Factorize:
(2a^3-8a)÷ 2a (a-2)

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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if vectors a and b are perpendicular and have the same nonzero magnitude, then the magnitude of their cross product, vector c, is equal to the square of the magnitude of a (or b).

To start, we know that vectors a and b are perpendicular, meaning they form a right angle. Additionally, we know that they have the same nonzero magnitude, so they are equal in length. If we sketch these vectors, we can see that they form a right triangle.

Now, let's consider the cross product of a and b, which is vector c. The magnitude of vector c is given by the formula ||c|| = ||a|| ||b|| sin(theta), where theta is the angle between a and b. Since a and b are perpendicular, sin(theta) = 1, so we have ||c|| = ||a|| ||b||.

Since a = b, we can simplify this to ||c|| = ||a||^2. Therefore, the magnitude of c is equal to the square of the magnitude of a (or b). In other words, if the magnitude of a (or b) is, for example, 5, then the magnitude of c is 25 (5 squared).
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The magnitude of c is equal to the square of the magnitude of a.

Given the information provided, let's analyze the relationship between vectors a, b, and c.

1. Vectors a and b are perpendicular: This means that the angle between them is 90 degrees.

2. Vectors a and b have the same nonzero magnitude: This means that their magnitudes are equal, and we can represent them as "a" (since a = b).
To find the magnitude of c, we need to use the formula for the cross-product of two vectors:

c = a x b

Since a = b, we can rewrite this as:

c = a x a

3. Vector c is the cross product of vectors a and b: c = a x b.

To find the magnitude of vector c, we can use the formula for the magnitude of the cross product:

|c| = |a| * |b| * sin(θ)

Here, θ is the angle between vectors a and b. Since they are perpendicular, θ = 90 degrees, and sin(θ) = sin(90) = 1.

Now, substitute the values of |a| and |b| in the formula:

|c| = |a| * |a| * 1 (since |a| = |b|)
|c| = |a| * |a| * sin(90)

Since sin(90) = 1, we can simplify this to:

|c| = |a| * |a| = a^2

|c| = a^2

So, the magnitude of vector c is the square of the magnitude of vector a (or vector b, since they have the same magnitude).

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From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.

Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

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The blanks in each statement about the line segment should be completed as shown below.

Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:

8x + 11 = 12x - 1

Solve for x

We now want to solve for x.

−4x+11=−1

−4x = -12

x= 3

Solve for TU, UV, and TV

This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(3)+11

TU= 35

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Based on the segment addition postulate, we have:

TU+UV=TV

35+35=TV

TV= 70

Find the detailed calculations below;

TU = UV

8x + 11 = 12x - 1

8x + 11 - 11 = 12x - 1 - 11

8x = 12x - 12

8x - 12x = 12x - 12 - 12x

-4x = -12

x = 3

By using the substitution method to substitute the value of x into the expression for TU, we have:

TU = 8x + 11

TU = 8(3) + 11

TU = 24 + 11

TU = 35

By applying the transitive property of equality, we have:

UV = TU and TU = 15, then UV = 35

By applying the segment addition postulate, we have:

TV = TU + UV

TV = 35 + 35

TV = 70

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The slope for the given coordinate points is 1/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

The given coordinates are (3,0) and (-5,-4).

Substitute (x₁, y₁)=(3,0) and (x₂, y₂)=(-5,-4) in slope formula, we get

Slope (m) = (-4-0)/(-5-3)

= -4/(-8)

= 1/2

Therefore, the slope is 1/2.

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Answer:

Step-by-step explanation:

Given :-

To Find :-

Solution :-

Let's assume:

We know that,

↠ (x)(x + 2) = 80

↠ x² + 2x - 80 = 0

↠ x² + 2x - 80 = 0

↠ x² + 10x - 8x - 80 = 0

↠ x(x +10) -8 (x + 10) = 0

↠ (x-8) (x + 10) = 0

↠ x = 8 or -10

↠ x = 8

Hence,

Answer:

Given:-

To Find :-

Solution:-

According to the question ,

Area = 80m²

putting the known values ,

(X)(X+2) = 80m

x² +2x - 80= 0

x² +10x-8x -80m= 0

x(x + 10) - 8(x+10) = 0

(x-8) = 0 ; (x+10) = 0

X = 8 ; X = -10

Length = X + 2 ; 10 m

Width = X ; 8 m

zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

Now that we have z and w in polar form, we can find the polar forms for the products and reciprocal of these complex numbers.

Product (zw): To multiply two complex numbers in polar form, we multiply their magnitudes and add their arguments. Applying this to z and w, we have: zw = 8(cos(30°) + isin(30°)) * 3√2(cos(45°) + isin(45°))

Multiplying the magnitudes: |zw| = 8 * 3√2 = 24√2

Adding the arguments: θzw = 30° + 45° = 75 degrees

Therefore, zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

Division (z/w): To divide two complex numbers in polar form, we divide their magnitudes and subtract their arguments. Applying this to z and w, we have: z/w = 8(cos(30°) + isin(30°)) / 3√2(cos(45°) + isin(45°))

Dividing the magnitudes: |z/w| = 8 / (3√2) = 8 / 3√2 = 8 / (3 * √(2)) = (8 / 3) * (1 / √(2)) = (8 / 3) * (√(2) / 2) = (4√2) / 3

Subtracting the arguments: θz/w = 30° - 45° = -15 degrees

Thus, z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

Reciprocal (1/z): To find the reciprocal of a complex number in polar form, we take the reciprocal of its magnitude and negate its argument. Applying this to z, we have: 1/z = 1 / [8(cos(30°) + i*sin(30°))]

Taking the reciprocal of the magnitude: |1/z| = 1 / 8 = 1/8

Negating the argument: θ1/z = -30°

Hence the 1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

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Answer:

slope: -4

y-intercept(0,-2)

Step-by-step explanation:

A bird flies from a nest that is 822 3/10 feet above sea level to the bottom of a canyon that is 56 1/10 feet below it.

The canyon is 737 feet higher than the bird's nest, by a difference of 3 feet.

based on the facts provided, we know that;

The depth below sea level is 52 3/ 5 feet, hence the value would be negative.

The height above sea level is 789 3/ 10, which requires a positive number.

Let's convert the improper fractions from the mixed fractions;

= - 263/ 5 = - 52. 6 feet

789 3/ 10 = 7893/ 10 = 789. 3 ft

the canyon's and the bird's nest's contrasting elevations;

= -52. 6 + 789. 9

Equals 737. 3 feet

Consequently, there is a 737. 3 foot difference in height between the canyon and the bird's nest.

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Answer:

Step-by-step explanation:

The standard deviation of a data set is represented by the following equation:

Therefore, for the given sample:

For each data point, find the square of its distance to the mean.

Now, solving for the standard deviation:

Answer:

86

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

Multiply the two numbers together as if there was no decimal, then move the decimal in the number of places that it is given in one of the factors.

176/2^10 = 0.171875.

n=10, p=1/2, q=1/2

probability of student passes the quiz only if he answers 7 or more than 7 questions correctly and let it be x

P(x)=10C7(0.5)^7(0.5)^3 + 10C8(0.5)^8(0.5)^2 + 10C9(0.5)^9(0.5)^1

+ 10C10(0.5)^10(0.5)^0

=120 /1024 + 45/1024 + 10/1024 + 1/1024

P(x)=176 / 1024

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Answer:

y = 2x + 4

Step-by-step explanation:

Two points on this line are (-2, 0) and (0, 4).  Going from the first to the second, x increases by 2 (this is the 'run') and y increases by 4 ('rise').

Thus, the slope of this line is m = rise / run =  4/2 = 2

Using the slope-intercept formula, we get y = mx + b = 2x + b

Let x = -2 and y = 0 to find b:  0 = 2(-2) + b, so b = 4, and the desired equation is then:

y = 2x + 4

Answer:

There are 3 ways

Step-by-step explanation:

The formula for a sector's area is:

1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2)

3. A = (fraction of the circle) * (pi * r2)

Answer:1/9 maybe?

Step-by-step explanation:

The width of the flooring room is 50m.

The cost of flooring the room is Rs. 56,000.

The rate of flooring in the room is Rs. 14 per sqm.

Area of the room = Cost of flooring the room/rate of flooring per sqm

Area = 56,000/14 = 4,000 sqm

Length of the room = 80m

Area of rectangle = length × width

4,000 = 80 × width

Width = 4000/80

             = 50m

Thus, the width of the room is 50m.

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The equation based on the information is:

34 = x - 18

In mathematics, an equation is an expression that states that two expressions are equal by joining them with the equal sign =. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation. To solve an equation involving variables, it is necessary to determine which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values ​​of the variable. A constraint expression applies only to specific values ​​of a variable.

Given that :

Bella is baking 34 cookie for the holiday party tonight. She baked 18 before leaving for school and will bake the ret when he return home.

Therefore, the equation is:

34 = x - 18

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If the value x =12 then 2x - 5 = 19 the statement is true if 2x -5 = 19 then x = 12. The correct options are A and D.

The mathematical expression combines 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 denote the logical syntax's operation order and other properties.

Given that the statements are:-

x = 12, then 2x - 5 = 19.

2x - 5 = 19

(2 x 12 ) - 5 = 19

24 - 5 = 19

19 = 19

If 2x - 5 = 19, then x = 12. The value of x will be calculated as,

2x - 5 = 19

2x = 19 + 5

2x = 24

x = 24 / 2

x = 12

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$0.38×192=$72.96

So the answer is $72.96

Answer:

.25

Step-by-step explanation:

400 cents ÷ 4= 100 and 1/4 of 100 is 25 so it .25

Answer:

the answer to x+(-9)=32 is x=41

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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Answer:

27 :)

Step-by-step explanation:

$27 it D

Step-by-step explanation:

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Apply the Binomial Probability Distribution, The Answer is 0.044.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.

The required formula is:

\(P(x)= C(n,x) p^{x}q^{n-x}\)

n=10

x=8

p(8)= \(C(10,8) * 0.5 ^ {8} *0.5 ^{2}\)

=0.044

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Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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Answer:

answer is 187.2

Step-by-step explanation:

5.2 times 4 times 9= 187.2

He will catch up at 15.00. The two sentence to describe the process is: Find Christ total finish solved question at noon then compare both of arithmetic Un.

Lets assume Christ start hour as x ,Tyler star hour as y ,Christ speed as b and Tyler speed as c. So we can find:

x = 9. AM = 9.00

y = noon = 12.00

c = 15 exam

d = 25 exam

As we determine the variable, first we find the total number of exam Christ finished at 12.00 (3 hours pass). So n = 3 based on starting hour = 9. Lets determine it as Ua. So:

Ua = a + (n - 1)c      

Ua = 15 + (3 - 1)15

Ua = 15 + 30

Ua = 45

After that compare both sequence to find the time Tyler Catch up Christ

Ua + Uchrist = Utyler

45 + (c + (n - 1)c = d + (n-1)d

45 + 15 + (n - 1)15 = 25 + (n - 1) 25

60 + 15n -15 = 25 + 25n - 25

45 + 15n = 25n

45 = 15n

n = 3

Hence, Tyler will catch up to Christ after 3 hours after 12.00 or he will catch up at 15.00

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