Assume, you want to cluster 8 observations into 3 clusters using
K-Means clustering algorithm. After the first iteration clusters
C1, C2, C3 have the following observations:
C1: {(2,3), (4,3), (6,6)}

Answer:

Reflection

Step-by-step explanation:

(x, y) --> (x, -y) is a reflection over the x-axis

Answer:

q=-14

Step-by-step explanation:

Answer:

a=5 ;b=10 ;c= 5 ; d= 5√3

Step-by-step explanation:

sin 45=9/5√2

a=5√2 sin 45

a= 5

tan45= 5/c

c=5/tan45

c= 5

tan 30=a/d

=5/d

d=5/tan 30

d=5√3

sin 30=5/b

b= 5/sin 30

b= 10

The probability that exactly two out of ten buyers prefer green is 0.0439 when 50% of the population prefers green.

This can be calculated using the binomial distribution formula, which calculates the probability of a certain number of successes (in this case, two) out of a certain number of trials (in this case, ten) given a probability of success (in this case, 0.5).

The formula is P(X=2) = (10 choose 2) * 0.5^2 * (1-0.5)^8

= 0.0439

where "10 choose 2" represents the number of ways to choose two buyers out of ten.

This result indicates that there is a moderate probability that exactly two-fifths of the buyers would prefer green in a random sample of ten buyers.

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Answer:

(y+5)(y-3)

Step-by-step explanation:

..........

Answer:

y^2-3y+5y-15

y(y-3)+5(y-3)

(y-3) (y+5)

The equation\(y ′ = 4y − 3x/ (12xy − 1)\) is not separable , the given statement is False.  A differential equation is said to be separable if it can be written in the form `dy/dx = f(x)g(y)`. It can then be separated into two separate equations in the form of`g(y)dy = f(x)dx`, and then integrated on both sides to get the general solution.

In this equation,\(y' = 4y − 3x/ (12xy − 1)\)is not separable because the variable x and y can not be separated. we cannot write the equation in the required form. The equation is not a separable equation. In conclusion, the statement that the equation\(y' = 4y − 3x/ (12xy − 1)\) is separable is False because the equation cannot be separated into two different variables x and y.

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Answer:

The domain of a function is the set of values that we are allowed to plug into our function. The Range is the difference between the lowest and highest values

Step-by-step explanation:

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

$ 7.52

Step-by-step explanation:

Find charge per minute

 59 - 23 min = 36 minutes   cost   16.32 - 10.56 = $ 5.76

      or   $5.76 / 36 min = 16 cents per min

   from 59 to 78 = 19 more minutes        x .16/min =  $ 3.04

            so from 59 to 78 will leave 10.56 - 3.04 = $7.52

Answer:

to solve this, first you need to write the equation -4x + 7 = 15, then you take 7 off both sides like this -4x + 7-7=15-7 -4x=8, after than you divide both sides by -4 like this -4x/-4=8/-4 x=-2 and theres you're anwser

Step-by-step explanation:

Answer:

-4x+7=15

collect like terms

-4x=15-7

-4x=8

divide both sides by the co-efficient of x

-4x/-4=8/-4

x= -2

ans

The age breakdown of supermarket shoplifters who are at least 21 years old is 163.5.

Given that,

The information used in the following was obtained from the national retail federation. Following is the age distribution of 895 occurrences of shoplifting taken as a random sample. Calculate the shoplifters' sample variance, sample standard deviation, and sample mean age. Use 45. 5 as the class midpoint for students who are 41 and older.

We have to find what is the age breakdown of supermarket shoplifters who are at least 21 years old.

We know that,

To estimate the mean age ,

The formula is x = ∑ (xi×fi) /∑fi

x = (6222+ 126735 +13377) / (244+357+294)

x = 146344/895

x= 163.5

Therefore, The age breakdown of supermarket shoplifters who are at least 21 years old is 163.5.

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Answer:

it is a 30 degree angle

Step-by-step explanation:

Is this selection (A) the best one? a high positive number. The result of multiplying a negative number by a positive number is always negative.

The result of multiplying two numbers, whether they are positive or negative, is always positive. 3 plus 4 equals 12. The result is minus 12 since there is only one optimistic and one negative number.

Why does adding two negative numbers together results in a positive number?

Repeated subtraction equals multiplication by a negative. Negative numbers were reduced in negative value after they have been multiplied together. Students may easily relate both ideas thanks towards this comparison among both multiplication and addition.

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Answer:  \((-\infty, -4]\)

Curved parenthesis at negative infinity

Square bracket at -4

====================================================

Work Shown:

\(5(x+4) \le 0 \\\\x+4 \le \frac{0}{5} \\\\x+4 \le 0 \\\\x \le 0-4 \\\\x \le -4 \\\\\)

The last inequality shown above is the same as saying \(-\infty < x \le -4\)

Converting this to interval notation leads to the final answer of \((-\infty , -4]\)

Note the use of a square bracket at -4 to include this endpoint. We can never include either infinity, so we always use a parenthesis for either infinity.

Answer:

Step-by-step explanation: it  bbbb

Answer: it an edge

Step-by-step explanation:

Plato

Answer:

40 multiply by area of the table

Step-by-step explanation:

force = pressure *  area of the table

Let's say imput is i and that output is o.

The formula is 2 ^ i = o

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

Notice how the numbers match?

Hope this helped :)

The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

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Step-by-step explanation:

A + B = 0

A = -B

(-B)B) = -36

-B^2 = -36

B^2 = 36

B = 6, -6

So, A = -6, 6

A - B = -12

or

A - B = 12

Answer:

A - B = ± 12

Step-by-step explanation:

Given

A + B = 0  → (1)

AB = - 36 → (2)

Subtract B from both sides of (1)

A = - B ← substitute into (2)

- B(B) = - 36 ( multiply both sides by 0 1 )

B² = 36 ( take square root of both sides )

B = ± 6

Substitute into (1)

If B = 6 then A =- 6 and A-B = - 6 - 6 = - 12

If B = - 6 then A = 6 and A - B = 6 - (- 6) = 6 + 6 = 12

Answer:

-4 or 4

Step-by-step explanation:

We can solve for the value of y by using the first equation to express y in terms of x and then substituting the resulting expression for y into the second equation.

From the first equation, we have:

4x - y = 4

Rearranging this equation to solve for y, we get:

y = 4x - 4

Now, we can substitute this expression for y into the second equation:

2x^2 - y = 4

Replacing y with 4x - 4, we get:

2x^2 - (4x - 4) = 4

Expanding the brackets and simplifying, we get:

2x^2 - 4x + 4 = 4

Subtracting 4 from both sides, we get:

2x^2 - 4x = 0

Factorizing, we get:

2x(x - 2) = 0

Using the zero product property, we see that this equation is satisfied when either 2x = 0 or x - 2 = 0.

If 2x = 0, then x = 0, and we can use the expression for y that we found earlier to get:

y = 4x - 4 = 4(0) - 4 = -4

If x - 2 = 0, then x = 2, and again using the expression for y, we get:

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

Therefore, the possible values of y are -4 and 4. We would need more information to determine which value of y is the correct one in this context.

The given expression, \(d(n)d(n)d(n)\), represents the duration in seconds for Hailey to run her \(n^{th}\) lap. The specific values provided, 333, 777, 999, correspond to the durations of the 3rd, 7th, and 9th laps, respectively. The values 858585, 999999, and 110110110 are unrelated and do not provide any additional information about lap durations.

The expression \(d(n)d(n)d(n)\) suggests that each lap duration is represented by the function \(d(n)\), where \(n\) denotes the lap number. The specific values given (333, 777, 999) correspond to the 3rd, 7th, and 9th laps, respectively. However, the remaining values (858585, 999999, 110110110) do not appear to have a direct connection to the lap durations or the function \(d(n)\).

Without further information or a specific pattern, it is difficult to interpret the significance of the remaining values. It's important to note that more context or information about the pattern or relationship between the values would be necessary to provide a more detailed explanation or analysis.

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Most common is 7

So

Use distributive law to verify

Verified

GCF is 7

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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Answer:

assuming that "x" is a multiplication symbol

(4.2*2)10^-5

0.00001 * 8.4

The total amount is given by 2080 pesos.

At discounts of 14% , the discount amount will be

So amount due due to 14%

So the amount due due to 14% discount is

Now at 6% discount we have

And abount due will be

Answer:

f(3) = 2/5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 4/5x - 2

f(3) is x = 3

Step 2: Evaluate

Answer: 2/5

Step-by-step explanation:

We need to replace x with 3

f(x)= 4/5*(3)-2= (12/5)-2=(12-10)/5= 2/5

Answer:

Suppose: M, N, P, Q are the midpoints of AB, BC, CD, AD respectively

=> MNPQ is the quadrilateral inside ABCD

connect B to D, ΔABD has : M is the midpoint of AB

                                              Q is the midpoint of AD

=> MQ is the midpoint polygon of ΔABD

=> MQ // BD and MQ = 1/2.BD (1)

ΔBCD has: N is the midpoint of BC

                  P is the midpoint of DC

=> NP is the midpoint polygon of ΔBCD

=> NP // BD and NP = 1/2.BD    (2)

from (1) and (2) => MQ // NP ( //BD)

                            MQ = NP  (=1/2.BD)

=> MNPQ is a parallelogram.​

=>  the quadrilateral inside ABCD is a parallelogram.​

Step-by-step explanation: