To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:
1) Each element of G belongs to some left coset of H.
2) Any two distinct left cosets of H are disjoint.
Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.
Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.
Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.
Solving for x,
x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.
Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.
Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.
This satisfies the second condition, and hence the left cosets of H constitute a partition of G.
A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.
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(PLEASE HELP! Im using a ton of points)
A new curved projection system for a small media room states the optimal viewing angle is
74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The
depth of the curved screen is 2 feet (length of DE = 2 ft). Find the length of line segment AB, in feet, that corresponds to the width of the television. (Round your answer to the nearest foot)
(Thx for any help!)
The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ 12 feet
We have to given that;
A new curved projection system for a small media room states the optimal viewing angle is 74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The depth of the curved screen is 2 feet (length of DE = 2 ft).
Now, We can formulate;
CE = 10 - 2 = 8 feet
∠ACD = 74/2 = 37°
Hence, We can formulate;
tan 37° = AE / CE
0.75 = AE / 8
AE = 0.75 × 8
AE = 6
Hence, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ AB = 6 x 2
⇒ AB = 12 feet
Thus, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,
⇒ 12 feet
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Question Content Area Tanning Company analyzes its receivables to estimate uncollectible accounts. The accounts receivable balance is $310,000 and credit sales are $1,000,000. An aging of accounts receivable estimates that $21,700 of the outstanding receivables will be uncollectible. What adjusting entry will Tanning Company make if Allowance for Doubtful Accounts has a credit balance of $2,200 before adjustment?
The adjusting entry that Tanning Company will make for Allowance for Doubtful Account will be:
Debit: Bad Debt Expense $21,500Credit: Allowance for Doubtful Accounts $21,500How will Tanning Company adjust the allowance?Data:
Total credit sales = $1,000,000
Accounts receivable balance = $310,000
Estimated uncollectible receivables = $21,700
The adjusted balance for allowance for doubtful accounts will be:
= Credit balance + Estimated uncollectible receivables
= $2,200 + $21,700
= $23,900
So, the Company will make an adjusting entry by debiting Bad Debt Expense for $21,500 and crediting Allowance for Doubtful Accounts for $21,500 which will increase the balance of the allowance for doubtful accounts to $23,900.
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Less than 53% of adults would erase all of their personal information online if they could . The hypothesis test results in a p-value of 0.0059
A conclusion on the null hypothesis is C. Reject H_{0} because the P-value is less than or equal to a.
What should happen to the null hypothesis ?Stated in the initial description is the null hypothesis, establishing that adults who possess a desire to eliminate all personal information available online would equate to or exceed 53%, while the alternative conjecture rests on this percentage being under 53%.
The statistical significance level at hand designated as alpha equals 0.05 indicates that a P-Value having less than or equal value of 0.05 is necessary for declining the null hypothesis. As provided by the task's question, the computed P-value registers a score of 0.0059 which falls below the established significance level of 0.50 and thus resulting in null hypothesis rejection.
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A store manager kept track of the number of newspaper sold each week over a seven week period.the result were as fellows 71,81,202,113,269,248,242
The median number of newspapers sold is 202 newspaper. So, correct option is C.
To find the median, we need to arrange the given data in ascending or descending order.
The given data in ascending order: 71, 81, 113, 202, 242, 248, 269
Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.
Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.
The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.
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Complete question is:
A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242
Find the median number of newspapers sold.
A. 175 newspapers
B. 113 newspapers
C. 202 newspapers
D. 242 newspapers
If the given expression is multiplied by 36
, which expression is NOT equivalent?
Responses
A (32
)(38
)( 3 2 )( 3 8 )
B 910
9 10
C 310
3 10
D (35
)(35
)
Answer:
The correct answer is (C) 310.
Multiplying the given expression by 36 gives:
(32)(38) + (35)(35) - (33)(37)
= 1216 + 1225 - 1221
= 1220
So the equivalent expression is 1220.
Option (C) 310 is not equivalent to 1220.
Madam Antiowwah at oseikakookrom charged her phone to full (100%). She browse two hours. The battery life fell to 60% How many hours later would the phone or She continues to browse?
Answer:
Phone dies in 6 hours
Step-by-step explanation:
Someone help i really need help with this
The percentage increase in the number of water bottles from February to April is 19%.
How to find the percentage increase?A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.
Therefore,
February: 4100 water bottles
March: 7% more water bottles than in February
April: 500 more water bottles than in march
Therefore,
Number of water bottles in march = 4100 + 7% of 4100
Number of water bottles in march =4100 + 7 / 100 × 4100
Number of water bottles in march = 4100 + 287
Number of water bottles in march = 4387
Hence,
Number of water bottles manufactured in April = 4387 + 500 = 4887
Therefore,
percentage increase from February to April = 4887 - 4100 / 4100 × 100
percentage increase from February to April = 787 / 4100 × 100
percentage increase from February to April = 78700 / 4100
percentage increase from February to April = 19.1951219512
percentage increase from February to April = 19%
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State whether the decay is linear or exponential, and answer the associated question.
The value of a car is decreasing by 12% per year. If the car is worth $9,000 today, what will it be worth in two years?
_________________________________
= 12 × 9,000 ÷ 100= 1,080= 1,080 × 2= 2,160= 9,000 - 2,160= $6,840The Car Will Be Worth $6,840 After 2 Years_________________________________
Answer:
$6,840
Step-by-step explanation:
HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answer:
No I don't. The editor will receive 360 undelivered mail.
Step-by-step explanation:
He sends 12000 emails, 3/100 of them come back undelivered.
Multiply to find the answer:
12000 x 3/100 = 36000/100 = 360
Simple as that; the editor will find that 360 of his sent emails will come back undelivered.
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment, and they have an average credit score. How much is the PRINCIPAL BALANCE after applying their first month’s payment of $925.67?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
A. $89,249.80
B. $88,245.05
C. $88,912.03
D. $89,021.98
Need answer asap. Thank you for helping me.
The estimate of the cost for a 20-ft cord is given as follows:
$74.66.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points in the context of the problem are given as follows:
(3, 12.75), (5, 16), (6, 25.99), (50, 185).
Inserting these points into a calculator, the regression equation is given as follows:
y = 3.6794x + 1.06462.
Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:
y = 3.6794(20) + 1.06462
y = $74.66.
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What is the circumference of the circle in terms of pi? (C = td) О Тл О 147 О 21л * 28 л
The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.
A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.
To get a circle's circumference, use the following formula:
C = 2πr
where;
r = radius of the circle
π = mathematical constant pi (approximately equal to 3.14).
Given the radius of the circle as 10 cm, we can use the formula to find its circumference:
C = 2πr
C = 2π(10 cm)
C = 20π cm
Hence, option C is correct.
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The correct question is:
What is the circumference of the circle with radius = 10 cm (leave your answer of π).
A) 10π cm
B) 5π cm
C) 20π cm
D) 10π cm
Carmen invested $2,000 in a mutual fund that is front-loaded, with a loading rate of 4.75 %. What was the
loading charge of this fund? (3 points)
Answer:
$95
Step-by-step explanation:
Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.
2. Triangle ABC with A(2, 3), B(7, -1), and C(-4, 2) is reflected across the line x = -2. Find the
coordinates of B'
Answer:
B’ = (-11, 1)
Step-by-step explanation:
Because the triangle is reflected across the line x = -2, it is being reflected across a vertical line.
Therefore only the x-coordinate will change.
As B is 9 units right of the line x = 2, the coordinates of B’ will be (-2 - 9, 1)
Which will be (-11, 1)
Elaina is trying to fit the longest stick she can into her pet lizard’s tank. She knows running it diagonally from the front corner to the back will give her the most room but she is uncertain what size she should buy. What is the biggest length stick that will fit into her 12 by 8 by 8 tank?
The biggest length stick that will fit is 16.49 units long.
What is the biggest length stick for the tank?The length stick which will fit into Elaina's 12* 8*8 tank can be found using the Pythagorean theorem.
The diagonal length, of tank will be equal to square root of the sum of the squares of its length, width and height.
So, the diagonal length of the tank, using Pythagorean theorem, is
= √(12² + 8² + 8²)
= √(144 + 64 + 64)
= √272
≈ 16.49.
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Can you help me with this
Answer:
[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]
Step-by-step explanation:
The square is 1 unit long and 1 unit wide
There are 3 smaller rectangles in the horizontal direction
Length of each rectangle is therefore 1/3 unit
There are 6 rectangles along the vertical direction
The height of each rectangle is therefore 1/6 unit
The shaded area is 2 rectangles wide and 3 rectangles in height
Width of shaded area = 2 x 1/3 = 2/3
Height of shaded region = 3 x 1/6 = 1/2
Area of shaded rectangle is
[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]
Help please quickly calculus
Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
Base of b = y.Height of h.Hence the formula is:
A = 0.5yh.
Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.
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help with this question
Question 2 (1 point)
Thomas's football team lost 3 yards in their first drive while Derrek's
football team gained 5 yards in their first drive. The first drives for each
team can be compared on a number line, where 0 represents the line
of scrimmage for each play.
Select the correct numbers for Derrek and Thomas' football teams.
Oa Derrek's Team has-5
Ob Thomas' Team has +3
OcThomas' Team has -3
Od Derrek's Team has +5
The correct numbers for Derrek and Thomas' football teams are :
c. Thomas' Team has -3d. Derrek's Team has +5How to find the numbers ?According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.
On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.
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Category: nr percentages
question_id: 5782
Alex is really upset. He invested a lot of money in shares and only has $72,800 left of his original
investment. His shares dropped in value by 35% in 4 days. What amount did Alex pay for his shares
to being with?
Answer:
Let's start by using algebra to solve for the original amount that Alex paid for his shares.
Let X be the original amount that Alex paid for his shares.
We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:
0.65X = $72,800
Solving for X:
X = $72,800 / 0.65
X = $112,000
Therefore, Alex paid $112,000 for his shares to begin with.
pleaseeeee helpppppp
Which of the following are necessary when proving that the opposite angles
of a parallelogram are congruent? Check all that apply.
A. Corresponding parts of similar triangles are similar.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Opposite sides are congruent.
SUBMIT
Answer:
B. CPCTC
D. opposite sides are congruent
Step-by-step explanation:
You want to know the necessary claims for proving opposite angles are congruent in a parallelogram.
ProofGiven parallelogram ABCD and diagonal AC, you can prove opposite angles congruent in this way:
AB≅CD and BC≅DA . . . . . opposite sides are congruent
AC≅CA . . . . . . . . . . . . . . reflexive property of congruence
∆ABC≅∆CDA . . . . . . . . . . . SSS congruence
∠B ≅ ∠D . . . . . . . . . . . . Corresponding parts of congruent triangles
When doing the proof, the necessary claims are ...
B. Corresponding parts of congruent triangles are congruent
D. Opposite sides are congruent.
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A new car sells for 25000 the value of the car decreases by 15% each year what is the approximate value of the car 5 years
The answer is $11,092.63.
This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.
After 1st year:
$25,000 : 100% = x1 : 85%
x1 = $25,000 · 85% ÷ 100%
x1 = $21,250
After 2nd year:
$21,250 : 100% = x2 : 85%
x2 = $21,250 · 85% ÷ 100%
x2 = $18,062.5
After 3rd year:
$18,062.5 : 100% = x3 : 85%
x3 = $18,062.5 · 85% ÷ 100%
x3 = $15,353.12
After 4th year:
$15,353.12 : 100% = x4 : 85%
x4 = $15,353.12 · 85% ÷ 100%
x4 = $13,050.15
After 5th year:
$13,050.15 : 100% = x5 : 85%
x5 = $13,050.15 · 85% ÷ 100%
x5 = $11,092.63
Therefore, the value of the car 5 years after it is purchased is $11,092.63.
Is this a parallelogram and why?
Answer:
Yes, it's a parallelogram bcz the opposite sides are parallel and equal.
Can someone help me with my accounting assignment please?
The State Cash Flow Statement using the direct method.
OP INV FIN
Personnel emolument 2,000,000
CRF charges 1,000,000
Statutory revenue allocation 20,000,000
Proceeds from sale of fixed assets 100,000
Purchase of marketable securities 50,000
Purchase & construction of fixed assets 500,000
Share of VAT 200,000
Share of excess crude oil 100,000
Internally generated revenue 10,000,000
Gratuities and pension 15,000,000
Miscellaneous income 50,000
Overhead expenses 36,000
Recurrent grant made 20,000
Miscellaneous expenses 10,000
Servicing & repayment of public debts 100,000
Grants & subventions from NGO 200,000
Proceeds from loan & other borrowings 300,000
Dividends received 100,000
12,234,000 -450,000 500,000
Net Cash Flow for the year ended 31 December 2006: 12,284,000
How was the cash Flow Statement using the direct method solved?To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.
Operating Activities:
(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000
Investing Activities:
(100,000 - 50,000 - 500,000) = -450,000
Financing Activities:
(-100,000 + 200,000 + 300,000 + 100,000) = 500,000
Net Cash Flow for the year ended 31 December 2006:
12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000
The above answer is in response to the question below;
The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:
Personnel emolument 2,000,000
CRF charges 1,000,000
Statutory revenue allocation 20,000,000
Proceeds from sale of fixed assets 100,000
Purchase of marketable securities 50,000
Purchase & construction of fixed assets 500,000
Share of VAT 200,000
Share of excess crude oil 100,000
Internally generated revenue 10,000,000
Gratuities and pension 15,000,000
Miscellaneous income 50,000
Overhead expenses 36,000
Recurrent grant made 20,000
Miscellaneous expenses 10,000
Servicing & repayment of public debts 100,000
Grants & subventions from NGO 200,000
Proceeds from loan & other borrowings 300,000
Dividends received 100,000
You are required to:
Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)
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find the diameter of a circle whose circumference is 44cm
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:
2,14,1,2,−6
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
What is Critical value ?
In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.
To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.
Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.
Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
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PLEASE HELP I NEED TO PASS THIS Using the probability distribution represented by the graph
below, find the probability that the random variable, X, falls
in the shaded region.
Answer: C: 5/8
Step-by-step explanation:
Simply 5/8 of the bar is filled in
Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.
Here, we have,
Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.
Positive Outcomes/Total Results = x/n = Probability(Event)
Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.
Here in the question,
Total region = 8.
Shaded region = 5
So, probability of falling in the shaded region = 5/8
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What is equivalent to x^2-5x+6
Answer:
[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]
Step-by-step explanation:
Given:
[tex]x^2-5x\:+6[/tex]
To find:
Equivalent to x^2-5x+6
Explanation:
[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]
Final Answer:
(x-2)(x-3)
The whole page tysmmmm plsss step by step explanation
Answer:
Step 1:
a.) 16 pets in total (1 + 0 + 2 + 0 + 3 + 8 + 0 + 2)
b.) the mean is 2 (16 is the total number of pets, divide that by 8 which is the total number of students asked, 16/8 = 2)
Step 2:
a.) 0, 0, 0, 1, 2, 2, 3, 8 (zero, one, two, three, four, five, six, seven, eight.)
b.) 0 and 3 are the middle numbers (center.)
c.) 3/2 = 1.5 (0+3 = 3 divided by 2 = 1.5)
Step 3:
- most of the students did not have any pets, so the mode would be 0 (it is zero because zero appears in the set of numbers 3 times. More than any other number).
Step 4:
They should use the mean of the amount of pets the students have; this is because the mean is the average amount of pets counting everyone in class—regardless on if there were zeros in the list.
