Answer:
Sn is the trivial subgroup
Step-by-step explanation:
To prove that α must be the identity permutation and also Sn is the trivial subgroup we have to make assumptions :
when we assume α is not an identity permutation
α(i) = -j but since n ≥ 3 we will make another assumption of a number k
hence we will choose : β = ( i k )
from these assumptions we can deduce that
αβ (i) = α(k) ≠ -j since α(i) = -j
also βα (i) = β(-j) = -j
from the equations above we can conclude that
αβ ≠ βα which is in contradiction to the expression : αβ=βα . this simply shows that α must be the identity permutation, and the number of permutations of Sn is true for every number of permutation of Sn provided it is other than the identity
hence the center Sn is the trivial subgroup
How many different five-card hands can be dealt from a standard deck of fifty-two cards?
Answer:
2598960 ways
Step-by-step explanation:
Given
Standard Deck = 52
Five-card hands
Required
Determine the number of ways
To solve this question, we make use of combination formula
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]
Where n = 52 and r = 5
[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex] becomes
[tex]^{52}C_5 = \frac{52!}{(52-5)!5!}[/tex]
[tex]^{52}C_5 = \frac{52!}{47!5!}[/tex]
[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48 * 47!}{47! * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48}{5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{52}C_5 = \frac{311875200}{120}[/tex]
[tex]^{52}C_5 = 2598960[/tex]
Hence, there are 2598960 ways
Integral..Could you help me,please?
Answer:
as we know, the integral of [tex]x^{n}[/tex] is [tex]\frac{x^{n+1} }{n+1}[/tex]
so, the integral of x.[tex]2^{x}[/tex] will be found as follows:
here, we will use a trick called 'integration by parts'
let x = u and [tex]2^{x}[/tex] = v
∫uv dx = u∫v dx - ∫[(du/dx)* ∫v dx] dx
∫x.[tex]2^{x}[/tex] dx = x∫[tex]2^{x}[/tex] - ∫[(dx/dx) * ∫[tex]2^{x}[/tex] dx ] dx
∫x.[tex]2^{x}[/tex] dx = x*[tex]\frac{2^{x+ 1}}{x+ 1}[/tex] - 1 * [tex]\frac{2^{x + 1} }{x + 1}[/tex]
= [tex]\frac{2^{x} }{x + 1}[/tex]( x - 1 )
The following image represents the correct way to name ____*
Answer:
Line Segment
Step-by-step explanation:
Because the start on a line and end on a line.
Answer:
line segment
Step-by-step explanation:
What is the value of x in the equation 6(x + 1) - 5x = 8 + 2(x - 1)?
A100
12
Answer:
x=0
Step-by-step explanation:
First, we distribute on both sides
6x+6-5x=8+2x-2
simplify
x+6=2x+6
subtract x from both sides
6=x+6
subtract 6 from both sides
x=0
(plz give brianliest ty)
Answer:
x = 0
Step-by-step explanation:
6 ( x + 1 ) -5x = 8 + 2 ( x - 1 ) (Distribute)
6x + 6 - 5x = 8 + 2x - 2 (Rearrange expression)
6x - 2x - 5x = 8 - 6 - 2 (Combine like terms)
-1x = 0 (Divide)
x = 0
Area of the Region Between Curves-Please help.
Answer: 32/3
Step-by-step explanation:
To find the area of the region between the curves, you first want to find the interval of both curves. You can do that by setting both curves equal to each other.
[tex]-\frac{1}{2}x^2+2=\frac{1}{2} x^2-2[/tex] [subtract both sides by 2]
[tex]-\frac{1}{2}x^2= \frac{1}{2} x^2-4[/tex] [subtract both sides by [tex]\frac{1}{2} x^2[/tex]]
[tex]-x^2=-4\\x=2,-2[/tex]
Now that we know the interval, we set this into an integral and subtract the top curve by the bottom curve. *Note: I can't type in -2 into the interval, therefore only a "-" will be displayed.
[tex]\int\limits^2_- {|-\frac{1}{2}x^2+2-(\frac{1}{2}x^2-2) | } \, dx[/tex] [distribute -1]
[tex]\int\limits^2_-{|-\frac{1}{2}x^2+2-\frac{1}{2}x^2+2 |} \, dx[/tex] [combine like terms]
[tex]\int\limits^2_- {|-x^2+4|} \, dx[/tex] [solve integral]
[tex]\frac{32}{3}[/tex]
The area between the curves is 32/3. This was also the reason why we had the absolute values because area can never be negative.
If FH = 9x + 15 and GH = 5x + 4,
then FG = ?
Answer:
FG = 39
Step-by-step explanation:
From the question given:
FH = 9x + 15
GH = 5x + 4
FG = ?
From the question given above, we can say that G is the midpoint of FH. This implies that:
FH = FG + GH
With the above idea in mind, we can obtain FG as follow:
FH = 9x + 15
GH = 5x + 4
FG = ?
FH = FG + GH
9x + 15 = FG + 5x + 4
Rearrange
FG = 9x + 15 - 5x - 4
FG = 9x - 5x + 15 - 4
FG = 4x + 11
Next, we shall determine the value of x. This can be obtained as follow:
Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e
FG = GH
With the above idea in mind, we can obtain the value of x as follow:
FG = 4x + 11
GH = 5x + 4
FG = GH
4x + 11 = 5x + 4
Collect like terms
11 - 4 = 5x - 4
7 = x
x = 7
Thus, we can obtain the value of FG as follow:
FG = 4x + 11
x = 7
FG = 4x + 11
FG = 4(7) + 11
FG = 28 + 11
FG = 39
***Check ***
FH = 9x + 15
x = 7
FH = 9(7) + 15 = 63 + 15 = 78
GH = 5x + 4
x = 7
GH = 5(7) + 4 = 35 + 4 = 39
FG = 4x + 11
x = 7
FG = 4(7) + 11 = 28 + 11 = 39
FH = FG + GH
FH = 78
FG = 39
GH = 39
FH = FG + GH
78 = 39 + 39
78 = 78
Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).
(a) If x denotes the number of nonconforming parts made during one hour, what distribution does x follow? Please define the parameter(s) needed for defining the distribution based on the information provided.
(b) What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?
(c) What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?
(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?
Answer:
(a) x follows a poisson distribution with parameter λ = 8 / hour
(b) P( X = 5 ) = 0.09160
P( X ≥ 5 ) = 0.9004
(c) the expected value of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes
The standard deviation = 4
(d) P(X ≥ 20) = 0.5297
P( X ≤ 10) = 0.0108
Step-by-step explanation:
Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).
(a) If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour
(b)
What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?
the probability that exactly 5 nonconforming parts are produced during a 1-hour period can be computed as:
P( X = 5 ) = [tex]e^{- \lambda } \lambda^x /x![/tex]
P( X = 5 ) = [tex]e^{- 8 }(8)^5 /5![/tex]
P( X = 5 ) = 0.09160
the probability that at least 5 nonconforming parts are produced during a 1-hour period
P( X ≥ 5 ) = 1 - P( X ≤ 4)
[tex]P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]
[tex]P( X \geq 5 ) = 1 - 0.0996[/tex]
P( X ≥ 5 ) = 0.9004
c) What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?
the expected value of the number of nonconforming parts produced during a 120-min period [tex]\lambda = 8 \times \dfrac {120}{60}[/tex]
= 16 nonconforming parts per 120 minutes
The standard deviation = [tex]\lambda^{1/2}[/tex]
The standard deviation = [tex](16)^{1/2}[/tex]
The standard deviation = 4
(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?
During a 2.5 - hour period , the expected value = 8 × 2.5 = 20
As such, the probability that at least 20 nonconforming parts produced during a 2.5-hour period is:
P(X ≥ 20) = 1 - P(X ≤ 19)
[tex]P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]
P(X ≥ 20) = 1 - 0.4703
P(X ≥ 20) = 0.5297
Probability that at most 10 nonconforming parts produced during this period is:
P( X ≤ 10) = [tex]\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]
[tex]P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}![/tex]
P( X ≤ 10) = 0.0108
Following are the calculation to the given points:
For point a)
With parameter, x follows the poisson distribution is [tex]\lambda=\frac{8}{hour}[/tex]
For point b)
The probability that exactly 5 nonconforming parts are generated in a one-hour period.
[tex]\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916[/tex]
There is a good chance that at least 5 nonconforming parts exist.
[tex]\to P(X\geq 5) =1-P(X\leq 4)[/tex]
[tex]=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004[/tex]
For point c)
Expected value for 120-minute period [tex]\lambda=8\times \frac{120}{60} =16[/tex] 120 minutes of nonconforming sections
[tex]\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4[/tex]
For point d)
Expected value for 2.5 hours
[tex]\to \lambda =8\times 2.5=20[/tex]
As a result, there is a good chance that at least 20 nonconforming items were manufactured.
[tex]\to P(X\geq 20)=1-P(X\leq 19)[/tex]
[tex]=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297[/tex]
There is a chance that no more than 10 nonconforming parts were created.
[tex]\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108[/tex]
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A team of 17 softball players need to choose three players to refill the water cooler. How many different ways are there to select 3 players?
=======================================================
Explanation:
If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.
So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.
An alternative is to use the nCr formula with n = 17 and r = 3. That formula is
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
where the exclamation marks indicate factorials
The number of different ways that are there to select 3 players is 680.
Calculation of the number of different ways:
Since there is A team of 17 softball players need to choose three players to refill the water cooler.
So here we can say there are [tex]17\times 16\times 15 = 4080[/tex]
And, since we have to select 3 people so the no of ways should be [tex]3\times 2\times 1 = 6\ ways[/tex]
So, here the number of different ways should be
[tex]= 4080\div 6[/tex]
= 680
Therefore, The number of different ways that are there to select 3 players is 680.
Learn more about ways here: https://brainly.com/question/24604425
7. Is plane TPS an acceptable name for plane R? Why or why not?
Answer:
Hi
Step-by-step explanation:
Hi
If c(x)=5/x-2 and d(x)=x+3,. What is the domain of (CD)(x)
Answer:
all real numbers except x=2
Step-by-step explanation:
We assume you intend c(x) = 5/(x-2), rather than c(x) = (5/x) -2 as written.
__
The domain of c(x) is real numbers, excluding 2. Multiplying c(x) by d(x) doesn't change that.
The domain of (cd)(x) = c(x)×d(x) = 5(x+3)/(x-2) is "all real numbers except 2".
__
2 is excluded because c(x) is undefined for that value.
Which size would you see on the box for a new television whose screen measures 32 inches wide by 18 inches high?
Answer:
37
Step-by-step explanation:
The calculation of size for a new television is shown below:-
With the help of Pythagoras theorem
[tex]h^2 = b^2 + p^2[/tex]
where
h indicates hypotenuse which is the diagonal length
b indicates the base which is the length of the horizontal side
p indicates perpendicular which is the TV length of the vertical side.
[tex]h^2 = \sqrt{b^2 + p^2}[/tex]
now, we will put the values into the above formula
[tex]= \sqrt{32^2 + 18^2} \\\\ = \sqrt{1024 + 324} \\\\ = \sqrt{1348}[/tex]
Which gives result
= 36.7
or
= 37
two - way frequency tables
Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.
Step-by-step explanation:
What is the product of (–22.1)(–5.6)?
Answer:
123.76
Step-by-step explanation:
a negative times a negative is a positive
22.1 times 5.6 is 123.76
hi :) i need help w this
Answer:
67
Step-by-step explanation:
Round to the nearest cent.
5. $406.439
Answer:
406.4
Step-by-step explanation:
When rounding you only look at the number you're rounding and the one before it. In this case it would be the 4 and 3 after the decimal since we're rounding to the nearest cent. If the numbers before the one you're rounding are 0-4 then you leave the number the same. If the numbers are between 5-9 then you add one to the number. Since the number before 4 is between 0-4 you leave it as 4. But if it was between 5-9 then you'd change the 4 to 5.
Solve 3(x + 1) + 6 = 33.
add 6 plus 33 then do x+1 then you divide
Step-by-step explanation:
sam has 24 muffins,which need to be split into dozens. 8 of the muffins are blueberry. how many boxes does he need?
Four big water bottles can hold 8 gallons of water. How much water can ten big water bottles hold.
Step-by-step explanation:
Part 1
To find out the amount of water ten big water bottles can hold, we have to find out how much water is in each water bottle. To do this, we divide the amount we are looking for by the number of items.
8 ÷ 4 = 2
Part 1 answer: Each water bottle can hold 2 gallons of water.
Part 2
Now that we know the amount of water in each water bottle, we can find out how much water 10 water bottles can hold. To do so, we multiply our previous answer, 2, by the number of items (10).
2 • 10 = 20
Part 2 answer: 10 water bottles can hold 20 gallons of water.
Our final answer: 20 gallons
I hope this helps you!
Find the inverse. f(x) = -2/3x - 7/6
To find the inverse, interchange the variables and solve for y. f−^1(x)=−3x/2−7/4
To find the inverse, interchange the variables and solve for
f − 1 ( x ) = − 3 x 2 − 7 4
hope this helped and I know this is the answer
How many thousands of blue crayons are in 327,412
Answer:327412000
Step-by-step explanation:
Order the following numbers from least to greatest.
Answer:
[tex]\Huge \boxed{-2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
We will convert the values into decimals for simplicity.
[tex]\sqrt{7} = 2.64575131106...[/tex]
[tex]-2.3=-2.3[/tex]
[tex]\sqrt{3} = 1.73205080757...[/tex]
[tex]5.1=5.1[/tex]
[tex]\displaystyle \frac{-1}{3} =-0.333333333...[/tex]
Arranging from least to greatest:
[tex]\displaystyle -2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1[/tex]
[tex]\rule[225]{225}{2}[/tex]
To which subset of the real number system does the number LaTeX: 1.\overline{5}1. 5 ¯ belong? Group of answer choices irrational numbers whole numbers natural numbers rational numbers
Answer:
rational numbers
Step-by-step explanation:
what is (- 4/5) x (- 5/8)
Answer:
- 1/2
Step-by-step explanation:
(-4/5) × (- 5/8)
- 4/5 × - 5/8
First we mulitply across
The top and the bottom.
- 20 / 40
because -4 × -5 = +20
and -5 × -8 = +40
Now we simplify the fraction
- 20 / 40
= - 2 /4
= - 1/2
Because we have to simplify it and so I divided it by 10 first.
-20 ÷ 10 = -2 and -40 ÷ 10 = -4
Then I simplified it again by dividing it by 2.
-2 ÷ 2 = -1 and -4 ÷ 2 = -2
So finally we have:
-1/2
And we cannot simplify that anymore so that is the answer.
Hope that helped!
Answer:
1/2
Step-by-step explanation:
since negative * negative= positive we multiply the top and bottom to get. 20/40 which simplifies
A survey was conducted at Giant Supermarket where 50 students were randomly chosen and asked
whether they liked apples or bananas. Of the 50,36 students said they like apples, 30 students like
bananas and 5 students do not like either apples or bananas. How many students like both apples
and bananas? How many students like only apples or only bananas?
Answer:
The answer for both apples and bananas is 21
The answer for only apples or only bananas is 45
Step-by-step explanation:
36 plus 30 minus 45
50-5 is 45
only apples or bananas is 15 + 9
What is the mean of the following data values? 52, 70, 88, 15, 65 A. 58 B. 82 C. 62 D. 78
Answer:
A) 58
Step-by-step explanation:
Mean = Sum of all the data ÷ total number of data
[tex]=\frac{52+70+88+15+65}{5}\\\\\\=\frac{290}{5}\\\\\\= 58[/tex]
715 thousands, 34 tens (compared to) 715,034
Answer:
715,340 > 715,034
Step-by-step explanation:
Robert has available 400 yards of fencing and wishes to enclose a rectangular area. Express the areaAof the rectangle as a function of the widthwof the rectangle. For what value ofwis the arealargest? What is the maximum area?
Answer:
The answer is below
Step-by-step explanation:
a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.
the perimeter of a rectangle is given as:
Perimeter = 2(length + width) = 2(l + w)
Hence;
400 = 2(l + w)
200 = l + w
l = 200 - w
The area of a rectangle is given as:
Area = length × width
Area = (200 - w) × w
Area = 200w - w²
b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a
Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:
w = -b/2a = -200/2(-1) = -200/-2 = 100
A width of 100 yard has the largest area
c) l = 200 - w = 200 - 100 = 100 yards
Area = l × w = 100 × 100 = 10000 yd²
The maximum area is 10000 yd²
Write a piecewise function. PLEAE HELP i really need this any help would be very appreciated!!
Answer:
see below
Step-by-step explanation:
Each age bracket defines a domain of the function. The function value is constant for that domain. This function gives admission price (P) as a function of age (a).
[tex]P(a)=\left\{\begin{array}{ccl}0&\text{for}&a\le5\\3&\text{for}&5<a\le18\\5&\text{for}&18<a<65\\4&\text{for}&a\ge65\end{array}\right.[/tex]
Megan expects to save an average of 5 dollars per
week from her babysitting earnings. The relationship
between time and the amount of money she saves is
shown on the graph. Which other ordered pairs would
fall on this line? Select all that apply.
A. (0.5, 2.5)
B. (3, 18)
C. (0,0)
D. (4.5, 30)
Answer:
Step-by-step explanation:
Ordered pair (0, 0) & (0.5, 2.5) will fall on the line of graph
Step-by-step explanation:
Megan expects to save an average of 5 dollars per week from her babysitting earnings.
=> Saving Per week = 5 $
Saving in 0.5 Week = 0.5 * 5 = 2.5 $
hence ordered pair (0.5, 2.5) will fall on the line of graph
Saving in 3 Week = 3 * 5 = 15 $
Hence (3, 18) will not fall on line
Saving in 0 Week = 0.5 * 0 = 0 $
hence ordered pair (0, 0) will fall on the line of graph
Saving in 4.5 Week = 4.5 * 5 = 22.5 $
Hence (4.5, 30) will not fall on line
Ordered pair (0, 0) & (0.5, 2.5) will fall on the line of graph
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
Megan expects to save an average of 5 dollars per week from her babysitting earnings.
=> Saving Per week = 5 $
Saving in 0.5 Week = 0.5 * 5 = 2.5 $
hence ordered pair (0.5, 2.5) will fall on the line of graph
Saving in 3 Week = 3 * 5 = 15 $
Hence (3, 18) will not fall on line
Saving in 0 Week = 0.5 * 0 = 0 $
hence ordered pair (0, 0) will fall on the line of graph
Saving in 4.5 Week = 4.5 * 5 = 22.5 $
Hence (4.5, 30) will not fall on line
Hence, Ordered pair (0, 0) & (0.5, 2.5) will fall on the line of graph.
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9,000 + 40 + 0.1 + 0.008 I need to put it in standard form. Please help!
Answer:
-12
Step-by-step explanation: