The finite subgroups of C*, the group of non-zero complex numbers under multiplication, are isomorphic to either the cyclic groups of order n or the dihedral groups of order 2n, where n is a positive integer.
A finite subgroup of C* is a group H consisting of finitely many complex numbers such that H is closed under multiplication, contains the identity element 1, and each element of H has an inverse in H. Since C* is an abelian group, any finite subgroup of C* is also abelian. By the fundamental theorem of finite abelian groups, any finite abelian group can be expressed as a direct sum of cyclic groups of prime power order.
Since the elements of C* can be written in polar form as z = re^(iθ), where r is the magnitude of z and θ is the argument of z, any finite subgroup of C* can be expressed as a collection of complex numbers of the form e^(2πki/n), where k and n are positive integers. It follows that any finite subgroup of C* is isomorphic to either the cyclic group of order n or the dihedral group of order 2n, where n is a positive integer. The cyclic group of order n consists of the n-th roots of unity, while the dihedral group of order 2n consists of the 2n-th roots of unity together with reflections.
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find x and the measure of each side. Round to two decimal places, if necessary.
The values of the triangles are as follows:
x = 7 unitsGH = 21 unitsHI = 21 unitsGI = 12 unitsHow to find angles and side of a triangle?The triangle is an isosceles triangle because two sides and angles are equal. Therefore,
4x - 7 = 2x + 7
4x - 2x = 7 + 7
2x = 14
x = 14 / 2
x = 7 units
GH = 4(7) - 7 = 28 - 7 = 21
HI = 2(7) + 7 = 14 + 7 = 21
GI = 7 + 5 = 12
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For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.
(fog)(x) =
Domain of fog:
Find fog
fog(x)f(g(x))f(√x-5)2√(x-5)+3For real range the domain
x-5≥0x≥5Domain is [5,oo)
Choose the equation that satisfies the data in the table.
Answer:
Option A.
Step-by-step explanation:
Demonstration
[tex]y=\frac{7}{4} x+7[/tex]
for x = -4
[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]
for x= 0
[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]
for x= 4
[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]
Hope this helps
Stronger evidence against the null hypothesis is indicated by: Group of answer choices lower levels of significance. smaller p-values. lower probabilities for the power of the test. smaller critical values.
Stronger evidence against the null hypothesis is indicated by: smaller p-values.
What is null hypothesis?A statistical conjecture known as a null hypothesis asserts that certain features of a population or data-generating process are not different from one another.
A mechanism to reject the null hypothesis with a predetermined level of confidence is provided by hypothesis testing.
The alternative hypothesis is supported if the null hypothesis can be rejected.
The foundation of the scientific falsification principle is null hypothesis testing. The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.
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Bens barbershop has a rectangular logo for their business that measures 7 1/5 feet long with an area that is exactly the maximum area allowed by the building owner. create an equation that could be used to determine m, the unknown side length of the logo.
A = 7M is the equation that might be used to find the unknown side length, M, of the rectangular logo.
Expression steps of the equationWe can determine the following details from the query:
Logo= rectangle with a
Length ,L= 7-foot
'A' stands for the logo's area, and 'M' for the side that isn't recognized.
The rectangle's area (A) is computed using:
A = L*W
⇒A = 7*M
(As per query, length, L=7 & W= M)
Consequently, the formula 'A = 7M' might be used to calculate the logo's undetermined side length, M.
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Suppose a random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random sample of Coldplay ticket prices was obtained. True or False: The two groups of data are independent samples.
A random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.
According to the questions,
A random samples of ticket prices for concerts by the Rolling Stones was obtained. For comparison purposes another random samples of Coldplay ticket prices was obtained.
The two groups of data are independent samples.
Hence, a random samples of ticket prices for concerts and the random samples of Coldplay ticket prices are independent . The answer is True.
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If WX= 82 cm, find the length of YZ. (OV = 9cm and OV is perpendicular to YZ)
The length of the measure of YZ is 80cm
Perpendicular linesPerpendicular lines are lines that are at angle 90 degrees to each other. From the given diagram;
WX = 82cm
Required
Length. of YZ
Using the pythagoras theorem
YV = VZ = √41²-9²
YV = VZ = √1600
YV = VZ = 40
Since YZ = YV + VZ
YZ = 40cm + 40cm
YZ= 80cm
Hence the length of the measure of YZ is 80cm
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Supergran runs from her chalet to the top of the mountain. She knows that if she runs at a speed of 6 mph she will arrive at 1 pm, whereas if she leaves at the same time and runs at 10 mph, she will arrive at 11 am. At what speed should she walk if she wants to arrive at 12 noon
Using proportions, it is found that she should walk at a speed of 8 mph to arrive at noon.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, considering the speeds of arrival at 11 am and at 1 pm, we have that for each 2 km slower, she arrives one hour later.
Walking at 10 mph she arrives at 11 am, hence she should walk at a speed of 8 mph to arrive at noon.
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Which of the following expressions has a product of 36?
A. (-3)(12)
B. (-6)(-6)
C. 2(-18)
D. 4 · 8
Answer:
B. (-6)(-6)
Step-by-step explanation:
- X - = +
and 6 x 6 = 36.
a total of $7000 is invested: part at 6% and the remainder at 10%. How much is invested at each rate if the annual interest is $470?
Answer:
680
Step-by-step explanation:
two hundred twenty five students play a team sport at lincoln high school these students represent 3/8 of the total
The total number of students in the school is calculated as; 600 students
How to find fraction of a total?Usually, some figures are expressed as a fraction of a whole as depicted in this case. Thus, when we are given a fraction of a whole to be equal to a particular figure, we will just cross multiply to get the total number.
We are told that;
Number of students that play a team sport at Lincoln high school = 225
Now, we are told that the number above represents a fraction of 3/8 of the total students in that school.
Thus, if the total number of students in the school is x, then we can say that;
(3/8)x = 225
Multiply both sides by 8 to get;
3x = 1800
x = 1800/3
x = 600 students
Thus, we can conclude that if two hundred and twenty five students play a team sport at Lincoln high school and these students represent 3/8 of the total, then we can say that the total number of students in the school is 600 students.
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You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why
Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
According to the statement
we have a given that the surgical unit that receives 87 new patients per week.
and we have to tell the data plan to collect the baseline data before testing your change to control the pain across the unit.
And We know that the Data collection is A representative sample is one technique that can be used for obtaining insights and observations about a targeted population group
So,
Collecting data on a representative portion of your population — that is, sampling — allows you to collect baseline data and start making improvements faster, using fewer resources, than would be possible if you tried to look at every patient. Baseline data is important so that you can see if the changes you are testing are leading to improvement. Collecting data about a non representative sample of your population, such as by looking only at patients with the most severe pain, won't show the broad impact of your project on your unit.
So, Collect data on a representative selection of patients for two weeks.
is the best data collection plan for this project.
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Disclaimer: This question is incomplete. Please read the full content below.
Question:
You work on a surgical unit that receives 87 new patients per week. In your spare time, you are trying to improve pain control across the unit. As you prepare to collect your baseline data before testing your change, you consider your plan to gather this information. Which of the following would be the best data collection plan for this project, and why?
(A) Collect data on the pain level of every patient for at least a year.
(B) Collect data for at least a year, focusing only on patients who have undergone especially painful surgeries.
(C) Collect data on a representative selection of patients for two weeks.
(D) There is no reason to collect baseline data.
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Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
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If a circle has a radius of 4 meters, what is its circumference?
Answer: 12.56
Step-by-step explanation:
4 x 3.14
pi = 3.14
The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!! show all work
a. The median is 70, the mode is 60, and the mean is 70.8.
b. Mean best captures the data.
c. When there are outliers, the mean might be a deceptive center measure.
Calculating the Mean, Median, and Mode
Mean: Total number of sunglasses / total quantity of pries
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median is equal to the (n/2 + 1)th term.
The number of sunglasses in this case is n.
(25/2 + 1)th term as the median
Median = 13th term
Median is 70
Mode is the most frequent data
Therefore, mode = 70
Why is mean the most appropriate central measure ?
The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.
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Answer:
Step-by-step explanation:
Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job. Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5
One landscaper's hourly rate is $15 lower than the other landscaper's. Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.
What is system of linear equations?
A set of two linear equations with two variables is a system of linear equations. Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly rate. A set of linear equations was appropriately written and solved by Casey using substitution. He solved for the other variable and substituted an expression for one in his work. The intersection of the lines that represent the linear equations is where a system of linear equations finds its solution. Each landscaper bills a fee for each job in addition to an hourly cost. Casey produced a system of linear equations that was correctly written and solved. The hourly rates for both landscapers are the same, however their rates for individual jobs vary.
Casey is deciding between hiring one of two landscapers. Each landscaper bills a fee for each job in addition to an hourly cost. By using substitution, Casey created and properly figured out a set of linear equations. He solved for the other variable and replaced an expression for one in his work, producing the equation 5 = 20.
equation 5=20
20-5 = 15
Therefore, One landscaper's hourly rate is $15 lower than the other landscaper's.
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The following two-way table describes student's
after school activities. find the probability that a
randomly selected student either does sports or
works.
grade
sports
music/drama
work
20
7
sophomore
3
junior
20
13
2
25
5
senior
5
p(sports u work) = [?]
round to the nearest hundredth.
lol
P ( work/ senior ) = 0.14
The attached table
required
P ( work/ senior )
This is calculated using:
P ( work/ senior ) = n ( work/ senior )/ n ( senior ).
n ( work/ senior ) = 5
n ( senior ) = 25 + 5 + = 35
So:
P ( work/ senior ) = 5/35
P ( work/ senior ) = 0.14
Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
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Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?
A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers. The whiskers represents the minimum and maximum scores.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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What is the common ratio of the geometric sequence below?
10, 15, 22.5, 33.75, ...
A. 2/3
B. 1.5
C. 5
D. 7
The common ratio of the geometric sequence is 1.5
Common ratio can be described as difference between two numbers in a sequence.
The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term
= 15/10
= 1.5
Hence the common ratio of the sequence is 1.5
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Answer:
B
Step-by-step explanation:
The common ratio of the geometric sequence is 1.5
Common ratio can be described as difference between two numbers in a sequence.
The first term of the sequence is 10 and the second term is 15, the common ratio can be calculated by dividing the first term by the second term
= 15/10
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1.5
help me pls
if you write a wrong answer you will be reported by the app.
The complete proof of the theorem is
Statements Reasons
1. p||q 1. Given
2. ∠1≅∠3 2. Alternate interior angles theorem
3. ∠1≅∠3 3. Definition of congruent angles
4. ∠3 + ∠2 ≅ 180° 4. Definition of linear pair
5. m∠3 + m∠2 = 180° 5. Linear pair theorem
6. m∠1 + m∠2 = 180° 6. Substitution prop. of equality
7. ∠1 and ∠2 are supplementary 7. Consecutive interior angles theorem
Proof of Angle theoremsFrom the question, we are to complete the given proof
The proof is completed as shown below
Statements Reasons
1. p||q 1. Given
2. ∠1≅∠3 2. Alternate interior angles theorem
3. ∠1≅∠3 3. Definition of congruent angles
4. ∠3 + ∠2 ≅ 180° 4. Definition of linear pair
5. m∠3 + m∠2 = 180° 5. Linear pair theorem
6. m∠1 + m∠2 = 180° 6. Substitution prop. of equality
7. ∠1 and ∠2 are supplementary 7. Consecutive interior angles theorem
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Chantelle has 56 stickers. she will give all of the stickers to 8 friends. each friend will receive the same number of stickers. which equation will help chantelle decide how many stickers, n, to give to each friend?
Chantelle can use the following equation,
n = (Number of stickers) / (Number of friends)
or n = 56/8
Given Information
Chantelle has 56 stickers
⇒ Number of stickers = 56
She will distribute all of the stickers to 8 friends
⇒ Number of friends = 8
The number of stickers each friend will get = n
We have to form an equation for n.
Forming the Equation
Equation for the number of stickers to be given to each friend is as follows,
n = (Number of stickers) / (Number of friends)
n = 56/8
n = 7
Therefore, Chantelle needs to give 7 stickers to each of her 8 friends. And, the equation used to find this count, n is n = (Number of stickers) / (Number of friends) or n =56/8
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please answer both asap!!!
How do I put the pairs for the values in the domain
Answer:
Step-by-step explanation: use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
Which geometric shape could be used to model the building?
cylinder
pyramid
cone
rectangular prism
Answer:
Rectangular Prism
Step-by-step explanation:
We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.
Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. x + y = 6 x - y = 0
The solution of the system of equations contains one point
How to determine the number of solutions?The system is given as:
x + y = 6
x - y = 0
Add both equations
2x = 6
Divide by 2
x = 3
Substitute x = 3 in x - y = 0
3 - y = 0
Solve for y
y = 3
So, we have x =3 and y = 3
Hence, the solution of the system of equations contains one point
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Select the correct answer. Find the solution(s) for x in the equation below. x^2 -25 =0
Answer:
Step-by-step explanation:
Find the roots of x^2-25=0 by solving for x.
Add 25 to both sides
x^2=25
Square root both sides
x=-5
x=5
Answer:
x=5;x=-5
Step-by-step explanation:
It was right for me
find the slope of the line on the graph write your answer as a fraction or a whole number
Answer:
-3/2
Step-by-step explanation:
Slope=rise/run
Pick any 2 points and you can see that for every increase in 2 increases for x, there are 3 decreases for y.
26. Aluminum bronze consists of copper and aluminum, usually in the ratio of 10:1 by weight. If a machine made of this alloy weighs 66 pounds, how many pounds of aluminum does it contain? (A) 660 (B) 60 (C) 6.6 (D) 6
Answer:
(D). 6.
Step-by-step explanation:
The number of parts = 1 + 10 = 11.
So 10/11 of the alloy is copper and 1/11 is aluminium.
So the answer is 1/11 * 66
= 66/11= 6 pound,s
Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.
How can the distance between Vic and Dan be calculated?Location of Vic relative to the tower = South
Vic's sight angle of elevation to the top of the tower = 61°
Dan's location with respect to the tower = West
Dan's angle of elevation in order to see the top of the tower = 72°
Height of the tower = 553.3m
[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]
[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]
[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]
Vic's distance from the tower ≈ 306.7 mSimilarly, we have;
[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]
Dan's distance from the tower ≈ 179.8 mGiven that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;
d = √(306.7² + 179.8²) ≈ 356Therefore;
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Please HELP!!!!
will give brainliest!!
Answer:
Original equation:
y = a sin(b(θ -c)) + d
a = vertical dilation (stretch) of the amplitude
b = horizontal compression (shrink) of the period
c = horizontal shift (left/right)
d = vertical shift (up/down)
Your function is:
y = 3 sin(3θ + π) - 2
First, put it into the general from by factoring out the three in the argument of the sine:
y = 3 sin(3(θ + π/3)) - 2
a = vertical (amplitude) dilation = 3
b = horizontal (period) compression = 2π/period = 3
c = horizontal shift = π/3 to the left
d = vertical shift = -2