The slope of the line is -4, which means that the swimmer will complete 4 laps every minute. For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).
The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.
To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x
10x + 25 = 5x + 50
5x = 25
x = 5
So, after 5 weeks, the two siblings will have the same amount of money saved.
The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.
The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.
Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles
AB/DE = BC/EF = CA/FD
Plugging in the known values, we get
11/2.2 = 7.9/EF = 7.6/FD
Solving for FD, we get
FD = (7.6 * 2.2)/11 = 1.52
So, FD has a length of 1.52 units.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula
slope = (y2 - y1)/(x2 - x1)
Plugging in the given values, we get
slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2
So, the slope of the line is negative three halves.
The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials
P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%
So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.
Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.
To know more about Probability:
https://brainly.com/question/11234923
#SPJ1
the odds in favor of an event are give compute the probability of the event enter the probability as a fraction 4 to 9
The probability of the event is 4/13 when the odds in favor of the event are 4 to 9.
When the odds in favor of an event are given as a ratio of "a to b", the probability of the event can be calculated as:
Probability of the event = a / (a + b)
In this case, the odds in favor of the event are 4 to 9.
Therefore, we have:
a = 4 (the number of favorable outcomes)
b = 9 (the number of unfavorable outcomes)
Substituting these values into the formula, we get:
Probability of the event = 4 / (4 + 9)
Probability of the event = 4 / 13
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ1
Need help please !!
Geometry
Answer:
complementary since the angles sum up to 90
The table reports the distribution of pocket money, in bills, of the 6 students in a statistics seminar. Student Hannah Ming Keshaun Tameeka Jose Vaishali Amount, in dollars 2 4 4 5 5 7 For a random sample of size two, find the probability, expressed as a percent rounded to the nearest tenth, that the sample mean will be within $1 of the population mean
The probability, expressed as a percent rounded to the nearest tenth, that the sample mean will be within $1 of the population mean is 91.5%.
To find the probability that a random sample of size two will have a sample mean within $1 of the population mean, we need to first calculate the population mean and standard deviation.
The population mean is the average of the given values:
(2 + 4 + 4 + 5 + 5 + 7) / 6 = 4.5
The population standard deviation can be calculated using the formula:
σ = [tex]\sqrt{S(x-u)^{2}/N }[/tex]
where S represents the sum of, x is each value, u is the population mean, and N is the population size.
Using this formula, we get:
σ = [tex]\sqrt{(2-4.5)^{2}+ (4-4.5)^{2}+(4-4.5) +(5-4.5)^{2} +(5-4.5)^{2}+ (7-4.5)^{2} /6}[/tex] = 1.5
Now we can find the probability of getting a sample mean within $1 of the population mean using the t-distribution since the population standard deviation is unknown and the sample size is less than 30. Since we are looking for the probability of the sample mean being within $1 of the population mean, we need to find the probability of getting a sample mean between 3.5 and 5.5 dollars.
We can use a t-distribution table or a calculator to find the probability. For a sample size of 2, the degrees of freedom is 1, and using a t-distribution table with a significance level of 0.05, we get a t-value of 12.71.
Therefore, the probability of getting a sample mean between 3.5 and 5.5 dollars is approximately 91.5% (calculated using a t-distribution calculator or the t-distribution table), rounded to the nearest tenth.
To learn more about probability here:
https://brainly.com/question/30034780
#SPJ1
Can someone help me with this problem?
This requires the circle theorem and the angle at the center postulate.
What does the angel at the center state?
It simply states that the angle subtended by an arc at the centre is twice the angle subtended at the circumference.
Thus
8) m∡CA = 72 x 2 = 144°
9) m∡AD = 144/2 = 72° - Angle Bisected by radius.
10) m∠C = ∠∡CA/2 = 72/2 = 36°
11) where the angles in the polygon are given as:
4y + 14)°
105°
7y+1)°
7x +1)°
Then, x and y are given as follows.
Note that 105° and (7y+1)° are opposite angles in a polygon = 180°
Also
(4y + 14)° + (4y + 14)° = 180
Thus
105° + (7y+1)° = 180 ......1
(7x +1)° + (4y + 14)° = 180 .....2
Simplifying the first equation:
105° + (7y+1)° = 180
7y + 106 = 180
7y = 74
y = 10.57
(7x +1)° + (4y + 14)° = 180
(7x + 1)° + (4 (10.57) + 14)° = 180
(7x + 1)° + 54.28° = 180
7x + 55.28 = 180
7x = 124.72
x = 17.82
So we can conclude that , x is approximately 17.82 and y is approximately 10.57.
Learn more about circle theorem:
https://brainly.com/question/19906313
#SPJ1
Determine whether the equation has no solution, one solution, or infinitely many solutions. -2 ( 11 - 12x )= -4 ( 1 - 6x) Explain your conclusion. Enter your answer, your work, and your explanation in the box provided.
Answer:
No solution
Step-by-step explanation:
-2(11-12x) = -4(1-6x)
Distribute the -2 and -4:
-22 + 24x = -4 + 24x
Subtract 24x from both sides:
-22 = -4
Since this is a contradiction, there is no solution. The equation is inconsistent.
Answer:
No Solution.
Explanation:
When solving for x, the two values do not equate to each other.
ASAPP Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80
Answer:
A. $1,166.40
Step-by-step explanation:
Since they have to travel a round trip, the total distance traveled will be 2*1,701 = 3,402 miles.
The total amount of gasoline needed can be found by dividing the total distance by the average gas mileage of the RV:
Gasoline needed = 3,402 miles ÷ 10.5 miles/gallon = 324.57 gallons
The total cost of gasoline can be found by multiplying the gasoline needed by the cost per gallon:
Total cost = 324.57 gallons × $3.60/gallon = $1,169.25
Therefore, Clinton and Stacy will spend approximately $1,169.25 on gasoline for the round trip to Yellowstone National Park and back home.
The closest option to this answer is A. $1,166.40.
Hope this helps!
You have a choice of receiving a wage of $34,000 per year, $2840 per month, $650 per week, or $18 per hour. Which pay choice would you take? Assume a 40-hour work week with 52 weeks per year.
Based on calculation, the highest hourly wage is $2,840 per month which gives us $17.75 per hour.
Which pay choice is the best choice take?For purpose of making a comparison, we can calculate the hourly wage for each option.
Hourly wage for $34,000 per year:
= $34,000 / (40 hours per week * 52 weeks per year)
= 16.3461538
= $16.35 per hour.
Hourly wage for $2,840 per month:
= $2,840 / (4 weeks per month * 40 hours per week)
= $17.75 per hour
Hourly wage for $650 per week:
= $650 / 40 hours per week
= $16.25 per hour
Hourly wage for $18 per hour.
Read more about wage
brainly.com/question/1622389
#SPJ1
I will give brainliest and ratings if you get this correct
Answer:
This is the equation we have to use in order to find the eigenvalues and eigenvectors of matrix A:
det(A - λI) = 0
where λ is the eigenvalue and I is the identity matrix.
So we have:
A - λI = [ -5-λ 1 2 ]
[ 0 -2-λ 0 ]
[ 4 2 -3-λ ]
And the determinant is:
det(A - λI) = (-5-λ)(-2-λ)(-3-λ) - 8(2+λ) = -λ^3 + 4λ^2 + 23λ - 40
We can factor this to get:
det(A - λI) = -(λ - 5)(λ - 2)(λ + 4)
So the eigenvalues are λ1 = 5, λ2 = 2, and λ3 = -4.
To find the eigenvectors for each eigenvalue, we need to solve the system of linear equations:
(A - λI)x = 0
For λ1 = 5, we have:
[ -5-5 1 2 ] [ x1 ] [ 0 ]
[ 0 -2-5 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3-5] [ x3 ] [ 0 ]
which simplifies to:
[ -10 1 2 ] [ x1 ] [ 0 ]
[ 0 -7 0 ] [ x2 ] = [ 0 ]
[ 4 2 -8 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -1/2 x2
x3 = -1/2 x2
So the eigenvector for λ1 = 5 is:
v1 = [ x1, x2, x3 ] = [ -1/2, 1, -1/2 ]
For λ2 = 2, we have:
[ -5-2 1 2 ] [ x1 ] [ 0 ]
[ 0 -2-2 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3-2] [ x3 ] [ 0 ]
which simplifies to:
[ -7 1 2 ] [ x1 ] [ 0 ]
[ 0 -4 0 ] [ x2 ] = [ 0 ]
[ 4 2 -5 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -2/3 x2
x3 = -4/3 x2
So the eigenvector for λ2 = 2 is:
v2 = [ x1, x2, x3 ] = [ -2/3, 1, -4/3 ]
For λ3 = -4, we have:
[ -5+4 1 2 ] [ x1 ] [ 0 ]
[ 0 -2+4 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3+4] [ x3 ] [ 0 ]
which simplifies to:
[ -1 1 2 ] [ x1 ] [ 0 ]
[ 0 2 0 ] [ x2 ] = [ 0 ]
[ 4 2 1 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -2/5 x2
x3 = 1/2 x2
So the eigenvector for λ3 = -4 is:
v3 = [ x1, x2, x3 ] = [ -2/5, 0, 1/2 ]
To determine matrix A's sign definiteness, we must compute the determinant of all of A's primary submatrices. A square submatrix generated by eliminating the equal amount of rows and columns from the top left corner of A is known as a primary submatrix.
The principal submatrices of A are:
A1 = [-5]
A2 = [ -5 1 ]
[ 0 -2 ]
A3 = [ -5 1 2 ]
[ 0 -2 0 ]
[ 4 2 -3 ]
The determinants of these matrices are:
det(A1) = -5
det(A2) = (-5)(-2) - (0)(1) = 10
det(A3) = (-5)(-2)(-3) + 2(0)(4) + (1)(0)(2) - (-3)(1)(4) - 2(0)(-5) - (-2)(2)(-5) = -92
Because A1's determinant is negative, A is not positive definite. A is not negative definite since the determinants of A1 and A2 have different signs. As a result, A is infinite.
Solve the equation.
Sin 0= -0.5; The angle must be 270< 0 < 360°
The value of tetha is 330°
What are positive Angles?If a ray rotates in an anticlockwise direction, then the angle formed as a product of the rotation is called a positive angle.
In other words if it rotates in clockwise direction, it is a negative angles.
If sin(tetha) = -0.5
to find the value of tetha we multiply both sides with the inverse of sin
therefore;
tetha = sin^-1(-0.5)
tetha = -30
therefore -30 is a negative angle, to find the positive angle of tetha, we add 360
therefore tetha = -30+360
= 330°
therefore the value if tetha that will be greater than 279 but less than 360 is 330°
learn more about positive Angles from
https://brainly.com/question/31173978
#SPJ1
using the gcf, what is the factored form of 75
Answer:
The prime factorization of 75 is:
75 = 3 * 5^2
The greatest common factor (GCF) of the number 75 is 1, since 1 is the highest factor that can be shared by all the prime factors of 75.
Therefore, the factored form of 75 using the GCF is:
75 = 1 * 3 * 5^2
PLEASE MARK BRAILYEST! :D
In a particular class of 29 students, 11 are men. What fraction of the students in the class are women?
Answer:
Step-by-step explanation:
Q:
In a particular class of 29 students, 11 are men. What fraction of the students in the class are women?
A:
29-11=18
18/29 are women
Prove that there exists infinitely many integers $n$ such that $n^2+1$ is squarefree. (a square-free integer is an integer which is divisible by no square number other than 1.)
Answer:
To prove that there exist infinitely many integers n such that n^2 + 1 is squarefree, we can use a proof by contradiction.
Assume the contrary, that there are only finitely many integers n such that n^2 + 1 is squarefree. Let's denote these integers as n_1, n_2, ..., n_k, where k is a finite positive integer.
Consider the number N = (n_1^2 + 1) * (n_2^2 + 1) * ... * (n_k^2 + 1) + 1.
Note that N is an integer and is greater than each of the numbers n_i^2 + 1 for i = 1 to k. Since n_i^2 + 1 is squarefree for each i, N is also squarefree, as it is not divisible by any square number other than 1.
However, N cannot be equal to any of the n_i^2 + 1, as N is strictly greater than each of them. This contradicts our assumption that n_1, n_2, ..., n_k are all the integers such that n^2 + 1 is squarefree.
Therefore, our assumption must be false, and there exist infinitely many integers n such that n^2 + 1 is squarefree. This completes the proof by contradiction.
Step-by-step explanation:
How many minutes does it take to travel 11 miles if your average speed is 55 miles per hour?
(Remember to convert 1 hour = 60 minutes)
Answer:
12 minutes
Step-by-step explanation:
11/x = 55/60
11 x 5 = 55
60/5=12
12.01 minutes
time = distance / speed
where distance is the distance traveled, speed is the average speed of the travel, and time is the time taken to cover the distance.
We are given that the distance traveled is 11 miles and the average speed is 55 miles per hour. To convert the speed to miles per minute, we can divide it by 60 since 1 hour is equal to 60 minutes:
55 miles per hour = 55/60 miles per minute
= 0.9167 miles per minute (rounded to four decimal places)
Now we can substitute the values into the formula:
time = distance / speed
= 11 miles / 0.9167 miles per minute
≈ 12.01 minutes (rounded to two decimal places)
Therefore, it would take approximately 12.01 minutes to travel 11 miles at an average speed of 55 miles per hour.
*IG:whis.sama_ent
'If clothes are returned, put them on the rail so
they can be reshelved. The blue rail is the one I
mean.'
Choose the clearest and most concise
restatement.
O 'When returning, put clothes on the blue
rail for reshelving.'
O 'Returned clothes go on the blue rail for
reshelving.'
'To return clothes, put them on the blue
reshelving rail.'
'The blue rail is for returned and reshelved
clothes.'
O 'To reshelve clothes, put them on the blue
rail.'
find inverse f(x)=x-3/x+4, g(x)=4x+3/1-x
Answer:
1984
________________________________________________________
Given:
To find the inverse of f(x), we first switch x and y and then solve for y. So, x = y-3/y+4, which we can rewrite as x(y+4) = y-3. Simplifying, we get xy + 4x = y-3, and then we can isolate y on one side: y-xy = 4x-3. Factoring out y on the left side, we get y(1-x) = 4x-3, and then we can divide both sides by (1-x) to get y = (4x-3)/(1-x). This is our inverse function.
Find:
To find the inverse of g(x), we follow the same process of switching x and y and solving for y. So, x = 4y+3/1-y, which we can rewrite as x(1-y) = 4y+3. Simplifying, we get -xy + y = 4x+3, and then we can isolate y on one side: y(-x+1) = 4x+3. Dividing both sides by (-x+1), we get y = (4x+3)/(-x+1). This is our inverse function.
Solve:
As for the given set of values, we have 187, 191, 202, 209, 218, and 1984. The outlier is obviously 1984, and its presence will not affect the range because the range is simply the difference between the largest and smallest values, which will be the same regardless of the presence of an outlier. However, the outlier will greatly affect the interquartile range, which is the difference between the upper and lower quartiles. This is because the upper and lower quartiles are the median of the upper half and lower half of the data, respectively, and including an outlier in one of these halves can greatly skew the median and thus the interquartile range.
a) Find the mean and median of the following gasoline prices per gallon in California:
regular:
$
3.14
$3.14, mid-grade:
$
3.21
$3.21, premium:
$
3.28
$3.28, diesel:
$
3.53
$3.53. Round to the nearest cent.
The calculated median and the mean gasoline prices per gallon in California are 3.25 and 4.49, respectively
Finding the median and the mean gasoline prices per gallon in California:From the question, we have the following parameters that can be used in our computation:
Prices = 3.14, 3.21, 3.28, 3.53
Start by sorting the number of prices in ascending order
So, we have
3.14, 3.21, 3.28, 3.53
As a general rule.
The median is the middle number
Using the above as a guide, we have the following:
Median = middle number = 1/2 *(3.21 + 3.28)
Evaluate
Median = middle number = 3.25
For the mean, we have
Mean = (3.14 + 3.21 + 3.28 + 3.53)/3
Evaluate
Mean = 4.49
Hence, the value of the median is 3.25
Read more about median at
https://brainly.com/question/15696302
#SPJ1
Find the partial fraction decomposition of 15/(x-7)(x+3)
Answer:
[tex]\frac{15}{(x-7)*(x+3)} = \frac{3/2}{x-7} + \frac{-3/2}{x+3}[/tex]
Step-by-step explanation:
Set up the partial fraction decomp:
[tex]\frac{15}{(x-7)*(x+3)} = \frac{A}{x-7} + \frac{B}{x+3}\\[/tex]
Multiply across:
[tex]15 = (\frac{A}{x-7} + \frac{B}{x+3})*(x+3)*(x-7)\\15 = A(x+3) + B(x-7)\\[/tex]
You can do this two ways from this point, you can plug in values for x to solve for A and B individually or set up a system of equations to find A and B
[tex]15 = Ax + 3A + Bx -7B\\Ax + Bx = 0\\3A - 7B = 15\\[/tex]
From the first equation we can see that A = -B, plugging into the second equation we get that
-10B = 15, so therefore B = -3/2 and because of the first equation A = 3/2 giving us our answer
6 Harpreet wants to put tiles on the ceiling of a room.
He has this sketch of the ceiling.
11 m
5.5 m
Harpreet knows one pack of ceiling tiles
covers an area of 3.24 m²
costs £34.95
4m
9m
Ceiling tiles can be cut and joined.
Calculate the total cost of the packs of ceiling tiles Harpreet has to buy.
(6)
The table shown represents a proportional realshipbship between a and b. Form an equation that represents the relationship between a and b and identify the constant of proportionality. Write your answer in the space provided
Answer:
y=3x
Step-by-step explanation:
y=kx
21/7=3
15/5=3
6/2=3
Each relationship in the table has a constant of proportionality of 3.
A sprinkler set in the middle of a lawn sprays in a circular pattern. The area of the lawn that gets sprayed by the sprinkler
can be described by the equation (z+6)2 + (y-9)² = 196.
What is the greatest distance, in feet, that a person could be from the sprinkler and get sprayed by it?
Answer: The greatest distance a person could be from the sprinkler and get sprayed by it is 14 feet.
Step-by-step explanation:
The equation given describes a circle with the general equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
In the provided equation, (z + 6)^2 + (y - 9)^2 = 196, we can identify the values for h, k, and r^2:
1. h = -6 (from z + 6)
2. k = 9 (from y - 9)
3. r^2 = 196
Now, we need to find the radius r, which is the greatest distance a person could be from the sprinkler and still get sprayed by it. To do this, we take the square root of r^2:
r = √196
r = 14
(b) How many ways are there to distribute two balls into four boxes if each box must have at most one ball in it if (i) both the balls and boxes are labeled? (ii) the balls are labeled, but the boxes are unlabeled? (iii) the balls are unlabeled, but the boxes are labeled? (iv) both the balls and boxes are unlabeled?
(i) distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex] . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex] (iv) to distribute the balls [tex](1+2+1)[/tex].
What is the statistical distribution?(i) Both balls and boxes are labeled:
Since one box already contains a ball, there are four options for where to place the first ball, and only three options remain for the second ball. The two balls can be distributed in [tex]4 \times 3 = 12[/tex] different ways.
(ii) Balls are labeled, but boxes are unlabeled:
There is just one method to arrange the balls if there is only one ball in each box. There are two ways to determine which box receives both balls if only one box possesses them. The statistical distribution of the balls is done in one of three ways.
(1 + 2 = 3).
(iii) Balls are unlabeled, but boxes are labeled:
There are four alternatives available to the box if they are both in the same box. If they are in different boxes, the first ball's box has two options, leaving the second ball with just one. Accordingly, there are 6 ways to divide the balls.
(4 + 2 * 1).
(iv) Both balls and boxes are unlabeled:
There is only one method to arrange the balls if there is one ball in each box. There are two methods to decide which box gets both balls if only one box has both balls.
There is just one method to arrange the balls if neither box incorporates a ball. There are therefore a total of 4 options to distribute the balls (1+2+1).
Therefore,(i) distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex] . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex] (iv) to distribute the balls [tex](1+2+1)[/tex].
Learn more about distribution here:
https://brainly.com/question/15077367
#SPJ1
URGENT HELP PLEASE PLEASE CAN YOU HELP
Answer:
1/2
Step-by-step explanation:
Let's check if this is a positive of negative slope. Remember that when checking slope, you need to read the graph from left to right.
So let's see: When we look at the graph from left to right, is it moving up or down?
It is moving up, correct!
Therfore, this must be a positive slope.
Ok, now we need to pick 2 points.
I will choose: ( 6 , 0 ) & ( 2 , -2 )
To move between those pouints, we need to move up 2 and 4 units to the right.
Slope is defined as:
Change is y over change in x
Change in y is positive 2
Change in x is positive 2
Therfore, slope is [tex]\frac{2}{4}[/tex]
or, 1/2
8) Elana's Math Class has 24 students. She miscounted the class total and
recorded it as 21 students. What is her percent error?
Find the slope of the line through these points.
(5,-3) and (-1, 6)
Answer:
-1.5
Step-by-step explanation:
Remember that the slope is the rise over the run, or: Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
[tex]\frac{6 - -3}{-1 - 5} = \frac{9}{-6} = -1.5[/tex]
So, your slope is -1.5.
(1)Consider an experiment that has N outcomes e1,e2,…,eN,where it is known that outcome ej+1 is twice as likely as the outcome ej for j=1,2,,N-1.Let Ek=E1,E2,…,Ek.Show that PEk=2k-12N-1
[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex] which is the desired equation.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information:Let P(ej) denote the probability of outcome ej for j=1,2,...,N. Then we know that:
P(ej+1) = 2P(ej) for j=1,2,...,N-1
Also, we know that the sum of probabilities of all outcomes is 1:
P(e1) + P(e2) + ... + P(eN) = 1
We can use the geometric sequence formula to find P(ek) in terms of P(e1) as follows:
[tex]P(ek) = P(e1) * (2^{(k-1)})[/tex]
Substituting for P(ej+1) in terms of P(ej) gives:
[tex]P(ej+1) = 2P(ej) = 2^1 * P(ej)[/tex]
[tex]P(ej+2) = 2P(ej+1) = 2^2 * P(ej)[/tex]
...
[tex]P(ek) = 2^{(k-1)} * P(e1)[/tex]
We can sum the probabilities of all outcomes to get:
[tex]1 = P(e1) + 2P(e1) + 2^2 P(e1) + ... + 2^{(N-1)}P(e1)[/tex]
Using the formula for the sum of a geometric series, we get:
[tex]1 = P(e1) * [(2^N - 1)/(2 - 1)][/tex]
Simplifying, we get:
[tex]P(e1) = 1/(2^N - 1)[/tex]
Substituting this value for P(e1) in the expression for P(ek) gives:
[tex]P(ek) = (1/(2^N - 1)) * (2^{(k-1)})[/tex]
Simplifying, we get:
[tex]P(ek) = 2^{(k-N)} / (2 - 1/2^{(N-k+1)})[/tex]
Multiplying by 2/2, we get:
[tex]P(ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]
Substituting k=N, we get:
P(Ek) = 1/2
Substituting k=1, we get:
[tex]P(E1) = 2^{(N-1)} / (2^N - 1)[/tex]
Therefore, we have shown that:
[tex]P(Ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]
for k=1,2,...,N.
To show that PEk=2k-1/2N-1, we can substitute k=N-j+1 for j=1,2,...,N:
[tex]PEk = P(EN-j+1) = 2^{(N-j)} / (2^j - 1)[/tex]
Letting t = j-1, we can rewrite this as:
[tex]PEk = 2^{(N-t-1)} / (2^{(t+1)} - 1[/tex]
Multiplying the numerator and denominator by 2, we get:
[tex]PEk = 2^{(N-t)} / (2^{(t+2)} - 2)[/tex]
Substituting t = N-k, we get:
[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]
which is the desired result.
To know more about equation visit:
https://brainly.com/question/29174899
#SPJ1
Which of these is found in only the pretest summary?
O a. df
O b. mean
O c. variance
O d. observations
The correct answer is d. observations, which is only the pretest summary.
Define the term pretest summary?A pretest summary is a summary of the data collected during a preliminary test or trial run.
The correct answer is d. observations.
The pretest summary is a summary of the data collected during a preliminary test or trial run, and it typically includes summary statistics such as the mean, variance, and degrees of freedom (df). However, the number of observations or sample size is typically not included in the pretest summary, as it is generally assumed to be the same as the number of observations in the full dataset. The number of observations is usually included in the full dataset summary, along with other descriptive statistics.
To know more about observations, visit:
https://brainly.com/question/15062310
#SPJ1
Wendy says that she can find the sale price of an item by multiplying by
the difference of 100% and the percent of the sale. Is Wendy correct?
Explain and give an example.
Answer:
yes she is correct
Step-by-step explanation:
write the integer as a product of two integers such that one of the factors is a perfect square
27
27 can be written as a product of 3 and 9, where 9 is a perfect square.
What is perfect square?In mathematics, a perfect square is an integer that is equal to the square of another integer. In other words, a perfect square is a non-negative integer that can be expressed as the product of an integer with itself.
According to given information:To write 27 as a product of two integers such that one of the factors is a perfect square, we need to find a perfect square that divides 27.
The perfect square that divides 27 is 9, which is equal to [tex]3^2[/tex].
So, we can express 27 as the product of two factors, 3 and 9. One of the factors, 9, is a perfect square because it is equal to [tex]3^2[/tex]. Therefore, we have written 27 as a product of two integers where one of the factors is a perfect square.
We can also express 27 as 1 x 27 or 27 x 1, but neither of these representations includes a perfect square as a factor.
To know more about perfect square visit:
https://brainly.com/question/27307830
#SPJ1
Prove the proposition following this:
The proposition can be proven by showing that the left and right cosets of H in G form a partition of G.
How to prove the proposition ?As H is a G subgroup, it comprises the identity element e within G. For any g element in G, the left coset gH comprises ge = g and the right coset Hg contains eg = g. Thus, there are non-empty left as well as right cosets.
G's each element belongs to both the left and the right cosets of H. Hence, all left (or right) cosets' union in G covers every G element. The left and right cosets of H in G build non-empty subsets that do not intersect with one another. Their union equals G; thus, they certainly construct a partition for G.
Find out more on propositions at https://brainly.com/question/30027013
#SPJ1
what's the area of a circle with a 74ft diameter use 3.14 for pie
Area of a circle is given by
[tex]\text{A} = \pi \times r^2[/tex]
We need to know the radius
[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]
[tex]\text{r} = \dfrac{\text{74}}{2}[/tex]
[tex]\text{r} = 37 \ \text{mm}[/tex]
The radius is 37 mm and pi = 3.14
[tex]\text{A} = 3.14 \times (37)^2[/tex]
[tex]\text{A} = \boxed{\bold{4298.66 \ \bold{mm}^2}}[/tex]