The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.
Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.
Proof: We have to prove (g/n)/(m/n) ≅ g/m (1)
g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.
To describe the isomorphism from the left side to the right side
φ: g/n \to g/m
ψ(gn) = gm
So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.
The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.
Also, the map is surjective because any coset gm is present as the image of gn under ψ.
Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem
(g/n)/(m/n)≅g/m where ≅ shows isomorphism
another problem to prove whether f is an isomorphism:
brainly.com/question/19865639
#SPJ4
13+14=3×f;f=9 helppp
Answer: 3x=13+14
3x=27
x=27/3
x=9
Step-by-step explanation: Maybe.
According to the rules of significant figures 7.898 + 5.23 = 13.13. This is because the least precise value in the problem is 5.23, which is precise only to the hundredths digit, so the answer must also be rounded to the nearest hundredths.True or False
The given expression is
[tex]7.898+5.23=13.13[/tex]It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.
In other words, the answers can't be more precise than the least precise number in the sum.
Therefore, the given statement is true.
Whats the Point-Slope Equation for the line that goes through
(-3, 5) and (-7, 4)
If the cost of an 800 number is $29.95 per month plus 28 cents per minute, then the monthly cost varies directly as the number of minutes.TrueFalse
We have the monthly cost is fixed: $29.95.
The cost varies directly as the number of minutes since the total cost per month will be:
[tex]29.95+\frac{28}{100}x[/tex]If we make a call and spend 30 minutes. We need to add this cost to the payment:
[tex]undefined[/tex]describe the transformation of f represented by G then graph each function
Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Transformation 2: the function is shifted 2 units up
Explanation
[tex]f(x)=x^4[/tex]Step 1
the first transformation is the function multiplied by a constant ( 1/2)
If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction
so
[tex]\begin{gathered} f(x)=x^4\Rightarrow\frac{1}{2}x^4 \\ \frac{1}{2}is\text{ smaller than 1, so} \end{gathered}[/tex]Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Step 2
the second transformation is add 5
[tex]f(x)=x^4\Rightarrow\frac{1}{2}x^4\Rightarrow g(x)=\frac{1}{2}x^4+5[/tex]If a positive number is added, the function shifts up the y-axis by the amount added.
so,
Transformation 2: the function is shifted 2 units up
I hope this helps you
2 Four friends go to the ice cream shop to purchase frozen
yogurt. Each friend gets a part strawberry and part
vanilla.
• Lucas gets 0.25 strawberry.
Adrianna gets % strawberry.
Ricardo gets 0.8 strawberry.
Jasmine gets % strawberry.
•
•
Arrange the friends in order from least to greatest amount of
strawberry in their yogurt.
Least
Greatest
Answer:
12
Step-by-step explanation:
Use the figure to find the measures of the numbered angles. The problem number 2. I’m just trying to make sure I’m doing these correctly.
Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,
[tex]m\angle2=34\degree[/tex]Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,
[tex]m\angle6=34\degree[/tex]Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,
[tex]m\angle4=34\degree[/tex]Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle7+34\degree=180\degree \\ m\angle7=180\degree-34\degree \\ m\angle7=146\degree \end{gathered}[/tex]Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,
[tex]\begin{gathered} m\angle4+m\angle3=180\degree \\ 34\degree+m\angle3=180\degree \\ m\angle3=180\degree-34\degree \\ m\angle3=146\degree \end{gathered}[/tex]Angles 7 and 5 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle5=m\angle7 \\ m\angle5=146\degree \end{gathered}[/tex]Angles 1 and 3 are vertical angles, then they are congruent, that is,
[tex]\begin{gathered} m\angle1=m\angle3 \\ m\angle1=146\degree \end{gathered}[/tex]
A basket contains 12 black marbles and 8 blue marbles. What is the probability Josiah will
select a blue marble, replace it, and then a black marble? Express your answer as a percent.
Answer:
24%=====================
GivenBlack marbles = 12,Blue marbles = 8.SolutionTotal number of marbles:
12 + 8 = 20Probability of selecting a blue marble:
P(blue) = number of blue / total = 8/20 = 2/5Probability of selecting a black marble after replacing the blue:
P(black) = number of black / total = 12/20 = 3/5Probability of selecting blue and black marbles in same order with replacement:
P(blue, then black) = 2/5*3/5 = 6/25 = 24/100 = 24%The sum of 4 consecutive integers is 170. What is the largest number in the group?
The largest number when the sum of 4 consecutive integers is 170 will be 44.
According to the question,
We have the following information:
Sum of four consecutive integers = 170
Now, let's take the first integer to be x.
So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.
Now, the largest number will be (x+3).
Adding 4 consecutive integers:
x+ (x+1) + (x+2) + (x+3) = 170
4x+6 = 170
4x = 170-6 (Moving 6 from the left hand side to the right hand will result in the change of the sign from plus to minus.)
4x = 164
x = 164/4
x = 41
So, the next three consecutive integers will be 42, 43 and 44.
Hence, the largest of the four consecutive integers is 44.
To know more about consecutive integers here
https://brainly.com/question/1767889
#SPJ1
ASAP please Hurry
The number of issues of books from a library are given for the years 2001–2011. The numbers are in hundreds of thousands.
Answer:
See attached graph.
Step-by-step explanation:
Use DESMOS graphing software. Free.
Which of the binomials below is a factor of this expression?
25x^2-4y^2z^2
answer- 5x-2yz
The binomials 5x-2yz are a factor of this expression
25x^2-4y^2z^2
This is further explained below.
What are binomials?Generally, A binomial is a kind of polynomial that is used in algebra and is defined as the sum of two terms, each of which is a monomial.
After monomials, this is the sort of sparse polynomial that is the easiest to understand.
The word "binomial" refers to an algebraic expression that consists of just two different terms. This is a polynomial with two terms.
25 x^2-4 y^2 z^2
Rewrite 25 x^2 as (5 x)^2.
(5 x)^2-4 y^2 z^2
Rewrite 4 y^2 z^2 as (2 y z)^2.
(5 x)^2-(2 y z)^2
Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=(a+b)(a-b) where a=5 x and b=2 y z.
(5 x+2 y z)(5 x-(2 y z))
Simplify.
(5 x+2 y z)(5 x-2 y z)
Read more about binomials
https://brainly.com/question/13870395
#SPJ1
Which integer is the farthest from the origin on a number line? A. -11 O B.-1 Oc. O D. 10
In order to determine the farthest integer related to the origin ona a number line, apply the absolute value of the given numbers, this gives you the distance of the specific number to the origin.
The absolute value of a number, negative or positive, is always equal to the same positive number.
Then,for the given asnwer choices you have:
|-11| = 11 where the bars |-11| expresses absolute
The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are less than 250 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places
For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.
The average total number of shoppers on a grocery store in 1 day is 506; the standard deviation is 115.
The number of shoppers is normally distributed.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 506 and standard deviation of 115.
Then, we can say that,
Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P(X<200)
[tex]=P(Z < \frac{200-506}{115})[/tex]
=P(Z<-2.66)
Where, Z is the standard normal variate.
ρ = -0.266
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.0039
For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.
To learn more about probability visit:
https://brainly.com/question/11234923
#SPJ1
The graph of a figure is shown below.
Which graph represents the reflection of this figure across the x-axis?
the first triangle in the photo
which is reflected on the x-axis
A graph which represents the reflection of this figure across the x-axis is: graph 5.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y) = (3, 1) → (3, -1).
(x, y) → (x, -y) = (4, 0) → (4, 0).
(x, y) → (x, -y) = (3, -1) → (3, 1).
(x, y) → (x, -y) = (4, -2) → (4, 2).
(x, y) → (x, -y) = (2, -4) → (2, 4).
(x, y) → (x, -y) = (0, -2) → (0, 2).
In conclusion, a reflection across the x-axis would transform the geometric figure to that shown in the graph attached in the image below.
Read more on reflection here: brainly.com/question/20602330
#SPJ1
2. What is the equation of a line that passes through the points (-0.92, 2.49) and (-5.62, 9.76)? Write your answer in point-slope form.
Answer:
Step-by-step explanation:
-0.92 2.49
-5.62 9.76
Rise = 9.76 - 2,49 = 7.27
Run: -5.62 - (-0.92) = -4.7
Slope (Rise/Run) = (7.27.`-0.92) = -1.55
The line has the form:
y = 1.55x + b
We need to find a value of b that forces the line through both point, Use one of the points and solve for b. I'll use (-0.92, 2.49).
y = 1.55x + b
2.49 = 1.55(-0.92) + b
b = 2.49 - 1.426 = 1.064
The equation is y = 1.55x + 1.0
Provide an example and explain the steps to convert a fraction into a percent.
what is the size of the angle between south and south east
The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.
Please Help Please ASAP
a company purchases shipments of 600 machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defective components. it is known that this particular component has a 4% defective rate. what is the probability that shipment will be accepted?
25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.
Given that,
An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.
We have to find how probability is it that the shipment will be accepted.
By binomial we get,
Binomial Problem:
n = 25 ; p = 0.04
P(0<= p <= 2)
= 0.7323
Therefore, The probability is it that the shipment will be accepted is 0.7323.
To learn more about probability visit: https://brainly.com/question/11234923
#SPJ4
Photo plus charges $2 for each print plus a $6 processing fee. Picture time charges $3 for each print plus a $4 processing fee. for what number of prints is the price the same at both stores
How many more votes did bill clinton get than george bush? about 44 million about 6 million about 25 million
Answer:
Step-by-step explanation:
B - 6 million
b. 6 Million
You can learn more about this through the link below
https://brainly.com/question/15380823#SPJ4
Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?
Answer:
The three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
Explanation:
Given the base and height pairs in the question.
Let us use the corresponding pairs that gives the same area.
Firstly, for the first pair;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times10\times7=35cm^2 \\ A=\frac{1}{2}\times10\times2.5=12.5cm^2 \end{gathered}[/tex]Secondly, the second pair is;
[tex]\begin{gathered} A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times5\times3.5=8.75cm^2 \\ A=\frac{1}{2}\times5\times2.5=6.25cm^2 \end{gathered}[/tex]Thirdly, the third pair;
[tex]\begin{gathered} A=\frac{1}{2}\times14\times3.5=24.5cm^2 \\ A=\frac{1}{2}\times14\times7=49cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]Therefore, the three correct corresponding pairs that gives the same area are;
[tex]\begin{gathered} A=\frac{1}{2}\times10\times3.5=17.5cm^2 \\ A=\frac{1}{2}\times5\times7=17.5cm^2 \\ A=\frac{1}{2}\times14\times2.5=17.5cm^2 \end{gathered}[/tex]The areas are the same in each case because the product of each pair is the same.
A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals, then how many of them can be dogs in a ratio
Answer:We have 70 dogs
Step-by-step explanation:
dogs: cats: total5 2 7We want 98 animals98/7 =14We need to multiply each number by 14dogs: cats: total…
hope this helps
what is Vivian's new account balance?
Answer: 218.65 US$
Step-by-step explanation: $187.56+$49.73= $237.29
237.29 US$- $18.64
Answer:
$218.65
Step-by-step explanation:
She starts with a balance of $187.56. When she deposits money she is adding to the account.
$187.56 + $49.73 = $237.29
When she spends money money is being subtracted from her account.
$237.29 - $18.64 = $218.65
Look at the table below. Which of the following is the constant rate of change?
Given data:
The first value of x is a=-16.
The first value of y is b=20.
The second value of x is c=-12.
The second value of y is d=15.
The expression for the rate change is,
x=(d-b)/(c-a)
Substitute the given values in thhe above expression.
x=(15-20)/(-12+16)
=-5/4
Thus, he constant rate of change is -5/4.
explain how you got the answer please
Answer:
I cannot include a picture, but the slope is -2/3, and the y-intercept is (0, 3).
Step-by-step explanation:
When given an equation like this, remember the formula y=mx+b that you should have learned. This formula is the slope-intercept formula that you can use. The m is the slope and the b is the intercept. In the equation, the x is what we are trying to find.
y=-2/3x+3
y=mx+b
m=-2/3
b= (0,3)
So, graph the slope as -2/3 and the y-intercept as (0,3).
Hope this helps!
Greg is at his house he gets in his car drives north 8. 9 miles and stops at a store then he turns around and drives south 7. 7 miles to his friends house how far is the friends house from Greg’s houses?
His friend's house is 1.2 miles away from his house.
How do you know his friend's house is 1.2 miles away from his house?Well, the solution to this math problem is very simple. We just need to remove a number away from another. In other words, we only need to do some subtraction.
Subtraction is one of four main arithmetic operations in which we use to take away a number or an amount from another number or amount. Remember that the commutative law doesn't apply to subtraction, so we really need to be careful to pick what number is subtracted by the other number.
The distance from Greg's house to the store is 8.9 miles away. That's the number that is going to be subtracted. His friend's house is 7.7 miles away from the store. This is the number that we're going to subtract from the previous number. Mathematically, we can express this as:
8.9 - 7.7 = 1.2
We're left with 1.2, which is the distance in miles from Greg's house to his friend's house.
Learn more about subtraction here: https://brainly.com/question/29082131
#SPJ4
Find the slope of the line that passes through the following points: (-4,-2) and (-3,5)
A line passes through the point (–2, 7) and has a slope of –5.
A coordinate plane.
What is the value of a if the point (a, 2) is also on the line?
–7
–1
1
7
Based on the fact that the line passes through (-2, 7) and the slope, the value of a can be found to be -1
How to find the value of a?To find the value of a, you first need to find the y-intercept to complete the linear equation which takes the form:
y = slope (x) + y-intercept
7 = -5(-2) + y-intercept
7 = 10 + y-intercept
y-intercept = 7 - 10
y-intercept = -3
The line equation is:
y = -5x - 3
The line y = -5x - 3 is passing through the point (a,2) is:
2 = -5(a) - 3
3 + 2 = -5a
a = 5 / -5
a = -1
Find out more on a slope at https://brainly.com/question/3493733
#SPJ1
Answer:
the answer is -1
Step-by-step explanation:
two cyclists, 42 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
The speed of the faster cyclist is 14\ miles/hr.
What is speed?
It is the average distance coverd in unit time. It is also defined as the rate of change of distance with respect to time.
Since the speed of the first cyclist is double than the second cyclist hence, the first cyclist will cover the double distance than the second cyclist. Consider the first cyclist covers 2s distance and first cyclist covers s distance. The sum of these two distances should be 42 miles. Hence,
[tex]2s+s=42\\3s=42\\s=14[/tex]
Now, distance coverd by the first cyclist is [tex]2s=2\times 14\\=28 \ $miles[/tex].
Now, both the cyclists meet after 2 hr hence, time taken by the first cyclist is 2 hr.
[tex]Speed=\frac{Total\ distance}{Total\ time}\\=28\ miles/2 \ hr\\=14\ miles/hr[/tex]
Hence, the speed of the faster cyclist is 14\ miles/hr.
Learn more about speed from the following link:
https://brainly.com/question/13943409
#SPJ4