what is the class​ width? what are the approximate lower and upper class limits of the first​ class?

The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is \(\frac{N!}{n!(N-n)!}\)

=\(\frac{10!}{2!(8)!}\)

=\(\frac{10 \times 9 \times \times 8!}{8! \times 2 !}\)

=45

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To rotate a coordinate system onto another coordinate system using matrices, you can follow these steps:

1. Determine the angle of rotation: First, determine the angle by which you want to rotate the coordinate system. This angle will be used to create a rotation matrix.

2. Create a rotation matrix: The rotation matrix is a 2x2 or 3x3 matrix that represents the transformation of points in the original coordinate system to points in the rotated coordinate system. The elements of the rotation matrix can be determined based on the angle of rotation.

For a 2D rotation, the rotation matrix is:

 \(\[ \begin{matrix} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{matrix} \]\)

For a 3D rotation around the x-axis, y-axis, and z-axis, the rotation matrices are:

\(Rx = \left[\begin{array}{ccc}1&0&0\\0&cos\theta&-sin\theta\\0&sin\theta&cos\theta\end{array}\right]\)

\(Ry = \left[\begin{array}{ccc}cos\theta&0&sin\theta\\0&1&0\\-sin\theta&0&cos\theta\end{array}\right]\)

\(Rz = \left[\begin{array}{ccc}cos\theta&-sin\theta&0\\sin\theta&cos\theta&0\\0&0&1\end{array}\right]\)

Note that θ represents the angle of rotation.

3. Apply the rotation matrix: To rotate a point or a set of points, multiply the coordinates of each point by the rotation matrix. This will yield the coordinates of the points in the rotated coordinate system.

For example, if you have a 2D point P(x, y), and you want to rotate it by angle θ, the rotated point P' can be obtained by multiplying the column vector [x, y] by the rotation matrix:

  [ x' ]  =  [ cosθ  -sinθ ]   [ x ]

  [ y' ] =   [ sinθ   cosθ  ] * [ y ]

Similarly, for 3D rotations, you would multiply the column vector [x, y, z] by the appropriate rotation matrix.

Rotating a coordinate system onto another coordinate system using matrices involves the use of rotation matrices. These matrices define how points in the original coordinate system are transformed to points in the rotated coordinate system.

The rotation matrices are constructed based on the desired angle of rotation. The elements of the matrix are determined using trigonometric functions such as cosine and sine. The size of the rotation matrix depends on the dimensionality of the coordinate system (2D or 3D).

To apply the rotation, the coordinates of each point in the original coordinate system are multiplied by the rotation matrix. This matrix multiplication yields the coordinates of the points in the rotated coordinate system.

By performing this transformation, you can effectively rotate the entire coordinate system, including all points and vectors within it, onto the desired orientation defined by the angle of rotation.

Matrix transformations provide a mathematical and systematic approach to rotating coordinate systems, allowing for precise control over the rotation angle and consistent results across different coordinate systems. They are widely used in computer graphics, robotics, and various scientific and engineering fields.

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Answer:3 symmetrical lines

Step-by-step explanation: just look in the middle and draw a line

Answer:

2

Step-by-step explanation:

Find the discriminant:

D = b² − 4ac

If the discriminant is positive (D > 0), there are 2 real zeros.

If the discriminant is zero (D = 0), there is 1 real zero.

If the discriminant is negative (D < 0), there are no real zeros.

In this case, a = -5, b = 6, and c = 4.

D = (6)² − 4(-5)(4)

D = 36 + 80

D = 116

D > 0

There are 2 real zeros.

The solution to the system of equations is x = -1, y = 2.

A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation of two variables."

The adjective "linear" comes from the fact that the collection of solutions to such an equation forms a straight line in the plane.

These are the three types of linear equations:

By multiplying each equation by an appropriate constant, we may use the method of elimination to make the coefficients of x in both equations equal in size but opposite in sign. The following results from multiplying the first equation by 3 and the second equation by -2 in this situation:

a. 6x + 12y = 18

b. -6x - 10y = -14

To get rid of x, we can now combine these two equations:

a. 6x + 12y = 18

b. (-6x - 10y = -14)

2y = 4

By finding y, we obtain:

y = 2

We can find x by adding this value of y back into either of the initial equations:

2x + 4y = 6

2x + 4(2) = 6

2x + 8 = 6

2x = -2 x ⇒ -1

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the solution to the system of equations 2x+4y=6 and 3x+5y=7, after eliminating the x term, is x = -1 and y = 2.

The x term, we can multiply the first equation by -3 and the second equation by 2, so that the x term will have opposite coefficients and will cancel out when we add the two equations together.

\(-3(2x+4y=6) gives -6x - 12y = -18\)

\(2(3x+5y=7) gives 6x + 10y = 14\)

Adding these two equations gives:

\(-6x - 12y = -18\)

\(+6x + 10y = 14\)

\(-2y = -4\)

Solving for y, we get:

\(y = 2\)

Substituting this value of y back into either of the original equations, we can solve for x:

\(2x + 4y = 6\)

\(2x + 8 = 6\)

\(2x = -2\)

\(x = -1\)

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All members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

We will prove by structural induction that all members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

Base Case:

We start with the base case, where n = 1. In this case, 1∈ S, and we can see that 1 can be expressed as 2⁰3⁰, which is of the desired form.

Inductive Step:

Now, assume that for some positive integer k, if n = k, then k∈ S can be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

We will show that if n = k + 1, then k + 1 can also be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

Case 1: If n = 2k, then we know that 2k∈ S. By the induction hypothesis, we can express 2k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 2k+1 = 2(2k) = 2ᵃ₊₁3ᵇ, which is still of the desired form.

Case 2: If n = 3k, then we know that 3k∈ S. By the induction hypothesis, we can express 3k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 3k+1 = 3(3k) = 2ᵃ3ᵇ₊₁, which is still of the desired form.

Since we have shown that if n = k + 1, then k + 1 can be expressed as 2ᵃ3ᵇ, the proof by structural induction is complete.

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A) To 4 decimal places, the variance ≈ 0.0383.

B)  , P(0.21 < X < 0.76) ≈ 0.8054.

C)   The mean ≈ 0.6774.

D) The variance ≈ 0.0383.

a. To find P(X < 0.21), we can use a cumulative distribution function (CDF) calculator for the beta distribution with parameters a = 2.1 and b = 1. Using such a calculator, we get:

P(X < 0.21) ≈ 0.0668

Therefore, to 4 decimal places, the variance ≈ 0.0383.

b. Similarly, to find P(0.21 < X < 0.76), we can use the beta distribution CDF calculator and subtract the probability of X being less than 0.21 from the probability of X being less than 0.76. That is,

P(0.21 < X < 0.76) = P(X < 0.76) - P(X < 0.21)

Using the same beta distribution CDF calculator, we get:

P(0.21 < X < 0.76) ≈ 0.8722 - 0.0668 ≈ 0.8054

Therefore, to 4 decimal places, P(0.21 < X < 0.76) ≈ 0.8054.

c. The mean of a beta distribution with parameters a and b is given by:

Mean = a / (a + b)

Substituting a = 2.1 and b = 1, we get:

Mean = 2.1 / (2.1 + 1) ≈ 0.6774

Therefore, to 4 decimal places, the mean ≈ 0.6774.

d. The variance of a beta distribution with parameters a and b is given by:

Variance = (a * b) / [(a + b)^2 * (a + b + 1)]

Substituting a = 2.1 and b = 1, we get:

Variance = (2.1 * 1) / [(2.1 + 1)^2 * (2.1 + 1 + 1)] ≈ 0.0383

Therefore, to 4 decimal places, the variance ≈ 0.0383.

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Answer:

The area is 200.96 in^2

Step-by-step explanation:

Answer:

200.96 in^2

Step-by-step explanation:

circle area formula is πr^2

radius = diameter / 2, radius is 8

8^2.π  = 64π  

π  = 3,14

final answer is 64 X 3.14= 200.96 in^2

The area of a kite with a diagonal of 23 m and 16 m is 184 m²

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

The area of kite = product of diagonal / 2

Hence:

Area of kite = (20 + 3)(8 + 8) / 2 = 184 m²

The area of a kite with a diagonal of 23 m and 16 m is 184 m²

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Answer:

If the coin is fair, then the odds of getting heads or tails should be equal, 12. Then 3 tosses of tails will have a chance of 12⋅12⋅12=18.

Answer:

1/8 or 12.5%

Step-by-step explanation:

The odds of getting heads is 50% (1/2) each time.

So putting the odds to the power of three will provide the odds of getting heads 3 times.

1/2 * 1/2 * 1/2 = 1/8 or 12.5%

To find the third side of an inequality of a triangle, you must first use the Triangle Inequality Theorem.

This theorem states that for any triangle, the sum of any two sides of the triangle must be greater than the third side. This means that in order to find the length of the third side, you must subtract the sum of the two known sides from the smaller of the two sides, then the length of the third side will be equal to the difference between these two numbers. For example, if two sides of a triangle have lengths of 4 and 3, the third side must be greater than 1 (4 + 3 = 7 and 4 - 3 = 1). Therefore, the length of the third side must be greater than 1.

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Answer:the population of brook trout

Step-by-step explanation: Because population is half of a whole

Answer:

2 to two too

Step-by-step explanation:

    thats how much i think

Answer:

37.7 cm

Step-by-step explanation:

C = 2πr

diameter = 12cm

Answer:

B. 36 root7 = area of the rectangle

This quadratic equation has no real solution.

The given equation is 27 = -x⁴ - 12x².

Rearranging the equation :

x⁴+12x²+27=0

Lets use u=x².we can write the equation in terms of u:

u²+12u+27=0

To solve this Rearranging the equation:

x⁴ + 12x² + 27 = 0

Now, let's substitute a variable to make the equation more readable. Let's use u = x². We can rewrite the equation in terms of u:

u² + 12u + 27 = 0

To solve this *quadratic equation*, we can factor it:

(u + 9)(u + 3)=0

Setting each factor equal to zero and solving for u:

u+9=0 or u+3=0

solving for u:

u=-9 or u=-3

Substituting back the original variable:

x²=-9 & x²=-3

since both x²=-9 and x²=-3 have no real solutions(no real numbers can be squared to give negative values).

Therefore,the given equation has no real solution.

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The surface area and volume of a pentagonal prism is  5/2 × a² × √(5 + 2√5) + 5ab and (1/4) × (5 + 2√5) × a² × h respectively. We can find the solution in the following manner.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

To find the surface area and volume of a pentagonal prism, we need to know its height, the length of the sides of the pentagon, and the length of the rectangular faces.

Let's denote the height of the pentagonal prism as "h", the side length of the pentagon as "a", and the length of the rectangular face as "b".

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Area of each pentagonal face = 5/4 × a² × √(5 + 2√5)

Area of each rectangular face = a × b

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

= 5/2 × a² × √(5 + 2√5) + 5ab

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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The surface area and volume of a pentagonal prism is sum of the areas of its faces, and (1/4) × (5 + 2√5) × a² × h.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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The statements provided can be rewritten as follows: 1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2. 2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k. 3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.

Let's analyze these statements:

1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2.

  This statement is true and can be proven using the concept of the difference of squares. For any odd integer n, we can express it as the difference of two perfect squares: n = (a + b)(a - b), where a and b are integers. This shows that n can be written as the difference of two squares.

2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k.

  This statement is not true. Consider the counterexample where n = 1. In this case, 3n + 5 = 8, which is not of the form 6k + 8 for any integer k.

3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.

  This statement is true. For any even integer n, we can express it as n = 2k, where k is an integer. Substituting this into the given equation, we get 3n + 2 = 3(2k) + 2 = 6k + 2, which is of the form 6k + 2.

In conclusion, statement 1 is true, statement 2 is false, and statement 3 is true.

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Answer:

  1

Step-by-step explanation:

You want the standard deviation of a normal distribution.

The "standard normal distribution" is defined to have a mean of 0 and a standard deviation of 1.

__

Additional comment

The standard distribution is often shifted and scaled to have some other particular mean and standard deviation. The computation of a "Z-score" is a way to relate a value in the scaled distribution back to the characteristics of the standard normal distribution. The Z-score is the number of standard deviations a value is from the mean.

Answer: -84+48i

Step-by-step explanation: This was correct

The solution of the given expression will be 48i - 84.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given complex expression is (−9−6i)(4−8i). The solution of the expression will be:-

E = (−9−6i)(4−8i).

E = -9 ( 4 - 8i ) -6i ( 4 -8i )

E = -36 + 72i -24i + 48(-1)

E = 48i - 84

Therefore, the solution of the given expression will be 48i - 84.

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The number of ways can this test batch be chosen is 2380 ways  of combination.

Give an example of permutation and combination?

Calculation of the number of ways:

Since As part of a quality-control program, 4 batteries from a box of 17 is chosen at random for testing.

Here we used the combination

So,

        = 17!/4!(17 - 4 )!

         = 17!/4! * 13!

          = 17 * 16 * 15 * 14 * 13/4! * 3!

          = 2380 ways

Therefore, The number of ways can this test batch be chosen is 2380 ways.

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Answer:

Z = - 8/3.

Make brainlist please

Answer:

B). - 91

Explanation:

Answer:

1. n + 7 ≤ 9

2. 3w < 18

3. 3 < s + 4

4. 4 ≥ x/2.1

Answer:

x=3

y=7

Step-by-step explanation:

3x-4(x+4)=-19

3x-4x-16=-19

-x-16=-19

+16. +16

________

-x=-3

×-1 ×-1

______

x=3

y=3+4

y=7

By using the properties of parallelogram, it can be calculated that

Value of angle O is 105°

What is a parallelogram?

Parallelogram is a four sided two dimensional figure whose every pair of opposite sides are parallel.

x + 40 + 3x = 180 [Co interior angles are supplementary]

4x + 40 = 180

4x = 180 - 40

4x = 140

x = \(\frac{140}{4}\)

x = 35°

m\(\angle\)O = 35 \(\times\) 3 = 105°

The value of x in the parallelogram LMNO is 105°

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Complete Question

What is the measure of angle O in parallelogram LMNO? a) 35° b) 75°

c) 105° d) 155°