75

now

the chi-square at 3cm height is

\(X^2=\(\frac{(20-24.75)^2}{24.75}\)

=> \(X^2=0.91\)

the chi- square at 5cm height is

\(X^2=\(\frac{(23-24.75)^2}{24.75}\)

=> \(X^2=0.12\)

the value of chi-square at 10cm is

\(X^2=\(\frac{(27-24.75)^2}{24.75}\)

=>\(X^2=0.20\)

the value of chi-square at 20cm is

\(X^2=\(\frac{(29-24.75)^2}{24.75}\)

=> \(X^2=1.97\)

the not upright observed values are

10,7,3,1

the not upright expected values are 5.25

the chi-square test at 3cm height is

\(X^2=\(\frac{(10-5.25)^2}{5.25}\)

=> \(X^2=4.30\)

the chi-square test at 5cm height is

\(X^2=\(\frac{(7-5.25)^2}{5.25}\)

=> \(X^2=0.58\)

the chi-square test at  10cm height is

\(X^2=\(\frac{(3-5.25)^2}{5.25}\)

=> \(X^2=0.96\)

the chi-square test at 20 cm is

\(X^2=\(\frac{(1-5.25)^2}{5.25}\)

=> \(X^2=3.44\)

now,

the total

chi-square value at 3cm height is

=>X^2=0.91+4.30

=> \(X^{2}\)= 5.21

chi-square at 5cm height is

=> \(X^{2}=0.12+0.58\)

=> \(X^2=0.71\)

chi-square at 10cm is

=> \(X^{2}=0.20+096\)

=> \(X^2=1.16\)

chi-square at 20 cm is

=> \(X^{2}=0.73+3.44\)

=> \(X^{2}=4.17\)

now ,

the total chi-square statistic is

=>\(X^{2}=\)5.21+0.71+1.17+4.17

=>\(X^{2}=\) 11.26

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Answer:

Let, the c.p be x.

Given,

profit % = 20%

S.P = rs 816

c.p = x

We know,

profit = p% of c.p

         = \(\frac{20}{100}\) * x

         = \(\frac{x}{5}\)

now,

   C.p = profit + s.p.

        x = \(\frac{x}{5}\) + 816

        x = \(\frac{x+ 4080}{5}\)

       5x = x + 4080

       5x-x = 4080

       4x = 4080

         x = \(\frac{4080}{4}\)

         x = Rs 1080

Hence, the c.p is Rs. 1080

Answer:

Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer

Answer:

F = 250 N

Step-by-step explanation:

Given that,

Mass of an object, m = 50 kg

The coefficient of kinetic friction = 0.5'

We need to find the force of kinetic friction. The kinetic friction is given by the formula as follows :

\(F=\mu N\)

N is normal force, N = mg

\(F=0.5\times 50\times 10\\\\F=250\ N\)

Hence, the force of kinetic friction is 250 N. Hence, the correct option is (d).

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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