k-Nearest Neighbours with k=1 and Euclidean metric is performed
on a two-dimensional dataset. The training data is X_train =
[[1,1], [8,3], [2,6], [9,4], [7,2]]; Y = [0, 1, 2, 1, 3]. The test
data is

Answer:

37

Step-by-step explanation:

Answer:

D. 37

Step-by-step explanation:

Your choice is correct!

Answer:

y=−10Sx−3−70Sy=-10Sx-3-70S

Answer:

37.5%

Step-by-step explanation:

Based on the given conditions, formulate: 30/80

Reduce the fraction: 3/8

Rewrite a fraction as a decimal: 0.375

Multiply a number to both the numerator and the denominator:

0.375 * 100/100

Write as a single fraction:

0.375 * 100 / 100

Calculate the product or quotient:

37.5/100

Rewrite a fraction with denominator equals 100 to a percentage:

37.5%

Answer:

37.5%

Answer:

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

Step-by-step explanation:

We know that the slope-intercept of line equation is  

\(y=mx+b\)

Where m is the slope and b is the y-intercept

Given the equation of the line m

y = 1/2x - 4

comparing with the slope-intercept form of the line equation

y  = mx + b

Therefore,

The slope of line 'm' will be = 1/2

We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2

Checking the equation of the line 'n'

\(x-2y=4\)

solving for y to writing the equation in the slope-intercept form and determining the slope

\(x-2y=4\)

Add -x to both sides.

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

\(-2y = 4 - x\)

Divide both sides by -2

\(\frac{-2y}{-2}=\frac{-x+4}{-2}\)

\(y=\frac{1}{2}x-2\)

comparing ith the slope-intercept form of the line equation

Thus, the slope of the line 'n' will be: 1/2

Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.

For example:

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Answer:

Step-by-step explanation:

The absolute value, as "distance from zero", is used to define the absolute difference between arbitrary real numbers, the standard metric on the real numbers. Complex numbers [ edit ] The absolute value of a complex number z {displaystyle z} is the distance r {displaystyle r} of z {displaystyle z} from the origin.

Answer:

absolute number

Step-by-step explanation:

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

The angle for each slice is 45 degrees.

Step-by-step explanation:

In order to calculate the angle of each slice, we first need to calculate the total area of the pizza, because we will use that to find the area of each slice and as a result it's angle. To calculate the area of the pizza we must use:

pizza area = pi*r²

r = d / 2 = 14 /2 = 7 inches

pizza area = pi*(7)² = 153.86 square inches

Since the pizza was divided in 8 pieces, the area of each piece is given by the area of the pizza divided by the number of slices. We have:

slice area = pizza area  / 8 = 153.86 / 8 =19.2325 square inches

Each slice is a circle sector, therefore it's area is given by:

slice area = (angle*pi*r²)/360

Therefore we can solve for angle:

19.2325 = (angle*pi*7²)/360

angle*pi*49 = 6923.7

angle = 6923.7 / pi*49 = 45 degrees

The angle for each slice is 45 degrees.

Answer:

8.318

Step-by-step explanation:

writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.

to three decimal places= 8.318

Step-by-step explanation:

Pythagoras

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Plugging in numbers

\( {4}^{2} + {8}^{2} = {c}^{2} \)

If we do the math given

\(16 + 64 = {c}^{2} - - - 80 = {c}^{2} \)

Last but not least, we root both sides

\( \sqrt{80} = c\)

Which means C = 8.9

An ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100. Without any magnification, it is not possible to determine the number of grains per square inch.

ASTM grain size is a measure of the size of the grains in a metal sample. The ASTM E112 defines the grain size number as the number of grains per square inch of metal surface area at a magnification of 100 times. So, an ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100.

Without any magnification, it is not possible to determine the number of grains per square inch as the grains are too small to be visible to the  eye. However, the ASTM grain size number can still provide information about the grain size distribution in the metal sample.

A metal sample with a smaller grain size number (i.e., larger grain size) will have fewer grains per square inch at a magnification of 100 than a metal sample with a larger grain size number (i.e., smaller grain size). This is because larger grains take up more surface area than smaller grains, resulting in fewer grains per unit area.

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each matrix may be extended by the identity matrices to convert all entries to integers.
allow A' = A + 2I = [3 0 0; 0 2 1]
B' = B + I = [1 1 0; 0 1 1]

A' and B' are actually integer matrices, although they still have the same null area and column area as A and B. As a end result, A = [3 0 0; 0 2 1]
B = [1 1 0; 0 1 1]

these matrices share the same null space and column area and are not multiples of each other.
The elements of a matrices are generally denoted via a image, inclusive of a, b, c, etc., and are organized in a specific order. Matrices are used in many regions of arithmetic, including linear algebra, calculus, and geometry.

Matrices are represented by enclosing the elements in brackets or parentheses. as an example, a 2x3 matrix A can be represented as:
A = [ a11, a12, a13 ]
[ a21, a22, a23 ]

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Remainder theorem tells about the remainder of division of a polynomial with x - a. The roots of given function are: 1, -1, -3

If there is a polynomial p(x), and a constant number 'a', then

\(\dfrac{p(x)}{(x-a)} = g(x) + p(a)\)

where g(x) is a factor of p(x)

For the given case, we've got:

\(f(x) = x^3 + 3x^2 -x - 3\)

and

f(1) = 0

Thus, for a = 1, from remainder theorem, we get:

\(\dfrac{p(x)}{(x-a)} = g(x) + p(a)\\\\\dfrac{f(x)}{(x-1)} = g(x) + f(1)\\\\\dfrac{x^3 + 3x^2 - x - 3}{(x-1)} = g(x) + 0\\\\ \dfrac{x^2(x+3) -1(x+3)}{x-1} = \dfrac{(x^2-1)(x+3)}{(x-1)} = g(x)\\\\(x+1)(x+3) = g(x)\)

Thus, the other factor of f(x) is g(x) = (x+1)(x+3)

And we have:

\(\dfrac{f(x)}{x-1} = g(x)\\\\f(x) = (x+1)(x+3)(x-1)\)

Putting it equal to 0, we get:

\(f(x) = 0\\(x+1)(x+3)(x-1) = 0\\x = 1, -1, -3\)

Thus,

The roots of given function are: 1, -1, -3

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Answer:

A

Step-by-step explanation:

got it right on Edge 1943 whilst fighting the German Forces in Northern Italy while my friends were on the beaches of Normandy.

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answer: C

Step-by-step explanation:

See attached image.

The rate of change of the area of the square when the side length is 7cm is  112 .

In the question ,
it is given that

the decreasing rate of the side length of the square is 8 cm per second ,

let the side length of the square be =  "\(s\)" .

So , ds/dt = -8 cm/s

the formula for area of \(s\)quare is ,

area = side²

A = s²

On differentiating both sides with respect to \(t\) ,

we get

dA/dt = 2s*ds/dt

Since we have to find rate of change of area when the side length is 7 cm ,

we substitute s = 7 , and ds/dt is given as  -8 cm/s

On substitution of values , we get

dA/dt = 2(7)*(-8)

= 14*(-8)

= -112

the negative sign in the answer means that the area is decreasing .

Therefore , The rate of change of the area of the square when the side length is 7cm is 112  .

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Answer:

Step-by-step explanation:

1. 6x + 10 = 6x - 8

   10≠-8

no solution

2. 6x + 8 = 2x - 6

    4x + 8 = -6

     4x = -14

     x = -14/4= -7/2 one solution

3. 9x - 27 = 9x - 27

    0 = 0 All real no. infinitely many solution

Press the "cot" or "1/tan" button on your calculator to calculate the cotangent of 5π/12. The result will be a decimal approximation.

To evaluate csc(3π/14) and cot(5π/12) using a calculator, follow these steps:

1. First, find csc(3π/14):
  - Enter "3π/14" into your calculator, making sure it is in radians mode.
  - Press the "csc" or "1/x" button on your calculator to calculate the cosecant of 3π/14.
  - The result will be a decimal approximation.

2. Next, find cot(5π/12):
  - Enter "5π/12" into your calculator, ensuring it is in radians mode.
  - Press the "cot" or "1/tan" button on your calculator to calculate the cotangent of 5π/12.
  - The result will be a decimal approximation.

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a) The square root of complex number, 2i is equals to the ±( 1 + i).

b) The square root of complex number, (1 - √3i) is equals to the ±1/√2(√3 - 1). The rectangular coordinates plane of both present in above figure.

Square root of a number is defined as a value which on multiplication by itself, results the original number. If p is the square root of q then it is denoted as p=√q. We have to determine the square root of complex numbers and express them in rectangular coordinates. For a nonzero complex number z, its square roots are √z =√r exp( i(2πk + θ)/2), k = 0,1

(a) The magnitude of 2i is r =√(2² + 0) = 2, and the principal argument is θ = π/2. So, (2i)½ = r½ exp(i (2πk + π/2)/2) , k = 0, 1

For first root, substuting, k = 0

=> (2i)½ = 2½ exp(i (2π×0 + π/2)/2)

=> (2i)½ = √2 exp(i (π/2)/2)

=> (2i)½ = √2 exp(i π/4) = √2(cos(π/4) + i sin(π/4)

=> (2i)½ = √2( 1/√2 + i(1 /√2)) = 1 + i

For second root substuting, k = 1

=> (2i)½ = 2½ exp(i (2π×1 + π/2)/2)

=> (2i)½ = √2 exp(i (5π/2)/2)

=> (2i)½ = √2 exp(i (5π/4) = √2( cos(5π/4) + i sin(5π/4)

=> (2i)½ = √2(- 1/√2 + i(-1 /√2)) = - (1 + i)

Hence, square root of 2i is ±( 1 + i).

b) 1 -√3i

The magnitude and principal argument of 1 −√3i are respectively, r = √(1² + (√3)²) = 2 and θ = tan⁻¹ ( -√3/1) = - π/3. Similar to part(a), square root of (1 - √3i) is written as (1 - √3i)½ = r½ exp(i (2πk - π/3)/2), k= 0, 1

For first root , k = 0

(1 - √3i)½ = √2 exp(i (2π×0 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (- π/6) )

=> (1 - √3i)½ = √2( cos(-π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( cos(π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( √3/2 - i (1/2)) = 1/√2(√3 - 1)

For second root, k = 1

(1 - √3i)½ = √2 exp(i (2π×1 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/6))

=> (1 - √3i)½ = √2 (cos(5π/6) + i sin(5π/6))

=> (1 - √3i)½ = √2 (- √3/2 + i(1/2) ) = - 1/√2(√3 - i)

so, (√1- √3i ) is ± 1/√2(√3 - 1). Hence, we got all required square roots.

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Complete question:

1. Find the square roots of (a) 2i; (b) 1 - √3i and express them in rectangular coordinates.

Answer:

The position of the radio is (-9, 4).

The range of the radio is 9.

Step-by-step explanation:

The equation (x + 9)^2 + (y - 4)^2 = 81 is in the form of a circle, so we can use the standard equation for a circle to find the center and radius of the circle. The standard equation for a circle is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius of the circle

In the equation (x + 9)^2 + (y - 4)^2 = 81, we can see that:

Therefore, the center of the circle is at (-9, 4) and the radius of the circle is 9.

The position of the source of the radio signal is at the center of the circle, which is at (-9, 4). The range of the signal is the radius of the circle, which is 9. This means that the radio signal can be received by any device within a 9-unit radius of the source.

The source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.

The equation (x + 9)^2 + (y - 4)^2 = 81 represents the position and range of the source of a radio signal. By analyzing the equation, we can determine the position of the source and the range of the signals.

Position: The equation is in the standard form of a circle, (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle. Comparing this with the given equation, we can see that the center of the circle is at (-9, 4). Therefore, the position of the source of the radio signal is at the coordinates (-9, 4).

Range: In the equation, the term 81 represents the radius of the circle, denoted as r. So, the range of the signals is equal to the radius, which in this case is √81 = 9 units. This means that the radio signals from the source can reach a maximum distance of 9 units from the center.

In summary, the source of the radio signal is located at (-9, 4), and the range of the signals extends up to a distance of 9 units from the source.

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The percent change from 1994 to 1995 can be computed by which of the following methods.

The percent change from 1994 to 1995 would be computed by the following

Formula: Percent Change = ((New Value - Old Value) / Old Value) x 100Where,

Old Value = Annual caseloads in 1994 = 750

New Value = Annual caseloads in 1995 = 820

Let's put these values into the formula and calculate the percent change.

Percent Change = ((820 - 750) / 750) x 100

Percent Change = (70 / 750) x 100

Percent Change = 0.093 x 100

Percent Change = 9.3%

Therefore, the percent change from 1994 to 1995 would be 9.3%.

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Step-by-step explanation:

let x1=9 y1=6

x2=5 y2=15

now we khow that

slope (m) =y2-y1/x2-x1

= 15-6/5-9

=9/-4 ans

From the given information provided, the means of x₁, x₂,  and x₃ are 158.28, 41.3, and 43.75 respectively.

a. Handle the missing values using omission strategy:

The omission strategy involves removing any observation with missing values.

The resulting table after the omission strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

We can see that one observation with missing values was removed, which was observation 5.

b. Handle the missing values using simple mean imputation strategy:

The simple mean imputation strategy involves replacing the missing values with the mean of the non-missing values.

The means of x₁, x₂, and x₃ are calculated as follows:

mean of x₁ = (248 + 55 + 196 + 134) / 4 = 158.25

mean of x₂ = (3.5 + 150 + 4.5 + 6.2) / 4 = 41.3

mean of x₃ = (3.8 + 74 + 32 + 63) / 4 = 43.75

The resulting table after the simple mean imputation strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

5 158.25 41.3 43.75

We can see that all missing values were replaced, which were x₁ in observation 5 and x₃ in observation 3.

Question - The following table contains 3 variables and 5 observations including some missing values x₁ x₂ x₃ 248 3.5 3.8 55 150 74 196 4.5 32 134 6.2 63 a. Handle missing values using omission strategy. b. Handle missing values using simple mean imputation strategy. How many missing values are replaced? What are means of x₁, x₂, and x₃?

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Answer:

11 ft

Step-by-step explanation:

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The builder conducted a survey of employees based on their trades by selecting a random sample from each trade.

In order to gather information about the employees and their specific trades, the builder decided to conduct a survey. To ensure the survey results are representative of the entire employee population, the builder employed a random sampling method. This means that a sample group was selected from each trade, chosen in a way that gives every employee an equal chance of being included in the survey.

Random sampling is a widely used technique in survey research as it helps minimize bias and ensures the sample represents the larger population. By selecting a random sample from each trade, the builder can obtain a diverse range of perspectives and experiences across different trades within the company. This approach allows for a comprehensive understanding of the employees' opinions, needs, and concerns specific to their respective trades.

By conducting a survey based on trades and using random sampling, the builder can gain valuable insights into the workforce's specific dynamics, identify any common issues or areas for improvement, and make informed decisions regarding training, resource allocation, or policy changes to better support each trade within the organization.

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Distance from a circle's centre to any point along its perimeter is known as the radius of the circle. R or r is typically used to indicate it.

What does a circle mean mathematically?

A circle is just a simple rounded form without any edges or line segments. In geometry, it has the shape of a closed curve. Circle's arc's points are set apart from the centre by a predetermined amount.

                                      The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.

What are the circle's five characteristics?

If the radii of the circles are the same, the circles are said to be congruent.

The lengthiest chord that makes up a circle is its diameter.

Equivalent angles are subtended in the centre of earth by equal chords.

The chord is divided in half by the radius drawn perpendicular to the chord.

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The complete question is -

What is the radius of a circle?

Answer:

0.56

Step-by-step explanation:

To find the decimal equivalent, we can divide the numerator and denominator together.

14 ÷ 25 = 0.56

Best of Luck!

The solution set for the given equation is x=-1 .

Solution set is written as {-1}

for better understanding check the calculation below.

We need to solve the given equation

\(\frac{x+3}{x+2} =3+\frac{1}{x}\)

To solve any equation we take LCD.

LCD of the given equation is x(x+2)

Multiply LCD with each term to remove the denominator

\(\frac{x+3}{x+2}\cdot x(x+2) =3\cdot x(x+2)+\frac{1}{x}\cdot x(x+2)\\x(x+3)=3x(x+2)+x+2\\x^2+3x=3x^2+6x+x+2\\\)

Subtract x^2 and 3x from both sides of the equation to get 0 on the left side of the equation

\(0=3x^2+6x+x+2-x^2-3x\\0=2x^2+4x+2\\\)

Now divide the whole equation by 2 and then we factor it

\(0=x^2+2x+1\\0=(x+1)(x+1) \\x+1=0\\x=-1\)

The solution set for the given equation is x=-1

Solution set is written as {-1}

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Answer:

-1

Step-by-step explanation:

Answer:

31 1/2

Step-by-step explanation:

average speed = distance/time

average speed = (73 1/2 miles)/(2 1/3 hours)

= (147/2 miles)/(7/3 hours)

= 147/2 * 3/7 miles/hour

= 441/14 miles/hour

= 31 1/2 miles/hour