What is a 5th root of unity?
Answers
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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Related Questions
Is the following statement true or false, if false what is the correct statement. The square of the hypotenuse is always equal to the sum of the squares of the two legs in a right triangle.
Answers
the statement is true
this is
\(c^2=a^2+b^2\)Please help! what is 2 3/7-5 6/7? Thanks PLEASE HELP!
Answers
In a simple linear regression based on 30 observations, it is found that SSE- 2,540 and SST- 13,870 a. Calculate and se (Round your answers to 2 decimal places.) 5 b. Calculate the coefficient of determinationR. (Round your answer to 4 decimal places.) Coefficient of Determination
Answers
To calculate the standard error of estimate (SE), we can use the following formula:
SE = sqrt(SSE / (n-2))
where SSE is the sum of squared errors, and n is the number of observations.
Substituting the given values, we get:
SE = sqrt(2,540 / (30-2)) = 5.49
Therefore, the standard error of estimate is 5.49 (rounded to 2 decimal places).
b. The coefficient of determination (R-squared) is given by the ratio of the explained variation (SSR) to the total variation (SST):
R² = SSR / SST
where SSR is the sum of squared regression, and SST is the total sum of squares.
Since this is a simple linear regression, we have:
SST = SSR + SSE
where SSE is the sum of squared errors.
Substituting the given values, we get:
SST = 13,870
SSE = 2,540
Therefore, we can calculate SSR as:
SSR = SST - SSE = 13,870 - 2,540 = 11,330
Substituting these values into the formula for R-squared, we get:
R²= SSR / SST = 11,330 / 13,870 = 0.8188
Therefore, the coefficient of determination (R-squared) is 0.8188 (rounded to 4 decimal places). This means that 81.88% of the variation in the dependent variable (y) can be explained by the linear regression model with the independent variable (x).
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Carol bought 360g of flour. 8.5 of it was lost when she transferred the flour to a container. what was the amount of flour lost?
Answers
Answer:
8.5g
Step-by-step explanation:
A ski rental service charges a $37.30 initial flat rate and then an additional $2.70 per hour. In this situation, what is the value of the y-intercept?
Answers
The y-intercept is the initial value
Which of the following is a solution to the system of nonlinear equations below?
Answers
Answer:
the solution to the system of nonlinear equations is C. (0,3)
100 POINTS ILL GIVE BRAINLIEST PICTURE BELOW
Answers
Answer:
The correct answer is B. looking for work/total work force.
Unemployment rates are typically calculated by dividing the number of people who are looking for work by the total work force. The work force includes all people who are currently employed or actively looking for work, regardless of whether they are currently employed. The number of people who are looking for work is determined by surveying individuals and asking them whether they are currently seeking employment. The unemployment rate is then calculated by dividing the number of people who are looking for work by the total work force, and expressing this as a percentage.
The other answer choices are not accurate ways of calculating unemployment rates. Dividing the total work force by the number of layoffs (A) would not give an accurate measure of unemployment, as it would not account for people who are looking for work but have not been laid off. Dividing the number of people looking for work by the total population (C) would also not be an accurate way of calculating unemployment, as it would not take into account people who are not part of the work force (e.g. children, retirees, etc.). Therefore, the correct method for calculating unemployment rates is to divide the number of people looking for work by the total work force.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The unemployment rate for any area is the number of area residents without a job and looking for work divided by the total number of area residents in the labor force.
Can someone help me with this (picture)
Answers
You want to find the angle, you have the opposite and the adjacent. Therefore, we’ll use sin.
sin x= opp/adj
x= sin^-1(27/48)
x= 34.2
Hope it is useful!!
Find the length of RX. PLEASE HELP ASAP!
A.7.96
B.76.11
C.76.53
Answers
Answer:
B
Step-by-step explanation:
We want to find RX.
Note that RX is adjacent to ∠X and we also know the side opposite to ∠X.
Thus, we can use the tangent ratio. Recall that:
\(\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}\)
Substitute:
\(\displaystyle \tan6^\circ = \frac{8}{RX}\)
Take the reciprocal of both sides:
\(\displaystyle \frac{1}{\tan6^\circ}= \frac{RX}{8}\)
Multiply both sides by 8:
\(\displaystyle RX = \frac{8}{\tan6^\circ}\)
Use a calculator (make sure you're in Degrees mode!):
\(\displaystyle RX\approx 76.1149\)
Hence, our answer is B.
On the real number line, point E is at –18 and point F is at –9. What is the distance between point E and point F ?
Answers
Answer:
-9
Step-by-step explanation:
The continuous random variable X has a probability density function (pdf) given by f(x) Şi- & for 0 < x < 2 lo otherwise Part(a) Find the median of X, correct to 2 decimal places. 0.59 Part(b) Find P(X >>). Give your answer as a decimal, correct to 2 decimal places. 0.56 Part(c) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one is less than and the other is greater than 2. The order in which we take observations matters. 0.25 Part(d) Find Var(X), correct to 2 decimal places. 0.22 Part(e) Find E(X), correct to 2 decimal places. 0.75 Part(f) Find the value of q such that P(X
Answers
The median of X is 1; P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and the value of q such that P(X < q) = 0.95 is 1.9.
(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.
Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.
For 0 < x < 2, the CDF is:
F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x
Setting (1/2) * x = 0.5 and solving for x:
(1/2) * x = 0.5; x = 1
Therefore, the median of X is 1.
(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.
For x > 2, the PDF is 0, so P(X > x) = 0.
Therefore, P(X > 2) = 0.
(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.
P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)
Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.
Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.
(d) The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:
E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3
To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:
E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Now we can calculate the variance:
Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33
Therefore, Var(X) is approximately 0.33.
(e) The expected value of X, E(X), is given by:
E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Therefore, E(X) is 1.
(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:
∫(0 to q) f(x) dx = 0.95
Since the PDF is constant at 1/2 for 0 < x < 2, we have:
(1/2) * (x) | (0 to q) = 0.95
(1/2) * q = 0.95
q = 0.95 * 2 = 1.9
Therefore, the value of q such that P(X < q) = 0.95 is 1.9.
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The HRM Cafe desires to rent space for a second location. A lessor with sufficient space proposes either a fixed costs of $5,000 per month or 5% of monthly sales. Which option costs less if annual revenue is expected to be $120,000
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If the HRM Cafe expects to generate $120,000 in annual-revenue, renting space with a monthly cost of 5% of sales which is variable cost would be the cheaper option.
To determine which option costs less for the HRM Cafe, we need to compare the total costs of each option.
Option 1: Fixed costs of $5,000 per month.
This means that the monthly rent will always be $5,000 regardless of how much revenue the cafe generates.
Annual rent cost = $5,000 x 12 months = $60,000
Option 2:Variable costs: 5% of monthly sales.
This means that the monthly rent will be a percentage of the cafe's monthly sales.
Monthly rent cost = 5% x $120,000 (annual revenue) / 12 months = $500
Annual rent cost = $500 x 12 months = $6,000
Comparing the two options, we can see that option 2 (5% of monthly sales) costs less at an annual rent cost of $6,000 compared to option 1's annual rent cost of $60,000.
The variable rent option, which is 5% of monthly sales, costs less for HRM Cafe's second location.
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What is the volume of the solid shown above
First box is 4cm 4 cm 4 cm
Answers
The calculated volume of the solid figure is 64 cubic cm
How to determine the volume of the solid figureFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 4 cm by 4 cm by 4 cm
Using the above as a guide, we have the following:
Volume = Base area * Height
Substitute the known values in the above equation, so, we have the following representation
Volume = 4 *4 * 4
Evaluate
Volume = 64
Hence, the volume of the solid figure is 64 cubic cm
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Q. A circular pie has an area of 706.5 cm? What is the radius of the pie?
answer choices
A. 225 cm
B. 30 cm
C. 15 cm
D. 112.5 cm
Answers
Answer:
C. 15 cm
Step-by-step explanation:
The formula to find the area of a circle is: π × r²
But since we need to solve for the radius, we use the formula:
\(r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}\)
r = radius
A = area
π = 3.14
Now we substitute the information given in the text into the equation
\(r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}\)
Substitute values into the equation
\(r = \sqrt{ \dfrac{ 706.5 }{ 3.14 } \phantom{\tiny{!}}}\)
Divide 706.5 by 3.14
\(r = \sqrt{ 225 }\)
Take the square root of 225
\(r = {15 }\)
So, the radius of the pie is 15 cm
What statement makes the open sentence 3x + 20 = 5x + 6 true? x = 2 x = 4 x = 7 x = 13
Answers
Answer:
x = 7
Step-by-step explanation:
3x + 20 = 5x + 6
3x - 5x = 6 - 20
-2x = -14
x = 14/2
x = 7
the value of x = 7
what is the theoretical flow time? (the minimum time required to produce a garage door from start to finish.) the potential answers are: a: 50 minutes. b: 54 minutes. c: 26 minutes. d: 56 minutes. e: 58 minutes.
Answers
Theoretical flow time = 58 minutes
The complete question is
Mamossa Assaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (15 minutes per roof) and then formed in a roof forming press (8 minutes per roof). Bases are punched in a base punching press (3 minutes per base) and then formed in a base forming press (10 minutes per base), and the formed base is welded in a base welding machine (12 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per https://brainly.com/question/27786618garage) on an assembly welding machine to complete the garage. Assume one operator at each station.
Roof → Roof - punch(15 min) → Roof-form(8 min) →→→→→→→→↓
(10)Assembly→ Door
Base → Base - punch(3 min) → Base - form(10 min) → weld(12 min)↑
Roof path = 15 + 8 = 23
Base path = 3 + 10 + 12 =25
Theoretical flow time = Roof path + base path + assembly = 23 + 25 +10 = 58 mins
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the table shows data from a science fair experiment that studied the number of eggs that hatched at three different temperatures.what percentage of the eggs hatched ? do not include (%) in answer round the answer to the nearest number .
Answers
Total number of eggs = 6 + 19 + 14 + 11 + 23 + 2 = 75 eggs
Total hatched eggs = 6 + 14 + 23 = 43
\(\begin{gathered} \text{Percentage of eggs hatched = }\frac{43}{75}\times100\text{ } \\ \text{= 57.33 }\approx\text{ 57} \end{gathered}\)Therefore, the answer is 57 ( to the nearest whole number)
x^2-8x=-15 solve by completing the square
Answers
Answer:
Step-by-step explanation:
Given points (2, 4) and (1, -5), write an
equation in slope intercept for
Answers
m= 9
u welcome lol
Answer:
y = 9x - 14
Step-by-step explanation:
slope = rise over run
9 rise for every 1 run
y intercept = -14
a college algebra class has 48 female and 44 male students. suppose you select one student at random to solve a math problem, what is the probability that the selected student is a female?
Answers
Probability of selecting a female student from the given number of students is equal to 0.5217.
As given in the question,
Number of female students in algebra class = 48
Number of male students in algebra class = 44
Total Number of students in algebra class = 48 + 44
= 92
Total number of outcomes = ⁹²C₁
Number of favourable outcomes = ⁴⁸C₁
Probability of selecting a female student
= (Number of favourable outcomes) / (Total number of outcomes )
= ⁴⁸C₁ / ⁹²C₁
= 48 / 92
= 12/23
= 0.5217
Therefore, the probability of selecting a female students from the given number of male and female students is equal to 0.5217.
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If the water in the oceans represent 53 % of the total water in/on earth. Please Calculate the percentage occupied by the fresh water in/on earth? (REPORT VALUE ONLY I.E. NO NEED FOR UNIT) (ZERO DECIMAL PLACES, e.g. 10 not 10.1) Calculate the pH of a solution that has H* concentration equal to 0.08606951774271 M (REPORT VALUE WITH ONE DECIMAL PLACE, e.g. 1.2 not 1)
Answers
The percentage occupied by fresh water on Earth is 47%. The pH of the solution with H+ concentration 0.08606951774271 M is 1.1.
To calculate the percentage of fresh water on Earth, we can subtract the percentage of water in the oceans (53%) from 100%. This gives us 47%, which represents the percentage occupied by fresh water.
The pH of a solution is a measure of its acidity or alkalinity. It is determined by the concentration of hydrogen ions (H+) in the solution. In this case, the H+ concentration is given as 0.08606951774271 M. The pH scale ranges from 0 to 14, with values below 7 indicating acidity and values above 7 indicating alkalinity. By calculating the negative logarithm (base 10) of the H+ concentration, we find that the pH of the solution is approximately 1.1.
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here's a formula:
a=2b-c
what is the value of a if b=11 and c=3?
Answers
Answer:
a = 19
Step-by-step explanation:
a=2b-c
a= 2(11) - 3
a = 22 - 3
a = 19
Answer:
a = 19
Step-by-step explanation:
2 x 11 = 22 - 3 = 19
So a = 19
What is the length of the diagonal of a cube with a side length of 5cm? Round to the nearest tenth
Answers
Step-by-step explanation:
Cube ...so each side is 5 cm
Diagonal = sqrt ( 5^2 + 5^2 + 5^2 ) <====like Pythagorean theorem in 3-D
= sqrt (75) = 5 sqrt 3 = 8.66 cm
Answer:
7.071
Step-by-step explanation:
this is sqrt(25+25)
which is 7.071
Brainliest?
Find the length of the missing side. Assume that lines that appear to be tangent are tangent. Round your answer to the nearest tenth, if needed.
Answers
Solution:
Given:
The radius and tangent to a circle at the point of intersection are perpendicular to each other.
Hence, considering the right triangle;
Hence, the length of the missing side can be gotten using the Pythagorean theorem.
\(\begin{gathered} first\text{ leg}^2+other\text{ leg}^2=hypotenuse^2 \\ 8.4^2+x^2=10.5^2 \\ x^2=10.5^2-8.4^2 \\ x^2=39.69 \\ x=\sqrt{39.69} \\ x=6.3 \end{gathered}\)
Therefore, to the nearest tenth, the length of the missing side is 6.3
Please help i'm struggling with this help!
Answers
Which best describes sentence 7? it is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
Answers
A Simple sentence best describes sentence 7 (They rule the earthly world of men together)
This means that it consists of only one independent clause - meaning there is only one finite verb in the sentence. In this case, the verb rules.
A compound sentence has at least two independent clauses; a compound-complex sentence has at least two independent clauses plus at least one dependent clause; a dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case here.
Complete question:
Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
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A Simple sentence best describes sentence 7 (They rule the earthly world of men together)
It only has one independent clause, which means there is only one finite verb in the sentence, according to this definition. This time, the verb is in charge.
A dependent clause cannot exist on its own because it is just a fragment of a larger statement, which is obviously not the case in this sentence. A dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case in this sentence.
Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.
What is the surface area of a cylinder that has the following measurements
Area of each base 50.24
Area of lateral surface 75.36ft^2
Height of cylinder 3 ft
A. 150.72
B.175.84
C. 125.6
D. 128.6
Answers
What is the value of 3-(-2)
Answers
The factors of the polynomial 3x3 - 75x do NOT include which of the
following:
Ox+5
O x-5
O 3x
O3x+25
Answers
Answer:
3x + 25 is not a factor
Step-by-step explanation:
3x³ - 75x ← factor out common factor of 3x from each term
= 3x(x² - 25) ← x² - 25 is a difference of squares
= 3x(x - 5)(x + 5) ← in factored form
thus 3x + 25 is not a factor of the polynomial
I need help with this, can anyone help?
Answers
The above proof is given as follows;
FG ≅ HI - Given
FG ║ HI - Given
∠FHI ≅ ∠GFH - Alternate angles
FH ≅ FH - Reflexive Property
ΔFGH ≅ ΔHIF - Side-Angle-Side Postulate
FI ≅ GH - Definition of parallelogram.
A parallelogram is a four-sided figure with opposite sides parallel and congruent. Here are the properties of a parallelogram:
Opposite sides are parallel: The opposite sides of a parallelogram are parallel to each other. That is, they never meet even if extended infinitely.Opposite sides are congruent: The opposite sides of a parallelogram are of equal length.Opposite angles are congruent: The opposite angles of a parallelogram are of equal measure.Consecutive angles are supplementary: The consecutive angles of a parallelogram add up to 180 degrees.Diagonals bisect each other: The diagonals of a parallelogram intersect at their midpoint. That is, the line segment joining the midpoint of the two diagonals is half the length of the diagonal.Each diagonal divides the parallelogram into two congruent triangles: The two diagonals of a parallelogram divide it into four congruent triangles.Learn more about reflexive properties:
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