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The notation used for a vector pointing into the point is X.

A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.

Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.

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Answer:

<abd+<dbc=<Abc

50+40=90

triangle abc is a right angled triangle being one angle 90 degree

Answer:

Step-by-step explanation:

Answer:

<abd+<dbc=<Abc

50+40=90

triangle abc is a right angled triangle being one angle 90 degree

Therefore, the solution is: (a) Yes, x(1) is real.(b) No, x(1) is not even.(c) No, dx(t)/dt is not even.

(a) Yes, x(1) is real because the function x(t) is periodic and the given Fourier series coefficients are 2,

= {²¹4, ak = k = 0 otherwise}.

A real periodic function is the one whose imaginary part is zero.

Hence, x(t) is a real periodic function. Thus, x(1) is also real.(b) Is x(1) even?

To check whether x(1) is even or not, we need to check the symmetry of the function x(t).The function is even if x(t) = x(-t).x(t) = 2, = {²¹4, ak = k = 0 otherwise}.

x(-t) = 2, = {²¹4, ak = k = 0 otherwise}.Clearly, the given function is not even.

Hence, x(1) is not even.(c) Is dx(t)/dt even?

To check whether the function is even or not, we need to check the symmetry of the derivative of the function, dx(t)/dt.

The function is even if dx(t)/dt

= -dx(-t)/dt.x(t)

= 2,

= {²¹4, ak = k = 0 otherwise}.

dx(t)/dt = 0 + 4cos(t) - 8sin(2t) + 12cos(3t) - 16sin(4t) + ...dx(-t)/dt

= 0 + 4cos(-t) - 8sin(-2t) + 12cos(-3t) - 16sin(-4t) + ...

= 4cos(t) + 16sin(2t) + 12cos(3t) + 16sin(4t) + ...

Clearly, dx(t)/dt ≠ -dx(-t)/dt.

Hence, dx(t)/dt is not even.

The symbol "ak" is not visible in the question.

Hence, it is assumed that ak represents Fourier series coefficients.

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The number of negative and positive factors needed to guarantee a negative product with four factors with factors is 10 and there is a pastern

You should understand that the factors of a number is a number which can divide a number without a reminder

The factors must have a constant difference

Taking 1 as a factor for instance

1+5=5

Taking the number 20 for instance

The factors of 20 are

20=1,2,4,5,10,20

-1*20=-20

.1*-20=-20

-2*10=-20 and 2*-10=20

-4*5=-20 and 4*-5=20

The order is that the subsequent terms must be gotten by a difference of 1 and a divisor of 5

Therefore the number of factors is gotten by allocating by after the other a negative sign to the numbers

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Mean is the average of all of the numbers.

The Median is the middle number, when in order.

Mode is the most common number.

The range is the largest number minus the smallest number.

A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most often used measure of central tendency and is also known as the "average."

The median is the number in the middle of a sorted, ascending or descending list of numbers, and it might be more descriptive of the data set than the average.

The mode is the most common value in a set of data values. The difference between the lowest and highest numbers called the range. Example: The lowest value in 4, 6, 9, 3, 7 is 3, while the highest is 9. As a result, the range is 9 3 = 6.

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The breadth of the rectangular plot is equal to the area divided by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters.

The area of a rectangular plot is equal to the length multiplied by the breadth. This means that if the area of the plot is 180 square meters and the length is 15 meters, then the breadth can be calculated by dividing the area by the length. Therefore, the breadth of the plot is 180 divided by 15, which is equal to 12 meters. This means that the area of the plot is equal to 15 multiplied by 12 which is equal to 180 square meters. As the area and the length are given, the breadth can be easily calculated by dividing the area by the length. This is a simple way to calculate the breadth of a rectangular plot when the area and the length are known.

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The value of 315 sec is 5 minutes and 15 seconds.

The formula for converting seconds (sec) to minutes (min) and seconds (sec) is to divide the number of seconds by 60, then add the remainder to the quotient.

Seconds = Minutes x 60

Therefore, 315 seconds is equal to 315/60 = 5.25 minutes. To convert this to hours, we can use the following formula:

Hours = Minutes / 60

For example, 315 sec can be converted to minutes and seconds as follows:

Divide 315 sec by 60:

315 / 60 = 5.25

The quotient is 5, and the remainder is 25.

Therefore, 315 sec is equal to 5 min and 25 sec (5 minutes and 25 seconds).

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If the debt is normally distributed with a population standard deviation of $1100 and 15% of college seniors owe less than the amount of money is equals to the $2121.96.

The area under the standard normal curve represents to probability. The total area under the curve is equals to one. A Standard Normal Cumulative Probability, is a table which provides the cumulative probability of the left tail, as in the values less than the z-score in question. Here,

population mean, μ = $3262

standard deviation, σ = 1100

P- value = 15%

Using the normal distribution table, Z-score value is equals to - 1.0364. Now, we can use Z-scores formula is written \(Z = \frac{X - \mu}{\sigma }\)

Substitutes the known values in above formula, - 1.0364 = (X - 3262 )/1100

=> X - 3262 = 1100× ( - 1.0364)

=> X = 3262 - 1140.04

=> X = 2121.96

Hence, required value is $ 2121.96.

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The shape of the distribution is normal

The probability is 0.7764

What is Standard Deviation?

The standard deviation is a measure of the spread or dispersion of a set of data around its mean. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. It is used to quantify the degree of variability or diversity in the data.

(a)

The distribution of heights of young men follows a normal distribution with a mean of 69.3 inches and a standard deviation of 2.8 inches. The distribution of heights of young women also follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.

The difference between the height of a randomly selected young man (m) and a randomly selected young woman (w) follows a normal distribution with a mean of 69.3 - 64.5 = 4.8 inches (the difference in the means) and a standard deviation of √(2.8² + 2.5²) = 3.67 inches (the square root of the sum of the variances).

The shape of the distribution of the difference between the heights of a randomly selected young man and a randomly selected young woman is also normal, since the original distributions are normal. The centre of the distribution is 4.8 inches, and the spread is 3.67 inches.

(b)

We need to find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman, or in other words, we need to find P(m - w > 2).

Using the formula for the difference of two normal distributions, we have:

z = (2 - 4.8) / 3.67 = -0.76

We need to find the probability that a standard normal variable Z is greater than -0.76. Using a standard normal table or calculator, we find that P(Z > -0.76) = 0.7764.

Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is approximately 0.7764.

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The correct answer is A) F(x) = x*C, where C is an arbitrary constant. The set of antiderivatives of f(x) = 1, where F(x) is the derivative of f(x), can be described as F(x) = x + C, where C is an arbitrary constant.

To determine the antiderivatives of f(x) = 1, we need to find a function F(x) whose derivative is equal to f(x). In this case, since f(x) is a constant function, its derivative is zero. Therefore, we are looking for a function F(x) such that F'(x) = 1.

We know that the derivative of x with respect to x is 1 (i.e., d/dx(x) = 1). Hence, F(x) = x satisfies the condition F'(x) = 1.

However, we can also add any constant value to F(x) without affecting its derivative, as the derivative of a constant is zero.

So, the set of antiderivatives of f(x) = 1 is given by F(x) = x + C, where C represents an arbitrary constant. This means that for every choice of C, we obtain a unique antiderivative of f(x) = 1.

In summary, F(x) = x*C, where C is an arbitrary constant.

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Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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That the equation of the line is y = 7x - 50.

The equation of a line with slope m passing through the point (x1, y1) is given by: y - y1 = m(x - x1).

In this case, the line has a slope of 7 and passes through (8, 6). Therefore, we can plug in the values for m, x1, and y1 into the equation above to find the desired equation.

Substituting in 7 for m, 8 for x1, and 6 for y1, we can rewrite the equation as: y - 6 = 7(x - 8).

Simplifying, we find that the equation of the line is y = 7x - 50.

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Answer:

  528 cubic inches

Step-by-step explanation:

You want to know the volume of the L-shaped prism shown.

The area of the L-shaped face can be found a couple of ways. Drawing a diagonal line from the inside corner to the outside corner divides it into two congruent trapezoids with bases 12 in and 10 in, and height 2 in. The area of one such trapezoid is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(12 in + 10 in)(2 in) = 22 in²

The area of the L-shaped face is then ...

  base area = 2(22 in²) = 44 in²

As with all prisms, the volume is given by ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

  V = (44 in²)(12 in) = 528 in³

The volume of the prism is 528 cubic inches.

__

Additional comment

Another way to find the area of the L shape is to subtract the 10 in × 10 in cutout area from the 12 in × 12 in square that bounds that face.

  12² - 10² = 144 -100 = 44 in²

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The total number of students in the college is expressed as: 5x

The parameters given are:

1/2 of the students who learn the flute also learn the violin.

3 times as many students learn the violin as learn the flute.

x students learn both the flute and the violin

Thus, the total who learn the flute = 2x

Number who learn only flute = x

Since 3 times as many students learn the violin as learn the flute. Then, 3x students only learn the violin.

Thus, total number of students at the college is:

x + x + 3x = 5x

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Complete question is:

Every student at a music college learns the flute, the violin, or both the flute and the violin. 1/2 of the students who learn the flute also learn the violin. 3 times as many students learn the violin as learn the flute. x students learn both the flute and the violin. Find an expression, in terms of x, for the total number of students at the college. Flute X Violin​

ANSWER:

EXPLANATION:

Given:

To find:

Which triangle is cos B = 0.8

For the 1st Triangle:

We have to first determine the value of side BC using the Pythagorean theorem as seen below;

So cosine B will be;

For the 2nd Triangle:

For the 3rd Triangle:

We have to first determine the value of side AB using the Pythagorean theorem as seen below;

So cosine B will be;

For the 4th Triangle:

So in the below triangle cos B = 0.8

Answer: 1/2(16p+8)(p+2)

Explanation: There is a lot to do, but basically you must simplify the equation and then multiply by 4 on both sides

Juan's claim is incorrect. We have to disprove Juan's claim. He says that the solution to the given system of equations is unique only to the equations y = 5x-2 and y = 1/2x +7.

What we can do is that, we can introduce a third equation. This third equation should have the same solution as the first two.

Example of such an equation is,

y = -3x + 1

We can solve the system of three equations,

y = 5x - 2

y = 1/2x + 7

y = -3x + 1

We can use the first two equations first and find values of x and y,

5x - 2 = 1/2x + 7

Multiplying both sides by 2,

10x - 4 = x + 14

Subtracting x from both sides,

9x - 4 = 14

Adding 4 to both sides,

9x = 18

Dividing both sides by 9,

x = 2

Now we know x = 2.

We can use either of the first two equations to find y,

y = 5x - 2 = 5(2) - 2 = 8

This satisfies all three equations.

So finally we can say Juan's claim is not correct. There are other equations there having the same solution as the first two.

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Answer: i think its A

Step-by-step explanation: hope this helped

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)

The points that are on the line are given below.

(-9, -10), (-3, -1), and (3, 8)

The inequality of the line is given as,

(y - 8) ≥ [(8 + 1) / (3 + 3)] (x - 3)

y - 8 ≥ (3/2)(x - 3)

2y - 16 ≥ 3x - 9

2y - 3x ≥ 7

The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.

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Answer: c

Step-by-step explanation:

The half-life of radon-222 is approximately 3.84 days. We can find it in the following manner.

The half-life of a radioactive substance is the amount of time it takes for half of the initial amount of the substance to decay.

We can use the fact that the sample of radon-222 has decayed to 58% of its original amount after 3 days to determine its half-life.

Let N0 be the original amount of radon-222 and N(t) be the amount remaining after time t. We know that:

N(3) = 0.58N₀

We can use the formula for radioactive decay:

\(N(t) = N₀ * (1/2)^(t/h)\)

here h is the half-life.

Substituting in N(3) and simplifying:

\(0.58N₀ = N₀ * (1/2)^(3/h)\)

0.58 = (1/2)^(3/h)

Taking the natural logarithm of both sides:

\(ln(0.58) = ln[(1/2)^(3/h)]\)

ln(0.58) = (3/h) * ln(1/2)

h = -3 / ln(1/2) * ln(0.58)

Using a calculator, we get:

h ≈ 3.84 days

Therefore, the half-life of radon-222 is approximately 3.84 days.

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Answer:

To solve the above equation we will follow the BODMAS rule.

It stands for :

\(\quad\begin{gathered} \small \begin{array}{l} \star \: \rm B= bracket \\\star \: \rm O= order \: of \: power \: \\\star \: \rm D= division \\\star \: \rm M= multiplication \\ \star \: \rm A= addition \\ \star \: \rm S=subtraction \end{array}\end{gathered}\)

Solving the question by bodmas rule :

\( \tt{ = 2 \times 1 + 52 - 36 \div 2}\)

\( \tt{ = 2 \times 1 + 52 - \dfrac{36}{2}}\)

\( \tt{ = 2 \times 1 + 52 - \cancel{\dfrac{36}{2}}}\)

\( \tt{ = 2 \times 1 + 52 - 18}\)

\( \tt{ = 2 + 52 - 18}\)

\( \tt{ = 54 - 18}\)

\( \tt{ = {\underline{\underline{\red{ \: 36 \: }}}}}\)

Hence, the answer is 36.

Sexuality is boundary marker that organizers of New York City's annual India Day Parade use to exclude a particular group from participating.

The proclivity to think and act as members of a group: the proclivity to conform to a group’s cultural pattern at the price of individualism and cultural variety. Groupism… is founded not on evident group emergencies, but on the nebulous unease of lonely individuals. Mr. David Riesman.

Tangible culture (such as buildings, monuments, landscapes, literature, works of art, and artifacts), intangible culture (such as folklore, traditions, language, and knowledge), and natural heritage are all examples of cultural heritage (including culturally significant landscapes, and biodiversity).Sexuality, gender, religion, race, socioeconomic status, and area are examples of cultural identities.

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Answer:

x= -6

Step-by-step explanation:

Distribute 3x+3+6=-9

Add 3x+9=-9

Subtract 3x+9-9=-9-9

Simplify 3x=-18

Divide 3x/3=-18/3

Simplify x=-6

Answer:

a) \(f(2) = 5\), b) \(f^{-1} (x) = \frac{x-1}{2}\), c) \(f^{-1} (7) = 3\)

Step-by-step explanation:

a) We evaluate the function at \(x = 2\):

\(f(2) = 2\cdot (2) + 1\)

\(f(2) = 4+1\)

\(f(2) = 5\)

b) First, we determine the inverse of the function by algebraic means:

1) \(y = 2\cdot x + 1\) Given

2) \(y +(-1) = 2\cdot x + [1+(-1)]\) Compatibility with addition/Associative property

3) \(y + (-1) =2\cdot x\) Existence of additive inverse/Modulative property

4) \(2^{-1}\cdot [y+(-1)] = (2\cdot 2^{-1})\cdot x\) Compatibility with multiplication/Commutative and associative properties

5) \([y+(-1)]\cdot 2^{-1} = x\) Existence of multiplicative inverse/Modulative and commutative properties

6) \(x = [y+(-1)]\cdot 2^{-1}\) Symmetry property of equality

7) \(x = \frac{y-1}{2}\) Definitions of subtraction and division

8) \(f^{-1} (x) = \frac{x-1}{2}\) \(x = f_{-1} (x)\)/\(y = x\)/Result

c)  Now we evaluate the expression obtained on b) at the given number:

\(f^{-1} (7) = \frac{7-1}{2}\)

\(f^{-1} (7) = 3\)

The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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The inequality form of the given expression is:

x < -8 or x > 0

The interval notation is : (−∞,−8)∪(0,∞)

Given, the expression is |x + 4| - 4 > 0

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Isolate the variable by dividing each side by factors that don't contain the variable.

⇒  |x + 4| - 4 > 0

⇒  |x + 4|  > -4

Remove mod.

⇒ x + 4 > -4 or  x - 4 > -4

⇒ x > -4 -4 or x > -4 +4

⇒ x <-8 or x > 0

Hence the internal notation is :

(−∞,−8)∪(0,∞)

The required graph is plotted.

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Answer:

(5a3b)(2ab)

Expand

That's

15ab( 2ab )

we have the answer as

5y(-y² + 7y - 2)

Expand

That's

Hope this helps you

Answer:

y = -2x + 7

Step-by-step explanation:

In a equation thats parallel to y = -2x + 5, we have the same slope but different y intercepts (b).

SO we plug in point (3, 1) into y = mx + b

y = -2x + b

1 = -2(3) + b

1 + 6 = b

b = 7

So just plug in b back into the equation

y = mx + b

y = -2x + 7

Answer:

Step-by-step explanation:

y= -2x + 7

using point-slope formula:

y - y1 = m(x - x1)

Substitute:

y - 1 = m(x - 3)

Now, what is m and how do we find it?

m represents the slope. To find the slope in this circumstance, we have to look at the equation that we were given in the problem.

y= -2x + 5

Since we are trying to find a line parallel to this equation, we will be using the same slope that this uses.

The slope in the equation is -2.

Let’s substitute -2 for m.

y - 1 = -2(x - 3)

Now distribute:

y - 1 = -2x +6

Add 1 to both sides:

y = -2x + 7

Now we have an equation in slope-intercept form that is parallel to y= -2x + 5 and runs through the point (3, 1).

Answer:

Total cost of dinner = P + 0.15p = 23

Step-by-step explanation:

Consider the information provided.

The cost of dinner at a restaurant is $P.

The tip offered for the service was, $0.15p.

The total of the cost of dinner and the tip offered for the service is:

T = P + 0.15p = 23

The two values or x of roots of the polynomial are

\(x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}\)

This is further explained below.

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Generally, the equation for polynomial the is mathematically given as

x^2 - 11x + 13

Therefore

We know that,

\(x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)

Here,

a=1

b=-11

c=13

Putting the values,

\(x=\frac{-(-11) \pm \sqrt{(-11)^2-4 \times 1 \times 13}}{2 \times 1} \\\)

\(&=\frac{11 \pm \sqrt{121-52}}{2} \\\\&=\frac{11 \pm \sqrt{69}}{2} \\\)

Therefore

\(x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}\)

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