The cube root of unity are found to be 1, -1±i√3/2 and -1±i√3/2.
In order to find the cube root of unity let us say,
x³ = 1
Solving further,
x³-1 = 0
Now,
(x-1)(x²+x+1)=0
For, x-1=0
x = 1.
And,
For, (x²+x+1)
Solving by using quadratic formula,
x = -1±√(-3)/2.
x = -1±i√3/2
x = -1+i√3/2 and,
x = -1-i√3/2
also, x = 1.
So that cube root of unity are 1, -1±i√3/2 and -1±i√3/2.
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Simplify the rational expression. State any excluded values. x^2-64/16x-2x^2
Answer:
The answer is -x^2-4x
Step-by-step explanation:
△abc is similar to △lmn. also, angle b measures 35° and angle c measures 95°. what is the measure of angle l? enter your answer in the box. the measure of angle l = °
The measure of the angle I= is 50 degree
What is an example of geometry?A triangle has three sides and a total interior angle of 180 degrees. Four-sided shapes like a square, rectangle, or quadrilateral have a total interior angle of 360 degrees. Other polygons have different angles and different numbers of sides, such as the pentagon, hexagon, heptagon, and octagon.
Is geometry easier than algebra?Compared to algebra, geometry requires less math, and the math that is needed is simpler. Geometry, on the other hand, necessitates the memorization of numerous rules and formulas, which for some students can be more challenging than fundamental algebra. Ask your teacher for assistance if you need it in a math class.
The ratio of the respective sides is proportional when two triangles are comparable to one another.
Additionally, the corresponding angles coincide.
Given in this case are B= 35° and C= 95°
the angle sum property now
A + B + C = 180°
A + 35 + 95 = 180
A + 130 = 180
130 is subtracted from both sides, giving us
A = 180 - 130
A = 50°.
Now
ABC and LMN
Consequently, in terms of similarity
A = L
But A = 50°.
Thus, L = 50°.
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In investment of $1800 in the stock market are $278 in two years find the simple interest rate
The interest rate is -42.3%, where the negative sign indicates depreciation.
What is the interest rate?The percentage that a lender adds to the amount of money lent to them is called an interest rate.
Given that, the investment of $1800 in the stock market is $278 in two years.
Therefore, the amount depreciated is:
278 - 1800
= -1522
Since 1522 is depreciated in 2 years, the amount depreciated in one year is:
1522/2
= 761
The rate at which the amount depreciated is:
(761/1800)×100%
= 42.3%
Hence, the interest rate is -42.3%, where the negative sign indicates depreciation.
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E ≠ V + Ir
Solve for r
Answer:
r ≠ E – V/r
Step-by-step explanation:
E ≠ V + Ir
E – V ≠ Ir
divide both sides by I
E – V/I ≠ r
r ≠ E – V/r
i hope i helped
If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
10,000n(x/100)
The reasoning is from the following:The formula for simple rate of interest is F = P(1+rt) whereF = future valueP = present valuer = ratet = time
If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)
What is simple interest?Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.
F = P(1+rt), formula for simple rate of interest
Here,
=> Future value is F
=> Present value is P
=> Rate is R
=> Time is t
Substituting x for r
And, n for t
Also, 10,000 in for P
F = 10,000(1+xn)
The formula tells us principal + interest,
F = 10,000(xn)
Now, to get the x into terms of a percentage,
F = 10,000(n * x/100)
F = 10,000n(x/100)
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In the figure to the right, it AC=22 and BC=19, what is the radius?
exhibit 12-2 last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. a random sample of 300 students taken from this year's student body showed the following number of students in each class. freshmen 83 sophomores 68 juniors 85 seniors 64 we are interested in determining whether there has been a significant change in the distribution of class between the last school year and this school year. refer to exhibit 12-2. if the distribution is the same as the previous year, the expected number of freshmen is . a. 30 b. 10 c. 90 d. 83
Option D is the correct answer.
What is distribution?
To “distribute” means to divide something or give a share or part of something.
From the given information , 83 + 68 + 85 + 64 = 300 students.
30 % = freshmen, 24% =sophomores, 26% = juniors , 20% = seniors
Class Observed frequency Expected proportion
Freshman 83 0.30
Sophomores 68 0.64
juniors 85 0.26
seniors 64 0.20
Total 300 1
The expected number of students in freshman class can be calculated as
Expected Frequency = Total number of value x Expected Proportions
= 300 x 0.30
= 90
Therefore, the expected number of students in freshman class = 90
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what are the major differences between a population that is experiencing logistic growth and one that is experiencing exponential growth?
If resources are unlimited, population will increase exponentially. A logistic growth happens as those resources are less readily available.
Explain the term logistic growth and exponential growth?Exponential Growth:
The term "exponential growth" describes a population's expansion through time at a pace that is directly proportionate to its size. The population's size is influenced by both the birth and death rates. When there are plenty of resources for everyone in the population, exponential expansion happens. When the number of objects is plotted against time, it yields a J-shaped curve.Logistic Growth:
A population growth known as logistic growth is a group of people whose rate of growth reduces as the number of individuals increases and becomes zero whenever the population reaches its maximum.People in the population compete for resources so when food supply and available space are limited.Thus, there are several key distinctions between populations growing logistically and those growing exponentially.
If resources are unlimited, population will increase exponentially. A logistic growth happens as those commodities become less widely available.To know more about the exponential growth, here
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Use the number line to represent the solution to 2.4x−6>−13.2.
The required solution of the given inequality is given as x > -3.
Given that,
To determine the solution of the given inequality, 2.4x−6>−13.2.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
2.4x−6>−13.2.
2.4x > -7
x > -3
Thus, the required solution of the given inequality is given as x > -3.
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explain how you could use a regression model to estimate the wage gender gap using the data on earnings of men and women. what are the dependent and independent variables?
A regression model could be used to estimate the wage gender gap by comparing the earnings of men and women.
Regression is a statistical technique used in the fields of finance, investing, and other areas that aims to assess the nature and strength of the relationship between one dependent variable and another. In this case, the dependent variable would be the gender gap in wages and the independent variable would be the earnings of men and women. The regression model would be used to calculate the difference between the two variables, which would indicate the wage gender gap.
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50 POINTS! PLEASE HURRY!
f(x) = x2. What is g(x)?
Answer: g(x) = -x^2 -3
Step-by-step explanation:
We know that the y-intercept is -3, so we can eliminate the first 2 answers. For the last two answers, c is wrong because it is a negative slope and if we square root it, it will become a positive slope our graph slope is not positive, so the answer is d.
what is the probability that someone who tests negative does not have the disease? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The probability that someone who tests negative does not have the disease is 0.8451
Given that,
The information shows the outcomes of a test for a specific illness. Assume a member of the group is chosen at random.
From given data table,
N = 144+ 22 + 14+ 120 = 300
n(not disease) = 22 + 120 = 142
n( negative And not disease) = 120
P( Not disease) = 142/300
P( Negative and not disease) = 120/300
Therefore,
P(Negative/ not ..disease) =[tex]\frac{P(Negative and not,.disease)}{P(Not ,.disease)}[/tex]
=[tex]\frac{120/300}{142/300}[/tex]
=[tex]\frac{120}{142}[/tex]
=0.8451
Hence, The probability approximately is 0.8451
Hence, the probability that someone who tests negative does not have the disease is 0.8451
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E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022. Show how the bonds would be reported on the january 2, 2022, balance sheet if they are issued at 97. (deductions should be indicated by a minus sign. ).
The preparation of the bond that should be reported on the balance sheet is presented below:
E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022.
We need to present it on balance sheet balance sheet if they are issued at 97.
E-Tech Initiatives Limited
Partial balance sheet
As on January 2, 2019
Liabilities
Long term Liabilities
Bond Payable $500,000
Add: Premium on Bond $10,000 ($510,000 - $500,000)
Carrying value $510,000 ($500,000 * 97%)
Therefore, The preparation of the bond that should be reported on the balance sheet is presented above.
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167. for the training adaptation of maximum strength, what is the recommended number of repetitions per set?
Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
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a grandfather, two fathers and two sons bought passage for a voyage together and everyone paid for one berth each. how many berths did they buy in total?
Grandfather, two fathers and two sons purchased a total of three tickets.
What is a Mathmatical riddle?
Children must convert a few lines from a real-life incident into the appropriate set of mathematical equations in order to solve a math mystery. Mathematical riddles can be cracked by kids utilizing logic, inventive problem-solving, and common sense.
All three tickets:
Grandfather and His Son's Father
Father and his father's son.
Son.
Two fathers and two sons, then.
As a result, a total of 3 tickets were purchased by a grandfather, two fathers and two sons.
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Find the volume of a right circular cone that ha a height of 16. 4 in and a bae with a radiu of 20 in
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
U have to estimate!!!!!!!!!! Please help now asap
A swimming pool is on sale for $875.50. If the sale price is discounted 15% from the original price, what was the original price?
The original price of the swimming pool is $1030.
How to calculate the value?From the information, the swimming pool is on sale for $875.50 and the sale price is discounted 15% from the original price.
Let the original price be x.
This will be illustrated as:
(x - 15% × x) = 875.50
x - 0.15x = 875.50
0.85x = 875.50
Divide
x = 875.50 / 0.85
x = 1030
The original price is $1030.
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how much does each apple cost?
Apples
4 for $2
Evaluate each general power function at the indicated values.
1.
f(x) = x^n, where n is even
f(1) = ?
f(-1) = ?
2.
g(x) = x^n, where n is odd
g(1) = ?
g(-1) = ?
Step-by-step explanation:
remember, an exponent n just means that the base is multiplied by itself n times.
so, e.g.
a³ = a×a×a = (a×a)×a
a⁶ = a×a×a×a×a×a = (a×a)×(a×a)×(a×a)
as you can see, any even exponent can be written as products of squares.
and any odd (uneven) exponent can be written as product of squares multiplied by one base.
a square of a real number is always positive. therefore, an even exponent of a real number is always positive.
and an odd exponent has the sign of the base (as the result of these multiplications is the product of the squares, that are always positive and one instant of the base, and +×+ = +, +×- = -).
and 1^n = 1
no matter how often I multiply 1 by 1, I get 1 as result.
also : -×- = +
1.
f(x) = x^n, n is even
f(1) = 1^n = (1×1)×(1×1)×...×(1×1) = 1×1×1×...×1 = 1
f(-1) = (-1)^n = (-1×-1)×(-1×-1)×...×(-1×-1) = 1×1×1×...×1 = 1
2.
g(x) = x^n, n is odd
g(1) = (1×1)×(1×1)×...(1×1)×1 = 1×1×1×...×1×1 = 1
g(-1) = (-1×-1)×...×(-1×-1)×-1 = 1×1×...×1×-1 = -1
Please Help! - Algebra
Zachary purchased a computer for $1,800 on a payment plan. Two months after he purchased the computer, his balance was $1,540. Three months after he purchased the computer, his balance was $1,410. What is an equation that models the balance y after x months?
Using an exponential decay equation, the function that models the balance is y = 1800(1 + 0.081)⁻ˣ at a rate of 8.1%
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
To solve this problem, we need to find the rate at which the payment is calculated on.
The general equation for an exponential decay is given as
A = P(1 + r)⁻ˣ
x = timer = rateSubstituting the values and solving for r
1540 = 1800(1 + r)⁻²
r = 0.081
r = 8.1%
Comparing the third month to ascertain values
1410 = 1800(1 + r)⁻³
r = 0.081
r = 8.1%
The rate which the payment is calculated is 8.1%
An exponential equation that models the balance after y months will be
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Given: < 2. Choose the solution set. {x | x < 10/11} {x | x > 10/11} {x | x > 22/5} {x | x < 22/5}.
The solution set is {x | x < [tex]\frac{22}{5}[/tex]}.of the given evaluation.
What is a Solution Set?
The solution set of an equation is, however defined as the set of all solutions that satisfy the equation and since that set has no members the solution set is empty.
Given: [tex]\frac{5x}{11}[/tex][tex]< 2[/tex]
= [tex]5x < 22[/tex]
= [tex]x < \frac{22}{5}[/tex]
Hence, the correct solution set is {x | x < [tex]\frac{22}{5}[/tex]}.
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Complete the equation so that it has the solution c=4
5(2c −
) =2(c+11)
Answer:
Step-by-step explanation:
c=45(2c−)=2(c+11)
We can't solve that type of equation or it may contain an error
is your problem in complete?
you have a box with a square base and no top. the surface area of the box is 220 ????????????????2. find the maximum volume.
The required maximum volume of the box would be 85184 cube units.
The surface area of a box is the total area of all of the box's faces. For a box with a square base and no top, the surface area is equal to the sum of the areas of the four sides and the bottom.
To find the maximum volume of such a box, we can first find the length of one side of the square base. We can do this by dividing the given surface area by the number of sides of the box.
In this case, the box has 4 sides plus the bottom, so the length of one side is 220 / 5 = 44.
We can now use the length of one side to find the maximum volume of the box. The volume of a box with a square base and no top is equal to the length of one side cubed.
The length of one side is 44, so the maximum volume of the box is :
⇒ 44 × 44 × 44 = 85184.
Therefore, the maximum volume of the box is 85184 cube units.
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this exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 5????/11 rad is 15 m2. find the radius of the circle. (round your answer to one decimal place.) 4.5 incorrect: your answer is incorrect. m
A 15 square metres sector will have a radius of 8.1 m and a central angle of 26.04 degrees.
What is sector?The region of a disk encompassed by two radii and an arc is called a circular sector, also known as a circle sector or disk sector. The smaller area is referred to as the minor sector, and the larger area as the major sector. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Here,
area of sector=θ/360°*πr²
θ=5/11*180/π
θ=26.04 degree
area=15 m²
15=26.04/360*3.14*r²
15=0.227r²
r²=66.08 m²
r=8.13 m
The radius of the sector whose area is 15 m² will be 8.1 m with the central angle of 26.04 degree.
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a child finds a stack of old magazines in the basement and picks one out at random. find the probability that the magazine is a sports magazine if the pile consists of 25 sports magazines, 11 news magazines, and 2 travel magazines. (round your answer to three decimal places.)
The probability of the magazine is a sports magazine is 0.065.
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to data in the given question,
We have the given information:
The number of sports magazines = 25
The number of news magazines = 11
The number of travel magazines = 2
Now, we will calculate the probability of the magazine is a sports magazine,
Total number of magazine = 25+11+2 = 38
To find the probability that the random selected magazine is a sports magazine divide the amount of sports magazines by the total amount of magazines:
P( sports magazine ) = Number of sports magazine/Total number of magazine
[tex]=\frac{25}{38}\\ =0.065[/tex]
Therefore, the required probability is 0.065.
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Select the correct answer from each drop-down menu. Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Average rate of change plotted on coordinate plane linear graph. A solid boundary line intersects X-axis at unit minus 2.5 and Y-axis at unit 5. The Y-value for x= minus 1 is 3 and for x= minus 4 is minus 3. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
The average rate of change of f(x) over the interval [-4, -1], with coordinates, (-4, -3) and (-1, 3) is 2
How can the average rate of a function over an interval be found?The average rate of change of a function over an interval is found from the change in the output values of the function over the period indicated, divided by the change in the input values of the function over the specified interval.
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex]
The interval over which the average rate of change of the function is required = [-4, -1]
The formula for the average rate of change over the interval, [-4, -1], can be presented as follows;
Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex] = [tex]\dfrac{f(-1) - f(-4)}{\left(-1 - (-4)\right)}[/tex]
The coordinates of the points of the graph of the function in the indicated range are; (-1, 3), and (-4, -3)
f(-1) = 3, f(-4) = -3, therefore;
Average rate of change = [tex]\dfrac{3 - (-3)}{-1 - (-4)}[/tex] = 2
The average rate of the function over the specified interval is 2
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how many ways are there to seat n couples around a circular table such that no couple sits next to each other?
2n(n−1)! ways n couples around a circular table such that no couple sits next to each other.
What is combination?
The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant."Combining these two words indicates "Selection of things," where the order of the items is irrelevant.Depends on how you consider two ways as different ways.
If the seats are in fixed positions, then there are two possible seatings as the couple can swap with each other. In this case, choose a seat as reference. Swapping is available in each couple or between couples, on seat 0 and 2N sit one couple or different couples. So the answer is 2n+1n!If you consider seats as all same, pick a couple as reference. Still, husband can sit either on clockwise of his wife or counterclockwise. The remaining n−1 couples can choose their seats at will. In this case the answer is 2n(n−1)! when n>1. When n=1 there’s only 1 since the relative position becomes unimportant in this case.In case you still feel confused, take 2 for example. We have plan AaBb, AabB, aABb and aAbB
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an instructor has given a short quiz consisting of two parts. for a randomly selected student, let and . suppose that the joint pmf of and is given in the accompanying table.
Random variable
a. E (X+ Y) = 14.10
E|(X – Y)| = 5.1
b. E[max(X ,Y )] = 9.60
E[min(x, y)] = 4.5
Conversely, once Y=y is observed, we would more likely be interested in the quantity E(X∣Y=y)=ρy which is a scalar.
Maybe this seems like needless complication, but regarding E(X∣Y) as a random variable in its own right is what makes things like the tower-law E(X)=E[E(X∣Y)] make sense - the thing on the inside of the braces is random, so we can ask what its expectation is, whereas there is nothing random about E(X∣Y=y).
a. E (X+ Y)
=∑∑( x +y)p(x ,y)
= (0+0)(0+2) + (0 + 5)(.06) + … + (10 + 15)(.01)
= 14.10
E|(X – Y)| = ∑∑ |x – y| p(x,y)
= |(0-0)|(0.02) + |(0-5)|(0.06) + ……+ |(10-15)|(0.01)
= 5.1
b.
E[max(X ,Y )] = ∑∑max(x+y).p (x ,y)
= (0)(.02) + (5)(.06) +…+(15)(.01)
= 9.60
E[min(x, y)] = ∑∑ min (x,y) p(x,y)
= 0(0.02) + 0(0.06) + ……+ 10(0.14) + 10(0.01)
= 4.5
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Triangle A'B'C' is a reflection of triangle ABC across line l. Select all statements that must be true.
A Line l bisects segment AB.
B Line l bisects segment CC’.
C Angle ABC is 60 degrees.
D Line BB’ is perpendicular to line l.
E Angle ABC is congruent to angle A’ B’ C’.
F Triangles ABC and A’ B’ C’ are congruent.
G Segment BC is congruent to segment B’ C’.
H The distance from point A to line l is the same as the distance from point A’ to line l.
Answer:
A, B, D, E, F, G, H
Step-by-step explanation:
If triangle A'B'C' is a reflection of triangle ABC across line l, the following statements must be true:
A. Line l bisects segment AB.
B. Line l bisects segment CC’.
D. Line BB’ is perpendicular to line l.
E. Angle ABC is congruent to angle A’ B’ C’.
F. Triangles ABC and A’ B’ C’ are congruent.
G. Segment BC is congruent to segment B’ C’.
H. The distance from point A to line l is the same as the distance from point A’ to line l.
Statements C and H are not necessarily true. The angle ABC may not be 60 degrees, and the distance from point A to line l may not be the same as the distance from point A’ to line l.