How many three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even?

The complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

What is complex number?

A complex number is obtained by adding real and imaginary numbers. Complex numbers have the formula a + ib and are usually symbolized by the symbol z. Here the numbers a and real are both. The value "a" is known as the real component and is denoted Re(z), while "b" is known as the imaginary part and is denoted Im(z). Also known as imaginary number, ib. Hero of Alexandria, a Greek mathematician, first used the idea of complex numbers in the first century when he tried to calculate the square root of a negative integer.

a. A complex number is a number that consists of a real part and an imaginary part, where the imaginary part is the real number multiplied by the imaginary unit "i", defined as the square root of -1. The modulus of a complex number is the distance between the starting point and the point representing the complex number on the complex plane. This can be calculated using the Pythagorean theorem. For example, the real part of the complex number z = 3 + 4i is 3 and the imaginary part is 4, and its modulus is √(3²+4²)=5.

b. Let z = a + bi be a complex number, where a and b are real numbers. The modulus of z is defined as |z| = √(a² + b²). Therefore, for the complex number z = 1 + 2i, the modulus is |z| = √(1² + 2²) = √5.

c. To write the complex number 2 = ((2+ m) + 3i) in polar form, we need to find the modulus and argument of the complex number. The modulus is |2 + ((2+m) + 3i)| = |4 + mi + 3i| = √(4² + (m+3)²) = √(m² + 6m + 25). The argument is given by tan⁻¹(Im/Re) = tan⁻¹(3/(2+m)), which gives us the angle that the complex number makes with the positive real axis. Therefore, the complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

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Answer:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

55 divided by 10 = 5.5 around 5

Add all your numbers

Divide by the many numbers there are, go by the exact value or estimate if needed.

The hexadecimal number 0x3d is equal to 61 in decimal (base 10).

To convert the hexadecimal number 0x3D to decimal (base 10), we need to understand the positional system of both bases. In hexadecimal, each digit represents a power of 16, starting from the rightmost digit. The digits range from 0 to 9, and then from A to F, where A represents 10 and F represents 15, In hexadecimal (base 16) representation, each digit can have values from 0 to 15. The digits from 0 to 9 represent their respective values, and the letters A to F represent the values 10 to 15.

To convert 0x3d to decimal, we can break down the number as follows:

0x3d = (3 * 16^1) + (13 * 16^0)

Simplifying the expression:

0x3d = (3 * 16) + 13

0x3d = 48 + 13

0x3d = 61

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c. a = 3√2, b = 6√2

#1.First, you find the opposite of the left triangle using sin formula

#2.After you get the opposite, find the b using sin formula and a using tan formula

•Right triangle

Hypotenuse = 6

Adjacent = ?

Opposite = ?

• Left triangle

Hypotenuse = b

Adjacent = a

Opposite = ?

a. adjacent of right triangle

b. hypothenuse of left triangle

#1. Sin(∅)= opposite/hypotenuse

sin(45) = opposite/6

opposite = sin(45) × 6

opposite = 3√2

#2. a. tan(∅) = opposite/adjacent

tan(30) = 3√2 / a

a = 3√2 : tan(30)

a = 3√6

b. sin(∅) = opposite/hypotenuse

sin(30) = 3√2 / b

b = 3√2 : sin(30)

b = 6√2

#and so the a = 3√2 and b = 6√2

#you are welcome

#Moderators please don't be mean, dont delete my answers just to get approval from your senior or just to get the biggest moderation daily rank.

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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The two values of x best represent where the two functions are equal will be (12,11)

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

Given data;

Linear function passing through;

(1, 2), (3, 4), (6,7) and (8, 9)

Quadratic function passing through

(3, 4), (5, 0), (7, 4) & (8, 9)

Let x be two values of x best represent where the two functions are equal;

The value of the x is obtained from the graph where the two line meets.

The value of x willl be (12,11)

Hence, the two values of x best represent where the two functions are equal will be (12,11)

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Answer:

hey, i tried my best with this. lmk if its correct.

Step-by-step explanation:

(its the bold answer btw)

Answer:

Step-by-step explanation:

Properties used:

Answer:

− 1.52

Step-by-step explanation:

3 - 8 = x^3 + x

9514 1404 393

Answer:

Step-by-step explanation:

Opposite sides of a parallelogram are the same length.

  AB = CD

  5x -5 = 3x +9

  2x = 14

  x = 7

  AB = 5(7) -5)

  AB = 30

__

The diagonals of a parallelogram are bisected by each other.

  XB = XD

  7y -10 = 5y

  2y = 10

  y = 5

  BX = 7(5) -10

  BX = 25

Aaron has observed placebo effect.

The placebo effect is defined as a phenomenon in which some people experience a benefit after the  use of an inactive "look-alike" substance or treatment.

Here sugar water also increase the energy level of the individuals .  Sugar water is a placebo .

So Aaron observed the placebo effect in this experiment.

Therefore, placebo effect is correct answer.

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Answer:

25 km

Step-by-step explanation:

100/20=5

5*5=25

Answer:

52%

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

This is a 10 x 10 grid so you have 100 squares and 52 shaded blue so divide 52/100 for the percent, so 52% are shaded

Answer:

5

Step-by-step explanation:

To solve the problem we must know about Mode.

Mode is the data point that repeats the most number of times in a given data set.

The mode of the data set is 5.

Given to us

As in the given data points {5, 0, 5, 4, 12, 2, 14}, number 5 repeats twice, therefore, 5 is the mode of the given data set.

Hence, the mode of the data set is 5.

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Answer: 219.52 inch^2

Step-by-step explanation:

Given the dimensions of rectangular papaerboard:

Length = 20inches

Width = 16inches

Area of rectangle = Length × width

Area of rectangle = 20 × 16 = 320 in^2

Area of a circle = pi*r^2

Therefore, area of semicircle = (pi*r^2) / 2

Diameter of circle = width of rectangle = 16 inches

Radius = diameter / 2 = 16 /2 = 8inches

Therefore, area of semicircle = (pi*8^2) / 2

= (3.14 × 64) / 2

= 200.96 / 2

= 100.48 inch^2

Therefore, area of paperboard left :

Area of rectangle - area of semicircle

320 - 100.48

= 219.52 inch^2

Ricardo uses 1-centimeter cubes to build a tower. The expression for the volume of the tower will be V=1 cm³.

It is defined as the combination of constants and variables with mathematical operators.

It is given that, Ricardo uses 1-centimeter cubes to build a tower.

Volume is defined as a three-dimensional space enclosed by an object or thing. A three-dimensional space's occupied volume is measured. It is frequently expressed numerically in terms of SI-derived units or different imperial units. Volume definition and length definition are related.

The expression for the volume of the tower is,

V=1 cm³.

Thus, Ricardo uses 1-centimeter cubes to build a tower. The expression for the volume of the tower will be V=1 cm³.

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For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

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Answer:

\(4-6i\)

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

The maximum unsigned decimal number that can be obtained with O digits is (10^O) - 1.

To find the maximum unsigned decimal number that can be obtained with a given number of digits O, we need to consider the range of possible digits at each position. In decimal representation, each position can have values from 0 to 9.

For the maximum number, we would want to have the largest digit (9) at each position. Therefore, the maximum unsigned decimal number with O digits would be the number where each digit is 9.

If O is the number of digits, the maximum unsigned decimal number would be 999...9 (O times). This can also be expressed as (10^O) - 1, since 10^O represents a number with O digits, all filled with 9s, and subtracting 1 gives the maximum number.

In conclusion, the maximum unsigned decimal number that can be obtained with O digits is (10^O) - 1.

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Answer:

-24x²

Step-by-step explanation:

remove the parentheses, multiply the numbers, apply exponent rule and add the numbers

Answer:

B. 250 g

Step-by-step explanation:

An apple is about 100-300 grams. The answer choice that best fits our estimate is B. 250 g.

Answer:

its b:250g

                                                                                                          ................................................................                                      

Answer:

Step-by-step explanation:

The probability that one randomly selected jelly bean is red is 15% or 0.15. Because another jelly bean of the same color is replaced after each selection, the probability of selecting a red jelly bean on any given selection remains constant at 0.15.

The probability of selecting three red jelly beans in a row can be calculated using the multiplication rule of probability. According to this rule, the probability of two independent events occurring together is the product of their individual probabilities.

Therefore, the probability of selecting three red jelly beans in a row is:

P(three red jelly beans in a row) = P(red) x P(red) x P(red)

= 0.15 x 0.15 x 0.15

= 0.003375 or 0.3375%

Therefore, the probability that three beans in a row are red is 0.3375%.

Answer: B) \(f\left(x\right)=\frac{1}{3}\left(-x-1\right)^{5}\)

Step-by-step explanation:

When graphing x5 the parent function and plugging in the equation for B the only equation that fits the criteria of

*shifting left 1 unit

*vertically compressed by 1/3

*reflect over the y-axis

So the answer is B

The function after the transformation is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁵

On reflecting over the y axis , we get

f ( x ) = ( -x )⁵

On vertically compressing by a factor of ( 1/3 ) , we get

f ( x ) = ( 1/3 ) ( -x )⁵

And , shifting 1 unit to the left , we get

f ( x ) = ( 1/3 ) ( -x + 1 )⁵

Hence , the transformed function is f ( x ) = ( 1/3 ) ( -x + 1 )⁵

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Answer:

-3c^2+2c^2

Step-by-step explanation:

when you multiply the first part u get -3c^2

The second part, two negatives=1 positive so it is 2c^2\

PLZ tell me if this helps

The Sturm-Liouville problem y'' + 2y' + y = 0 with boundary conditions y(0) = 0 and y(1) = 0 has eigenfunctions yn = 0 and eigenvalues λn = 0.

The equation is already in self-adjoint form, with the weight function p(x) = 1, and the eigenfunctions are orthogonal with a square norm of 0.

To solve the Sturm-Liouville problem y'' + 2y' + y = 0 with boundary conditions y(0) = 0 and y(1) = 0, we can follow these steps:

a) Find the eigenfunctions and eigenvalues:

Assume the solution has the form y(x) = yn(x), where n is an integer. Substitute this into the differential equation to obtain yn'' + 2yn' + yn = 0. The general solution to this equation is yn(x) = C1e^(-x) + C2xe^(-x), where C1 and C2 are constants. Applying the boundary conditions, we find that C1 = 0 and C2 = 0. Therefore, the eigenfunction is yn(x) = 0 for all n, and the eigenvalue is λn = 0 for all n.

b) Transform the equation to self-adjoint form and find the weight function:

To transform the equation to self-adjoint form, we multiply the equation by a weight function p(x). In this case, p(x) = 1. Multiplying the equation by p(x), we get y'' + 2y' + y = 0. This is already in self-adjoint form, as the coefficients of y'' and y' are equal.

c) Show orthogonality and find the square norm of eigenfunctions:

Since the eigenfunction yn(x) is zero for all n, it is orthogonal to the weight function p(x) = 1. The square norm of the eigenfunction yn(x) is given by ||yn||^2 = ∫[0,1] yn^2(x)p(x)dx = ∫[0,1] 0^2 dx = 0.

In summary, for the given Sturm-Liouville problem, the eigenfunction yn(x) is zero for all n and the eigenvalue is λn = 0 for all n. The equation is already in self-adjoint form, and the weight function is p(x) = 1. The eigenfunctions are orthogonal to the weight function, and their square norm is zero.

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To determine how well Feng must score on exam B, we can use z-scores and the concept of standard deviations.

First, let's calculate the z-score for Feng's score on exam A:

z-score = (x - mean) / standard deviation

z-score for exam A = (81 - 76) / 10 = 0.5

This means that Feng's score on exam A is 0.5 standard deviations above the mean of exam A.

To find out how well Feng must score on exam B, we need to calculate the equivalent score in terms of z-scores for exam B.

x = mean + (z-score * standard deviation)

x = 300 + (0.5 * 50) = 325

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max_difference([4, 1, 5, 2, 3]) would return 4.

To find the maximum difference between two elements in a list of n integers, we can do the following:

Initialize two variables max_diff and min_val to 0 and infinity, respectively.

Iterate over the list and update min_val to be the minimum value seen so far.

Compute the difference between the current element and min_val and update max_diff to be the maximum of max_diff and the difference.

After iterating over the list, return max_diff.

Here is the Python code to implement this algorithm:

def max_difference(lst):

   max_diff = 0

   min_val = float('inf')

   for num in lst:

       min_val = min(min_val, num)

       max_diff = max(max_diff, num - min_val)

   return max_diff

For example, if we have the list [4, 1, 5, 2, 3], the maximum difference between two elements is 4 (between 5 and 1),

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Answer:

Area of big diagram = 33.32 m²

Step-by-step explanation:

Given:

Both given diagram is similar

Perimeter of small diagram = 20 m

Area of small diagram = 19.6 m²

Perimeter of big diagram = 34 m

Find:

Area of big diagram

Computation:

Both given diagram is similar So,

Perimeter of small diagram / Area of small diagram = Perimeter of big diagram / Area of big diagram

20 / 19.6 = 34 / Area of big diagram

Area of big diagram = [19.6/20][34]

Area of big diagram = 33.32 m²

Answer:

56.6

Step-by-step explanation:

this equation (34/20)^2 * 19.6 = 56.644

Answer:

answers are below

Step-by-step explanation:

1. k = -12

2. x = 14

3. y = -18

4. x = 34/3 or 11.3333333

5. x = -10

6. b = 17

7. x = 1/7

8. y = -2

Hope this heps!! Tell me if you need any explanations :)

Answer:

1. -12

2. 14

3. -18

4. 11 1/3

5. -1 3/5

6. -17

7. 1/7

8. 7 1/3

Step-by-step explanation:

Most of them should be right but sorry if wrong

Answer:

£150

Step-by-step explanation:

£200 is 100%. If you decrease it by 25%, you end up with 75% of £200.

75% of £200 =

= 0.75 × £200

= £150

Answer:

£150

Step-by-step explanation:

25% means 25 per hundred, and decreasing 200 by 25% means that we should subtract 25% of 200, from 200:

25% · 200

= \(\frac{25}{100}\) · 200

= \(\frac{1}{4}\) · 200

= 50

⇒ 200 - 25% · 200

= 200 - 50

= 150

Alternatively, decreasing by 25% is the same as keeping 75%

(as 100% - 25% = 75%)

75% · 200

= \(\frac{3}{4}\) · 200

= 150

0.368 .

The probability that a random variable x is exponentially distributed and less than 45 minutes,

given that the average value is 45 minutes, is 0.368.

This can be calculated by taking the negative of the natural logarithm of 1/2 (i.e. -ln(0.5)) and dividing it by the average value of 45 minutes.

The result, -ln(0.5)/45, equals 0.368, rounded to three decimal places.

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