Rewrite the decimals as fractions 3.34

The fifth root of unity is given by  Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

As given in the question,

Using the Euler Identity ,

e^(πi) = -1

Calculate the nth root of Unity so that it can be used to calculate for any value of n:

Zⁿ = 1

⇒Z = (1)^(1/n)

Apply Euler's Formula we get,

Z = cos (2kπ + 0)/n + i sin(2kπ + 0 )/n

⇒Z = cos ( 2kπ / n) + isin( 2kπ / n)

Using Euler' identity  we can write this as :

Z = e^(2kπ/n)

For k = 0 , 1 , 2 , 3..... (n-1)

Now substitute n = 5 to get the value of 5th root of unity we have

Z = e^(2kπ/5)

When k = 0 , 1, 2, 3, 4

k = 0 ⇒ Z = 1

k= 1 ⇒ Z = e^(2πi/5)

k = 2 ⇒ Z = e^(4πi/5)

k= 3 ⇒ Z = e^(-2πi/5)

k = 4 ⇒ Z = e^(-4πi/5)

Therefore, the value of 5th root of unity is equal to Z = 1, e^(2πi/5) ,e^(-2πi/5), e^(4πi/5), e^(-4πi/5).

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The coefficient of the variable x  in the expression 2-5x-4+8 is -5

Given that,

The expression is 2-5x-4+8 which can be simplified as -5x+6

To find : The coefficient of the variable x in the expression

The coefficient of x in 2-5x-4+8  is -5

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

Coefficient is the number that is beside the variable in the equation.

As we can see that the term that is in multiplication with x is -5.

Hence, the coefficient of x in the equation  is -5.

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The expected number of airplanes circling the airport, waiting in queue for clearance to land, if this new radar system were to be used is zero.

The new radar system is being considered as a means of reducing congestion, which implies that there is currently an issue with congestion at the airport. One way to reduce congestion is to process planes at a faster rate, which is exactly what the new radar system aims to do.

The statement "planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero)" indicates that the system is able to process planes at a consistent rate of 15 per hour, with no variation in this rate. This means that there should be no planes waiting in queue for clearance to land, as they can all be processed at the constant rate of 15 per hour. Therefore, the expected number of airplanes circling the airport and waiting in queue for clearance to land is zero.

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Answer: Profit = Rs 15, Profit %= 30%

Step-by-step explanation: When S.P.( Selling Price) is greater than C.P.(Cost Price), there is a Profit.

Profit= S.P-C.P

Hence Rs 15 is the profit.

To calculate Profit %, we use the formula Profit ÷ C.P. × 100%

Hence, the Profit % is 30%.

Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Considering the triangle that is containing angle 3 along with the angles 90° and 61° and as we know the sum of angles in a triangle = 180° so the angle 3 is 29°

As we know that opposite angles are equal we can say that angle 4 is 115°

Now considering the triangle that contain angle 3 which is 29° and angle 4 which is 115°  we can say that angle 6 is 36° by applying sum of angles in a triangle.

Considering the triangle that consists of angles 1 , 6 and 80°+ angle 3 we can say that angle 1 is 35°

now considering the trinaglewith angles 1, 2 and 80° we can say that angle 2 is  65°

As we know that opposite angles are equal we can that angle 5 is same as angle 2 which is 65°.

Finally as angle 6 + angle 7 sum = 180° as they are on the straight line

we can say that angle 7 is 144°

Angle 1 is 35°, angle 2 is 65°, angle 3 is 29°, angle 4 is 115°, angle 5 is 65°, angle 6 is 36° and finally angle 7 is 144° considering the shape triangle whenever possible.

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The total amount she needs to pay is ₹6396

A reduction made from the gross amount or value of something.

Given that,  Mrs. Jain goes to lunch with her friends at a restaurant which offers her a 20% discount. The cost of the food that they order is 6,480. Given that there is a service charge of 5% and GST is at 18%

Discount Offered is 20%, so price after discount will be-

= ₹6480-₹(20% of 6480)

= ₹5200

Service Charge she has to pay:

5% of ₹5200

= ₹260-Answer

Total Amount of Bill:

= ₹5200+Service Charge+GST

= ₹5200+₹260+₹(18% of ₹5200)

= ₹(5200+260+936)

= ₹6396

Hence, The total amount she needs to pay is ₹6396

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The sum of the roots of 3x² 10x 8 0 is -2.

The given equation, 3x² 10x 8 0, is a quadratic equation with two roots. To find the sum of the roots of this equation, we must first solve the equation. To do this, we use the quadratic formula, which states that the roots of the equation are x = [-b ± √(b² - 4ac)]/2a. Here, a = 3, b = 10 and c = 8.

Therefore, the roots of the equation are x = [-10 ± √(10² - 4(3)(8))]/2(3). This simplifies to x = [-10 ± √(-4)]/6. Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined. Therefore, the sum of the roots of 3x² 10x 8 0 is -2.

x = [-10 ± √(10² - 4(3)(8))]/2(3)

x = [-10 ± √(-4)]/6

x = [-10 ± √(-4)]/6

Since the square root of a negative number is not a real number, the roots of the equation are not real numbers, and the sum of the roots is undefined.

Therefore, the sum of the roots of 3x² 10x 8 0 is -2.

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If a statement is true, then it cannot be falsified no matter what.

A true statement will yield a true statement.

A false statement can yield a true or false statement.

The answer to your question is no, we cannot do anything to make the statement "2=2" false

Answer:

To solve the equation 5x - 4y = -12, we can first get all of the terms containing x on one side of the equation and all of the terms containing y on the other side. To do this, we need to add 4y to both sides of the equation. This gives us 5x = -12 + 4y. Then, we can divide both sides of the equation by 5 to get x = (-12 + 4y)/5. This is the value of x that makes the equation true.

Step-by-step explanation:

Answer: I= 3÷y-5x÷12

solve for y

​ Step-by-step explanation: 5x−4y=−12I

Swap sides so that all variable terms are on the left-hand side.

−12I=5x−4y

Divide both sides by −12.

-12I/-12= 5x−4y/-12

Dividing by −12 undoes the multiplication by −12.

I=-12I/-12= 5x−4y/-12

Divide 5x−4y by −12

I=3÷y-5x÷12

​

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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Answer:

a=b=0

Step-by-step explanation:

y=(ax)/b so now plug in the points

first 0=6a/b

next 2=3a/b

0=6a

2b=3a

a,b =0

You probably put the wrong problem but this is what I got.

Answer:

Step-by-step explanation:

Hi

Answer:

The mean price for this sample is $1,385.00

Step-by-step explanation:

⭐What is the "mean" of a sample?

To find the mean for this data, we need to divide the sum of the prices for the computers bought by the total number of computers bought.

Sum of the prices for the computers:

[tex]14(1400)+12(1050)+5(2150)[/tex]

[tex]= 19,600 + 12,600 + 10,750[/tex]

[tex]= 42,950[/tex]

Total number of computers bought:

[tex]14+12+5[/tex]

[tex]= 31[/tex]

Mean price:

[tex]\frac{42,950}{31}[/tex]

[tex]= 1,385.00[/tex]

0.83 is the average rate change of length of vine from weeks 3 to 9.

In mathematics, the average value of a set of integers is the middle value, which is determined by dividing the sum of all values by the number of values.

When we need to get the average of a set of data, we add all the values and then divide this sum by the number of values.

The length of the plant at the end of the third week is 6 inches.

At the conclusion of week nine, the length of the vine is 11 inches.

So the change in the length of the plant is 11-6 = 5 inches.

The change in weeks is 9-3 = 6 weeks.

We know that average growth = [tex]\frac{change in x}{ change in y}[/tex] = Δx÷Δy

∴ change in length/ change in time = [tex]\frac{5}{6}[/tex] = 0.833

0.83 is the average rate change of length of vine from weeks 3 to 9.

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Answer:

Step-by-step explanation:

X = ?

y = ?

The big triangle ABC is a right triangle,  we can use Pythagoras theorem to find side y,  then use SOH CAH TOA to find angles   :)

also, there is a special rule for a triangle set up like this one

2CD = BD

for this triangle then,

2CD = 9

CD = 4.5

X = 13.5

now use Pythagoras to find y

[tex]13.5^{2}[/tex] = [tex]6^{2}[/tex] + [tex]y^{2}[/tex]

182.25 -36 = [tex]y^{2}[/tex]

[tex]\sqrt{146.25}[/tex] = y

12.093386 = y

now that you have all 3 sides of the big triangle, use which ever trig function you are most comfy with to find  angle B or C, i'll find C

CAH  =  Cos(C) = Adj / Hyp

Cos(C) = 6 / 13.5

arcCos(Cos(C)) = arcCos(6/13.5)

C = 63.6122°

now find B

180 = 90 + 63.6122 + B

26.3877° = B

got it?

The one way of determining the factors of x³ + 4x² + 5x + 20 by grouping is (b) x²(x + 4) + 5(x + 4) .

The Grouping in a polynomial is done by the taking the GCF( greatest common factors) from the different terms .

the expression is given as : x³ + 4x² + 5x + 20 ;

in order to determine the factors by grouping ,

we first take x² common from the first two terms and 5 common from the last two terms .

we get ;

⇒ x²(x + 4) + 5(x + 4)

Therefore , the one way of determining the factors is x²(x + 4) + 5(x + 4)  .

The given question is incomplete , the complete question is

Which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping ?

(a) x(x² + 4) + 5(x² + 4)

(b) x²(x + 4) + 5(x + 4)

(c) x²(x + 5) + 4(x + 5)

(d) x(x² + 5) + 4x(x² + 5)

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Answer:

  75

Step-by-step explanation:

You want the remainder when n is divided by 100, where VISIONERS is the n-th word in the alphabetically-ordered list of the permutations of REVISIONS.

The letters of the word REVISIONS are, in alphabetic order, are EIINORSSV. We notice there are two each of the letters I and S.

When the permutations of the letters of REVISIONS are written in lexicographical order, the list will first have all of the permutations beginning with E, then those beginning with I, and so on until the permutations beginning with S are exhausted.

To find the rank (number n) of the first permutation beginning with V, we must count the number of permutations ahead of it in the list. This will be the sum of the numbers of permutations beginning with E, I, N, and so on through S.

The straightforward way to do this is to consider the letters individually, and the number of permutations associated with each one. For example, the letters following E will be the 8 letters IINORSSV, which have two repeat pairs. The number of permutations of these 8 letters is 8!/(2!·2!) = 10080.

The next leading letter in the list is I, which can be followed by any of the letters EINORSSV, for a total of 8!/2! = 20160 permutations.

The letter N will be the next leading letter, and it will have a number of permutations equal to the number for the letter E, 10080.

At this point, we have exhausted 4 of the 8 letters that must precede V in the ordered list, and have counted 10080 +20160 +10080 = 40320 permultations. We notice this is, in effect, 10080 permutations per letter, the number of permutations of the letters not including V.

If we were to work through the remaining letters (including the repeated S), we would find the total to be 8·10080 = 80640 permutations before any starting with V.

Effectively, our formula for the number of added permutations preceding words matching up to the k-th letter of our target word is ...

  p(9-k)!/q

where p is the number of letters in the (remaining) ordered letter list preceding the k-th letter of VISIONERS, and q is the factor that compensates for repeated letters among those remaining. "q" is the product of the factorials of the number of times a letter is repeated. For 2 letters, each repeated once, q = 2!·2! = 4.

V is the 9th letter of EIINORSSV; there are 8 letters preceding, including 2 repeated twice. k=1, so there are 8·(9-1)!/(2!·2!) = 80640 permutations preceding ones starting with V.

I is the 2nd letter of EIINORSS; there is 1 letter preceding, including 2 repeated twice. k=2, so there are 1·(9-2)!/(2!·2!) = 1260 permutations preceding ones starting with VI.

S is the 6th letter of EINORSS; there are 5 letters preceding, including 1 repeated twice. k=3, so there are 5·(9-3)!/2! = 1800 permutations preceding ones starting with VIS.

I is the 2nd letter of EINORS; there is 1 letter preceding, with no repeats. k=4, so there are 1·(9-4)! = 120 permutations preceding ones starting with VISI.

O is the 3rd letter of ENORS; there are 2 letters preceding. k=5, so there are 2·(9-5)! = 48 permutations preceding ones starting with VISIO.

N is the 2nd letter of ENRS; there is 1 letter preceding. k=6, so there are 1·(9-6)! = 6 permutations preceding ones starting with VISION.

We note that the remaining letters, ERS, are in alphabetical order, so there are no additional permutations preceding VISIONERS.

Then the number of permutations preceding VISIONERS is ...

  80640 +1260 +1800 +120 +48 +6 = 83874

and the rank of VISIONERS is 83875.

The remainder when this is divided by 100 is 75.

__

Additional comment

The usual counting method goes into more detail than the one described here. For problems of reasonable size, it is often easier to count the permutations generated ahead of the one of interest using a "next permutation" function.

In the attachment, we generated them all, and searched for the one of interest.

Answer:

90 degrees

Step-by-step explanation:

the centre angle of the triangle is 180°.
ABC is its circumference angle, that is half the centre one

The probability of 2 people insists on sitting side by side is 2/7. In the next, the probability of 2 people insists on sitting side by side is 2/5

The possibility of occurring a particular events is called probability.

it is expressed in ratio of two data. The probability has no unit to measure.

Number of students =7, among them 2 are insists on sitting side by side

now probability to sit in such a way = 2/7

again, 2 students will never sit side by side so the number became 5.

probability to sit side by side = 2/5

hence, the result is 2/7 and 2/5

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The sides of a triangle with all respective angles equal, i.e. AAA condition, may or may not be equal. Only if two triangles with the same respective angles are identical would the congruence stay true.

Knowing only angle-angle-angle (AAA) does not work because it can produce similar but not congruent triangles. When you're trying to determine if two triangles are congruent,

there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them. If the three angles (AAA) between two triangles are congruent, that does not imply that the triangles must be congruent. They have the same shape (and can be considered comparable), but we don't know how big they are.

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Answer:

If 10% of the students at Ridgewood Junior High School bring their lunch to school every day, and there are 700 students at the school, then 10% of 700 students is equal to 0.1 * 700 = <<10*.01*700=70>>70 students.

Therefore, on Thursday, 70 students brought their lunch to school.

The arrow diagram is

2 3 5

| | |

v v v

2 3 5

To prove that R is a function, we must show that "a R b" exists for each element an in X. R is a function since the only element b in X that fulfills the relation is a.

The range of R is X = {2, 3, 5}.

Generally, The relation R on X is defined as "a R b" if and only if "a = b" for all a,b in X. This means that for any element a in X, the only element b in X that satisfies the relation is a itself. We can represent this relation using an arrow diagram as follows:

2 3 5

| | |

v v v

2 3 5

To show that R is a function, we need to demonstrate that for each element a in X, there is exactly one element b in X such that "a R b". In this case, we have already shown that the only element b in X that satisfies the relation is a itself, so R is a function.

The range of the function R is the set of all possible values of b for which "a R b" is true. In this case, the range of R is the set X itself, because for any element a in X, the only element b in X that satisfies the relation is a itself. Therefore, the range of R is X = {2, 3, 5}.

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A word expression example is "as busy as a bee." This phrase is used to describe someone who is very busy and active.

The phrase “as busy as a bee” is often used to describe someone who is very active and busy. This phrase is a testament to the hard work that bees have to do every day in order to ensure the survival of their hive. Similarly, people who live an active lifestyle can reap the same benefits of a hard-working bee. From physical health benefits to improved mental health, living an active lifestyle can have a profound impact on one’s overall well-being.

When it comes to physical health, engaging in regular physical activity can reduce the risk of chronic diseases, such as heart disease, stroke, and diabetes. Additionally, regular physical activity can help to improve physical fitness and boost energy levels. Not only does this make it easier for individuals to perform everyday tasks, but it can also help to improve one’s mood and reduce feelings of stress and anxiety. In addition to physical health benefits, an active lifestyle can also promote improved mental health. Exercise can help to reduce symptoms of depression, as well as improve one’s self-esteem and overall sense of well-being.

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Answer:

sin2theta

= (4root2)/9

cos2theta = -7/9

tan2theta

= (4root2)/-7

Step-by-step explanation:

see image.

Draw a picture to help see your angles and the triangle trigonometry. Use Pythagorean theorem and triangle trig to find sintheta and tantheta. Use Double Angle Formulas to find the answers to the question. See image.

The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The trigonometric equation is given below.

cos θ = 1/3

cos θ = 0.3333

θ = 289.47°

The value of the sine of angle 2θ will be given as,

sin 2θ = sin (2 × 289.47°)

sin 2θ = sin 578.94°

sin 2θ = -0.628

The value of the cosine of angle 2θ will be given as,

cos 2θ = cos (2 × 289.47°)

cos 2θ = cos 578.94°

cos 2θ = -0.778

The value of the tangent of angle 2θ will be given as,

tan 2θ = tan (2 × 289.47°)

tan 2θ = tan 578.94°

tan 2θ = 0.808

The value of the sin 2θ, cos 2θ, and tan 2θ will be - 0.628, -0.778, and 0.808, respectively.

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The system of equations has no solution because they are parallel lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.

The system of equations y=0 and y=-6 describes two lines in the coordinate plane.

The first equation, y=0, is the x-axis.

The second equation, y=-6, is a horizontal line 6 units below the x-axis.

As we know, y = 0 and y = -6 are two parallel lines.

Therefore, no solution exists.

Hence, the system of equations has no solution.

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Performed at about average on spelling, but about one standard deviation below average on math.

Any test that (1) requires all test takers to answer the same questions, or a set of questions from a common bank of questions, in the same way and (2) is scored in a "standard" or consistent manner, allowing for comparison of the relative performance of individual test takers, is considered to be standardized.

Students are frequently chosen for certain programs using standardized assessments. For instance, norm-referenced examinations like the SAT (Scholastic Assessment Test) and ACT (American College Test) are used to decide whether high school students get admitted to elite institutions.

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The equation with a solution s = 3/4 is the second option:

4s = 3

We want to see which of the given equations has a solution s = 4/3.

What you can do is take all the given equations and solve them, for example, if I solve the first one:

s - 1 = 1/4

We will get:

s = 1 + 1/4 = 5/4

So this one is not the correct one.

The second equation is:

4s = 3

Dividing both sides by 4:

s = 3/4

So this is the correct option.

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The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).

The appropriate set of axes to make a scatter plot of the data is a horizontal x-axis and a vertical y-axis. The horizontal x-axis would represent the age of the people while the vertical y-axis would represent the number of CDs bought. The ordered pairs of the data that should be used to plot the points on the scatter plot are (18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), and (34, 3).

A scatter plot is a graph that is used to represent the relationship between two variables. It is a graphical representation of data that shows the relationship between two variables by plotting a set of ordered pairs on a coordinate plane. The ordered pairs of the data are represented by a mark, usually a dot, on the graph. The horizontal x-axis is usually used to represent the independent variable and the vertical y-axis is used to represent the dependent variable. In this case, the x-axis is the age of the people and the y-axis is the number of CDs purchased.

A scatter plot can be used to find patterns in data and to identify relationships between two variables. By plotting the ordered pairs of the data on the coordinate plane, the scatter plot will show any correlations or trends that are present in the data. For example, if there is a positive correlation between age and the number of CDs purchased, the scatter plot will show a line of points that goes up and to the right. On the other hand, if there is a negative correlation between the two variables, the scatter plot will show a line of points that goes down and to the right. By plotting the data points on a scatter plot, it is possible to identify any patterns or trends that are present in the data.

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There are three ways to solve systems of linear equations in two variables:

System of Linear Equations :

A system of linear equations is two or more linear equations that are being solved simultaneously.

Solution of a System :

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common.  So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

A consistent system is a system that has at least one solution.

An inconsistent system is a system that has no solution.

There are three ways to solve systems of linear equations in two variables:

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Although it won't necessarily be harder, this will consume more of your time.

How much work performed by an element in a given timeframe, or the typical measure of work took care of by a substance at a specific moment of time. An estimate of an organization's performance and efficiency can be derived from the amount of work it handles. This term is used in computer science to describe the capacity of computer systems to handle and process work.

At the time of creation, components like databases and servers frequently receive an anticipated workload. Following that, a time-based comparison of their performance to the anticipated workload is carried out.

There is always more work to do in high school classes. You might have assignments that are more difficult, more homework, or more classes than you did in middle school. Although it won't necessarily be harder, this will consume more of your time.

Classes naturally become more challenging over time. After all, year after year, you tackle more difficult concepts. A component of education is that. Theoretically, middle school was "harder" than elementary school. There will be classes that are harder, and you might have to put in more work for some of them. But you should be able to handle these classes as long as you have a solid foundation. You can join the thousands of students who have made it this far.

Therefore, This will take up more of your time, despite the fact that it will not necessarily be harder.

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