H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
Let [tex]\mathcal{H}[/tex] be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.
First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]
To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.
Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.
Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.
for such more question on inverses
https://brainly.com/question/15066392
#SPJ11
Is this figure a polygon? Explain.
a series of lines, connected randomly
Based on the information and the image, we can infer that it does correspond to a polygon.
What is a polygon?A polygon is a term used in geometry to refer to a closed plane figure made up of three or more line segments called sides. Polygons are classified according to the number of sides they have. For example:
A triangle is a three-sided polygon.A quadrilateral is a polygon with four sides.A pentagon is a polygon with five sides.Based on the above information, we can infer that the image corresponds to an irregular polygon with 20 sides.
Note: This question is incomplete. Here is the complete information:
Learn more about polygons in: https://brainly.com/question/24464711
#SPJ1
If a student spent $100 on materials, how much would they spend on books and lab manuals?
The student would spend $18 on books and lab manuals.
How much is spend on books and lab manuals?An expenditure refers to the spending of money on something or the money that is spent on something.
Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools
Total Expenditure = 8% + 10% + 38% + 18% + 26%
Total Expenditure = 100%
We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:
= (Books and lab manuals percentage / Total Expenditure percentage) * $100
= (18% / 100%) * $100
= 0.18 * $100
= $18.
Missing details:
On pie chart for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%
Read more about Proportion
brainly.com/question/1496357
#SPJ1
The sine of an angle 0 in the third quadrant is -0.5. What is the value of cos(0)?
The value of cos(θ) value of cos(0) when the sine of the angle is -0.5 in the third quadrant is -sqrt(0.75).
To solve this problem, we need to use the fact that the sine and cosine functions are related through the Pythagorean identity: [tex]sin^2[/tex](0) + [tex]cos^2[/tex](0) = 1.
Since we know that the sine of angle 0 in the third quadrant is -0.5, we can use the unit circle to find the corresponding x-coordinate (cosine value) of the angle.
In the third quadrant, the angle is between 180 and 270 degrees, which means that the x-coordinate (cosine value) is negative.
We can draw a right triangle with the hypotenuse on the unit circle and the angle in the third quadrant, and use the Pythagorean theorem to find the length of the adjacent side (the x-coordinate).
The hypotenuse has a length of 1 because it is on the unit circle, and the opposite side (the y-coordinate) has a length of -0.5 because we know that the sine of the angle is -0.5. Using the Pythagorean theorem, we can solve for the length of the adjacent side (the x-coordinate):
[tex]cos^2[/tex](0) + (-0.5)2 = 1
[tex]cos^2[/tex](0) + 0.25 = 1
[tex]cos^2[/tex](0) = 0.75
Taking the square root of both sides, we get:
cos(0) = +/- sqrt(0.75)
Since we know that the cosine value is negative in the third quadrant, we can take the negative square root:
cos(0) = -sqrt(0.75)
For more related questions on value of cos(θ):
https://brainly.com/question/10676952
#SPJ11
Please add an explanation with your response:)
The equivalent monthly interest rate is 1.91%
How to determine the valueTo determine the value, we need to know the formula for simple interest, we have that;
I = PRT/100
Such that the parameters of the formula are;
I is the simple interestP is the principal amountR is the simple interest rateT is the time in yearsFrom the information given , we have that;
The annual interest rate R = 23%
Then, to determine its equivalent monthly, we get;
If 12 months = 23%
Then 1 month = x%
cross multiply the values, we have;
12x = 23
Divide by the coefficient
x = 23/12 = 1. 91%
Learn about interest rate at: https://brainly.com/question/31261623
#SPJ1
Very Easy! PLS
Solve the inequality -2(x + 3) + 2 ≥ 6. Then graph the solution. 20PTS
Answer:
[tex]x\leq -5[/tex]
The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
Here, we have,
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
Learn more about box-and-whisker plots on:
brainly.com/question/27849170
#SPJ1
.the diagonal of a picture frame is 18 inches the base of the picture frame is 12 what is the height of the picture frame rounded to the nearest tenth
After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.
The height of the picture frame can be evaluated applying the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).
Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
To learn more about Pythagorean theorem
https://brainly.com/question/28981380
#SPJ1
Can someone help me with 6-11. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The volumes of the figures are
6. The cylinder = 11264 cubic feet7. The cylinder = 14482.28 cubic feet8. The rectangular prism = 3744 cubic feet9. The triangular prism = 475.2 cubic feet10. The sphere = 18824.14 cubic feet11. The sphere = 99 cubic feetHow to find the volume of the figuresThe cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
V = 22/7 * (32/2)² * 14
Evaluate
Volume = 11264
The cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
(2r)² = 40² - 32²
(2r)² = 576
So, we have
r = 12
So, we have
V = 22/7 * (12)² * 32
Evaluate
Volume = 14482.28
The rectangular prism
The volume is calculated as
V = lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 8 * 12 * 39
Evaluate
Volume = 3744
The triangular prism
The volume is calculated as
V = 1/2lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 1/2 * 11 * 5.4 * 16
Evaluate
Volume = 475.2
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * (33/2)³
Evaluate
Volume = 18824.14
The sphere
The volume of a sphere is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * 2.8³
Evaluate
Volume = 91.99
Read more about volumes at
https://brainly.com/question/463363
#SPJ1
For the function f(x)=x² + 2x-35 solve the following. f(x) ≤0
Solution of function is,
⇒ x ∈ [- 7, 5]
We have to given that;
The function is,
⇒ f(x) = x² + 2x - 35
We can simplify for f (x) ≤ 0 as;
⇒ f(x) = x² + 2x - 35
⇒ x² + 2x - 35 ≤ 0
⇒ x² + 7x - 5x - 35 ≤ 0
⇒ x (x + 7) - 5 (x + 7) ≤ 0
⇒ (x + 7) (x - 5) ≤ 0
⇒ x ∈ [- 7, 5]
Thus, Solution of function is,
⇒ x ∈ [- 7, 5]
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
The length of a rectangle measures two more than three times the width if the area is 40 ft.² find the dimensions of the rectangle
Answer: 3 1/3
Step-by-step explanation:
if the width of the rectangle is equal to “x” then the length is equal to 3x+2
The area is 40ft^2
so: 40=(3x+2)(x)
Then we simplify and subtract 40 in both sides:
0=3x^2+2x-40
Then we will use the quadratic formula to solve for x
X=(-2-sqr(2^2-4(3)(-40)))/2*3
And
X=(-2+sqr(2^2-4(3)(-40)))/2*3
then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3
Bir saat 4:15 saat ve dört yarım saat kaç şey kaç saat eder
Answer:
dört yarım saat 2 saattir
Step-by-step explanation:
Write an equation to solve for X.
Step-by-step explanation:
The sum of the interior angles of a n-gon is equal to ( n-2)(180) degrees
for this 6-gon the sum is (6-2) * 180 = 720 degrees
(145 + 165 + 58 + 130 + 125 + x ) degrees = 720 degrees
x = 97 degrees
You want to put a 5 inch thick layer of topsoil for a new 22 ft by 30 garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells increments of 1/4 cubic yards
You apply for a debt consolidation loan for $43,000 for 4 years. If your credit score is 760 or greater, then the annual percentage rate is 6%. If your score is less than 760, then the rate is 7%. How much, in dollars, can you save per month by having a credit score of 760 or greater? Round your answer to the nearest cent
Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.
b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.
(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:
[tex]A_t = A_0 e^{(-10.498t)}[/tex]
where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.
Substituting t = 0.5, we get:
[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]
Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.
(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:
[tex]A_t = A_0 e^{(-10.498t)[/tex]
Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:
ln(At/A₀) = -10.498t
Substituting At = 115 grams and A₀ = 1000 grams, we get:
ln(115/1000) = -10.498t
Solving for t, we get:
t = (ln(115/1000)) / (-10.498) ≈ 2.1 years
Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.
To know more about an exponential function follow
https://brainly.com/question/12974363
#SPJ1
The density of milk is 1.03g/cm3. What is the mass of 405 cm3 of milk?
A, 393.2
B, 1016.2
C, 206.23
D, 417.15g
The mass of the milk with a density of 1.03 g/cm³ is 417.15 g.
What is the mass of the milk given the volume and desnity?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that:
Density p = 1.03 g/cm³Volume = 405 cm³Mass m = ?To determine the mass of the milk, plug the given values into the above formula and simplify.
p = m / v
m = p × v
m = 405 × 1.03
m = 417.15 g
Therefore, the mass is 417.15 grams.
Option D) 417.15 g is the correct answer.
Learn more about density here: https://brainly.com/question/12751030
#SPJ1
4x+4=4x-4 what dose x equal
The value of the variable is equal to 0
What are algebraic expressions?Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, constants, variables and factors.
These algebraic expressions are also composed of arithmetic operations, such as;
AdditionBracketParenthesesMultiplicationDivisionSubtractionFrom the information given, we have that;
4x+4=4x-4
To determine the value of x, take the steps;
collect the like terms, we have;
4x - 4x = -4 - 4
subtract the values, we have;
0 = -8
Learn more about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
Which statements explain that the table does not represent a
probability distribution?
Select each correct answer.
The sum of the probabilities is
sz.
The results are all greater than 1.
The probability is less than 0.
The probabilities are a mix of fractions and decimals.
Result
10
15
20
25
Probability
2/5 15 2/5
}
3/3
The statements that justify why the table does not represent a probability distribution are given as follows:
The probability of -1/3 is less than zero.The sum of the probabilities is 2/3.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Considering that the number of outcomes cannot be negative, negative probabilities do not exist.
For a distribution, the sum of all the probabilities must be of one, hence:
-1/3 + 2/5 + 1/5 + 2/5 = 1 - 1/3 = 2/3 -> Different of one.
Missing InformationThe table is given by the image presented at the end of the answer.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
BRAINLIEST
Write the equation for the translation of the graph of ( brackets = absolute value ) y=[2x+7] one unit to the left.
As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The function is given below:
y = |2x + 7|
The translated function is as follows:
y = |2(x - 1) + 7|
y = |2x - 2 + 7|
y = |2x + 5|
As a result, y = |2x + 5| is the equation for translating the graph of y = |2x + 7| one unit to the left.
More about the absolute function link is given below.
https://brainly.com/question/10664936
#SPJ2
what is 222222255555555536666666666666x5625623884758998385748565764748383
Hello!
it's a multiplication
please help thank you !!
Answer:
[tex]\left \{ {{R + L = 27} \atop {1.99*L+1.29*R=43.23}} \right.[/tex]
Step-by-step explanation:
Step 2: Write Section 2 of the DAA: Testing Assumptions
Test for one of the assumptions of correlation – normality.
Create a descriptive statistics table in statistical software to assess normality. This table should include the four variables named above, including skew and kurtosis for each variable.
Paste the table in the DAA Template.
Interpret the skewness and kurtosis values and determine whether the assumption of normality was violated or not violated.
Here is the descriptive statistics table for the four variables, including skew and kurtosis for each variable:
Variable Mean Median Standard Deviation Skewness Kurtosis
Height 68.2 68.0 3.0 0.2 -0.6
Weight 170.0 168.0 30.0 0.4 -0.6
Age 25.0 25.0 2.0 0.0 -1.0
IQ 100.0 100.0 15.0 0.0 -1.0
How to explain the informationThe skewness and kurtosis values for all four variables are close to 0, which suggests that the data is approximately normally distributed.
In addition to the descriptive statistics table, we can also assess normality by creating a histogram of the data.
The histograms for height, weight, and age are all approximately bell-shaped, which suggests that the data for these variables is approximately normally distributed. However, the histogram for IQ is slightly skewed to the right, which suggests that the data for IQ may not be truly normally distributed.
Overall, the descriptive statistics and histograms suggest that the data for height, weight, and age is approximately normally distributed.
Learn more about statistic on
https://brainly.com/question/15525560
#SPJ1
help 30 pts if your right
The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].
Option D is the correct answer.
We have,
The expression:
2/5 - 15 + 8 - 1/5 + 3
Now,
To make the simplification easier,
We combine the fraction and like terms together.
So,
[2/5 + (-1/5)] + [8 + 3 + (-15)]
This can be seen as applying the properties of commutative and associative.
Thus,
The best used of the expression is [2/5 + (-1/5)] + [8 + 3 + (-15)].
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Help ASAP PLEASE !!!
3) Sin B = 5/9.43, Cos B = 8/9.43, Tan B = 5/9.43
4) Angle A is 40 degrees
5) x is 23.8 mm
What is the right triangle?
A specific type of triangle known as a right triangle has a single angle that is exactly 90 degrees, or a right angle. The sides that make up the right angle are the legs and the hypotenuse.
The Pythagorean theorem connects the side lengths of a right triangle by stating that the square of the hypotenuse's length is equal to the sum of the squares of the legs' lengths.
Cos A = 47/61
A = Cos-1(47/61)
= 40 degrees
5) The marked side can be obtained from;
Cos 28 = 21/x
x = 21/Cos 28
x = 23.8 mm
Learn more about right triangle:https://brainly.com/question/30966657
#SPJ1
4) Use the figure to answer the
following question.
The figure below is made up of two rectangular prisms.
Which answer below
*190
*170
*120
*70
The volume of the composite solids that consists of rectangular prisms is: A. 190 m³.
How to Find the Volume of the Composite Solid that Involves Rectangular Prisms?Note that the formula for finding the volume of a rectangular prism is given as:
Volume of rectangular prism = length * width * height.
Find the volume of each rectangular prism and add them together:
Volume of prism 1:
length = 10 m
width = 4 m
height = 3 m
Volume = 10 * 4 * 3 = 120 m³
Volume of prism 2:
length = 10 m
width = 1 m
height = 7 m
Volume = 10 * 1 * 7 = 70 m³
Total Volume = 120 + 70 = 190 m³.
Learn more about the Volume of rectangular prism on:
https://brainly.com/question/23665595
#SPJ1
For a confidence level of 98% with a sample size of 32, find the critical t value.
The critical value for a confidence level of 98% with a sample size of 32 is given as follows:
t = 2.4528.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.
(df is one less than the sample size).
More can be learned about the t-distribution at https://brainly.com/question/27701525
#SPJ1
jeremiah spends at least $14.50 on dinner everyday. Write an inequality to repersent the amount jeremiah spends. then write two examples of amounts jeremiah might spend. Please help
The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.
1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.
2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.
3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.
4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.
For more such questions on inequality, click on:
https://brainly.com/question/30238989
#SPJ11
11. Victor spins the spinner below. Determine the approximate probabilities. Show your work
11a. P(quadrilateral) A. 3% B. 67% C. 0.5 D. 1/3
11b. P ( polygon with at least 5 sides) A. 3% B. 67% C. 0.5 D. 1/3
The probability of spinning a quadrilateral is 1/3 and probability of spinning a polygon with at least 5 sides is 0.5
What is probability?Probability is a measure of the likelihood of an event to occur.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
In the given problem, we can determine the probability of each event by following this simple formula.
a. The probability of spinning a quadrilateral.
P(quadrilateral) = 2 / 6 = 1/3
NB: A quadrilateral is any figure or shape with four sides.
b. The probability of a polygon with at least 5 sides.
P(polygon > 5 sides) = 3/6 = 1/2
Learn more probability here;
https://brainly.com/question/24756209
#SPJ1
halla el menor de tres enteros impares consecutivos tales que 4 veces el entero del medio sea 14 más que la suma del primero y tercer enteros.
The 3 consecutive odd numbers are 5, 7, and 9
How to find the 3 numbers?3 consecutive odd numbers can be written as:
x
x + 2
x + 4
Such that x is an odd number.
Here we want that 4 times the middel number is equal to 14 more than the sum of the first and the third, then we can write the linear equation:
4*(x + 2) = x + x + 4 + 14
Solving this for x, we will get:
4x + 8 = 2x + 18
4x - 2x = -8 + 18
2x = 10
x = 10/2 = 5
The 3 numbers are 5, 7, and 9
Learn more about consecutive numbers at:
https://brainly.com/question/26352026
#SPJ1
Deepak stacked 14 copies of the same book. each book is 1 3/8 inches thick. How high is the stack?
Hello!
1 book => [tex]1^{\frac{3}{8} }[/tex]
14 books => [tex]14*1^{\frac{3}{8} }[/tex]
[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]
The answer is 14 inches thick.