AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240
Permutation:
In probability, permutation refers the arrangement of objects in a definite order.
Given,
Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.
Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.
While we looking into the given question, we know that,
Total number of games = 6
Possible values = 3 ( win, loss, or draw)
Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,
=> 6! / (6 - 3)!
=> 6! / 3!
=> 120
Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,
=> 6!/ (6 - 3)!
=> 120
So, the number of ways can Alice win or draw exactly three times is
=> 120 + 120 = 240
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the screenshot is the work that i need help with
Answer:
Step-by-step explanation:
Find the least common denominator (LCD) of 11/10 and 4/15 .
I think its 30!
Please let me know if its right!
Convert to standard form:
[tex]y = \frac{5}{12}x - \frac{1}{2}[/tex]
Show work please
Answer: x=12y+6/5
Let's solve for x.
y=5/12x − 1/2
Step 1: Flip the equation.
5/12x + −1/2 =y
Step 2: Add 1/2 to both sides.
5/12x + −1/2 + 1/2 = y + 1/2
5/12x = y + 1/2
Step 3: Divide both sides by 5/12.
5/12x 5/12 = y + 1/2/5/12
x=12y + 6/5
Which of these tables (if any) represent a proportional relationship?
Answer: none of them
Step-by-step explanation:
they are not equal and dont look right i dont think im sorry if i get it wrong
A line passes through (9,-1) the point and has a slope of 2/3.
Write an equation in slope-intercept form for this line.
Answer:
y = 2/3 x - 7
Step-by-step explanation:
y = mx + b
y = 2/3 x + b
-1 = 2/3 × 9 + b
-1 = 6 + b
b = -7
y = 2/3 x - 7
Answer:
y = 2x-17
Step-by-step explanation:
We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-1 = 2(x-9)
Distribute
y-1=2x-18
Add 1 to each side
y-1+1 = 2x-18+1
y = 2x-17
This is slope intercept form
Step-by-step explanation:
a survey, 29 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $35.9 and standard deviation of $9.5. estimate how much a typical parent would spend on their child's birthday gift (use a 98% confidence level). give your answers to 3 decimal places. express your answer in the format of ¯ x ± e. $ ± $
Using test statistic z, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.
In the given question we have to estimate how much a typical parent would spend on their child's birthday gift using a 98% confidence level.
Given in the question
Number of sample (n) = 29
Sample mean (X) = 35.9
Sample standard deviation (S) = 9.5
We need to calculate 98% confidence interval which can be calculated as
CI = X± [tex]t_{\alpha/2}[/tex] * S/√n
Here confidence level CI = 0.98
Level of significance (\alpha) = 1-0.98=0.02
α/2 = 0.01
Degree of freedom (df) = n-1 = 29-1 = 28
from t table we found [tex]t_{\alpha/2}[/tex] = 2.821
So 98% confidence interval is
CI = 35.9 ± 2.821* 9.5/√29
CI = 35.9± 2.821* 9.5/5.39
CI = 35.9± 2.821*1.763
CI = 35.9± 4.973
CI = (35.9-4.973, 35.9+4.973)
CI = (30.927, 40.873)
30.927 < μ < 40.873
So, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.
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a rhombus has side lengths of 10 and a diagonal measuring 12. what is the length of the other diagonal?
When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.
What is rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.
Here,
The length of side=10 inch
The length of diagonal= 12 inch
Let the length of diagonal be x.
6²+(x/2)²=10²
(x/2)²=64
x/2=8
x=16 inch
The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.
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Consider matrix A
135
3 5
A =
2
8 -1 3
What matrix results from -8*4?
A?
Answer:
[tex]\begin{pmatrix}24&-40&-16\\ -64&8&-24\end{pmatrix}[/tex]
Step-by-step explanation:
Each element of the matrix is multiplied by -8
an initial population of 765 quail increases at an annual rate of 16%. write an exponential function to model the quail population. what will the approximate population be after 4 years?
An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
Population growth is seen to increase at an exponential rate. We use the following to model this growth.
y = A₀(1 + r)ⁿ
where
y = value at time
A₀ = original value
r = rate of growth
n = time elapsed
An exponential function that models the quail population is set up like:
y = 765(1+0.16)ⁿ
so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,
y = 765(1+0.16)⁴
y = 765(1.16)⁴
y = 765* 1.81
to get
y = 1384.65 quails after 4 year has elapsed.
Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
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you have a set of points with a y:x constant ratio of 3:7. what is the equation of the line passing through these points?
The equation of the line passing through these points i.e (7,3 ) and (14,6) is
y = (3/7) x or 3x - 7y = 0 ,
Which is linear equation of two variables.
A linear equation is an algebraic equation of the form y = mx + b , with only one constant and one first-order (linear) term, m is the slope and b is the y-intercept.
We have given that,
the ratio of y and x is y : x = 3 : 7
So the ratio of x and y can be expressed as ,
x : y = 7 : 3 ( reverse order)
So let's consider two points as
(x₁, y₁)=(7 , 3) and (x₂, y₂) = (14 , 6)
The equation of the line passing through these points will be,
( y - y₁ )/ (y₂ - y₁) = (x - x₁)/(x₂ - x₁)
=> (y - 3)/(6-3) = (x - 7)/(14 - 7)
=> (y - 3)/3 = (x - 7)/7
=> 7(y - 3) = 3( x - 7)
=> 7y - 21 = 3x - 21
=> 7y = 3x
=> y = (3/7) x
Hence, y = (3/7) x is required equation of line.
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I NEED HELP!! IM RUNNING OUT OF TIME!!!
Domain and range of G?
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Write answers as set notation
For the given set G = {(-8, 7), (-9, 0), (3, 7)}, domain is {-8, -9, 3} and range is {7, 0, 7}.
What is domain?Domain is the values of all inputs, In a function f(x), the set of all values of x is called domain
The given set is,
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Since, domain is the set of all values of x,
And range is the set of all values of y
In the given set,
Domain = {-8, -9, 3}
Range = {7, 0, 7}
The domain is {-8, -9, 3} and range is {7, 0, 7}.
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digoxin is a drug often prescribed to treat heart ailments. the purpose of a study by parker et al. (a-4) was to examine the interactions of digoxin with common grapefruit juice. in one experiment, subjects took digoxin with water for 2 weeks, followed by a 2-week period during which digoxin was withheld. during the next 2 weeks subjects took digoxin with grapefruit juice. for seven subjects, the average peak plasma digoxin concentration (cmax) when taking water is given in the first column of the following table. the second column contains the percent change in cmax concentration when subjects were taking the digoxin with grapefruit juice [gfj (%) change]. use the cmax level when taking digoxin with water to predict the percent change in cmax concentration when taking digoxin with grapefruit juice.
Cmax (ngl/ml) with Water Change in Cmax with GFJ (%)
2.34 29.5
2.46 40.7
1.87 5.3
3.09 23.3
5.59 -45.1
4.05 -35.3
6.21 -44.6
2.34 29.5
The graph of the change in Cmax is (see in attachments).
Cmax Change in Cmax predicted percentage
2.34 29.5 22.96%
2.46 40.7 20.62%
1.87 5.3 32.14%
3.09 23.3 8.32%
5.59 -45.1 -40.47%
4.05 -35.3 -10.42%
6.21 -44.6 -52.58%
2.34 29.5 22.96%
Graph:
A graph is a logical visual representation of any data in mathematics. The correlation between the variable values is depicted on the graph. A graph is used in graph theory to depict a group of items that are interconnected in some way. In essence, the vertices or nodes of the objects are mathematical notions, and the edges are representations of the connections between the nodes. In mathematics and statistics, many graph types are used to visually display data. The study of points and lines is the focus of the field of graph theory. It is a branch of mathematics with a focus on graph analysis. The mathematical truth is visually illustrated in this image. Relationships are studied using the graph theory.
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one leg of a right triangle has length 17 inches; the hypotenuse is 31.4 inches. what is the length of the other leg of the triangle?
The length of the other leg of the triangle is 26.4 inches.
Here, we are given that one side of a right angled triangle has length 17 inches and the hypotenuse is 31.4 inches.
Now, the Pythagoras theorem states that, in a right angled triangle, the following equation holds-
[tex]hypotenuse^{2} =height^{2} +base^{2}[/tex]
we already know two of these values so we can calculate the 3rd one.
Let the length of the 3rd side be x inches.
then, substituting the values in the Pythagoras equation, we have-
[tex]31.4^{2}[/tex] = [tex]17^{2}+ x^{2}[/tex]
985.96 = 289 + [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 985.96 - 289
[tex]x^{2}[/tex] = 696.96
x = 26.4
Thus, the length of the other leg of the triangle will be 26.4 inches.
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dr. chidi anagonye studied how self-esteem (high versus low) and success on a school project (passed/succeeded or failed) influences whether students attribute the cause of the outcome to themselves or others. high scores on the dependent variable mean they attribute the outcome to themselves and low scores mean they attributed the outcome to others. below are his results. look at the graph below and select the statement that is most true about the graph:
As per dr. Chidi Anagonye, self esteem and success on school project results in low distinctiveness.
What is all about the attribution theory?The focus of attribution theory is on how people make sense of events and how this influences their perceptions and actions. Heider (1958) was the first to suggest a psychological theory of attribution, but Wener and his colleagues (e.g., Jones et al., 1972; Wener, 1974, 1986) created a theoretical framework that has grown to be a significant research paradigm in social psychology. Attribution theory assumes that people try to figure out why people do what they do, i.e., attribute causes to behavior. If someone is trying to figure out why someone else did something, they could assign one or many reasons to that action. An attribution is based on a three-stage process: (1) the person must notice or watch the activity, (2) the person must think that the behavior was done purposefully.
Education, legislation, clinical psychology, and the field of mental health have all seen extensive use of Wener's thesis. Achievement and one's self-concept are closely related. Causal attributions control how we feel about success and failure, according to Wener (1980). For example, one is unlikely to feel satisfaction in achievement or competence while obtaining a 'A' from a professor who only delivers that grade, or when defeating a tennis opponent who always loses... An 'A' from a teacher who gives few high grades, on the other hand, or a victory over a highly rated tennis player after a lot of practice has a big impact. Higher self-esteem students and students who perform well academically have a tendency to credit success to internal, stable, uncontrolled causes.
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Need Urgent help please. Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) = f(1) = f(2) = 0. find the factored form of f.
Answer:
-2
Step-by-step explanation:
8283’a
If X be a random variable taking values x1,x2,x3,….,x???? with probabilities P1,P2,P3,…..P????, respectively. Then, Var (x) is equal to …….. .
Using the probabilities the variance of x represented by Var(x) is equal to var(X) = E(X²) – [E(X)]² , where E(x) represents the expected value of x.
Given the probabilities of the random variable given by x₁ , x₂ , x₃ ,... has the probabilities of P₁ , P₂ , P₃ ...
We know that Variance is given by the formula:
[tex]Var(x) = \sigma^2=\sum_{i=1} ^n (x_i-\mu)^2px_i)\\\\=\sum_{i=1} ^n(x_i^2-2x_i+\mu^2)\\\\=E(x^2)-[E(x^2)][/tex]
We know that expected value is denoted by E(x) .
Hence the variance is denoted by var(X) = E(X²) – [E(X)]² .
In probability theory and statistics, variance is the predicted squared deviation of a random variable from its population mean or sample mean.
The scattering, or how far apart from the mean a bunch of data are from one another, is measured by variance. A few ideas that involve variance are descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
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given cos(-x) = 3/4 and tanx= √7/3, find sin(-x)
The trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
cos(-x) =cosx= 3/4
and tanx=
We need to find sin(-x)
tank is ratio of sinx and cosx
We know that tanx=sinx/cosx
√7/3=sinx/3/4
Apply cross multiplication
sinx=√7/3.3/4
sinx=√7/4
sin(-x)=-sinx=-√7/4
Hence, Trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
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2. solve the equation p2 4p = 1 by completing the square. show your work.
The value of 'p' obtained by completing the square is √5 - 2.
Define the term completing square?Completing the square is the process of engineering the quadratic equation to produce a perfect square by adding and subtracting both from sides.The given equation in the question is-
p² + 4p = 1
4 divided by half is 2, but 2 squared is 4, therefore
p² + 4p + 4 = 1 + 4
Putting that part of "b" between parenthesis is the simplest method to describe it at this point.
(p + 2)² = 5
The result of multiplying (p + 2)(p + 2) is p² + 4p + 4.
A square root from both sides is now calculated.
p + 2 = √5
p = √5 - 2
Thus, the value of 'p' obtained by completing the square is √5 - 2.
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The correct question is-
Solve the equation p² + 4p = 1 by completing square.
a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 155.1-cm and a standard deviation of 1.4-cm. for shipment, 30 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is greater than 155.8-cm. p(m > 155.8-cm)
The probability that the average length of a randomly selected bundle of steel rods is 155.8 then P = 0.174 cm
Given sample size 'n' = 30 steel rods
Mean of the Population = 155.1 cm
Standard deviation of the Population = 1.4 cm
Given x⁻ be the random variable of Normal distribution
Let x₁⁻ = 155.8cm
The probability that the average length of a randomly selected bundle of steel rods is 155.8-cm.
P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)
= P(Z <Z₂) - P(Z<Z₁)
= 0.5 +A(1.629) - (0.5 +A(0.7541)
= A(1.629) - A(0.7541)
= 0.4474 - 0.2734
= 0.1
The probability that the average length of a randomly selected bundle of steel rods is 155.8 cm = 0.174
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The value of y varies exponentially with respect to x and the 1-unit growth factor is 1.7. Which of the following is the best explanation for the meaning of this growth factor?
Whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
Whenever x changes by 1, the value of y becomes 11.7 times as large as its previous value.
Whenever x changes by 1.7, the value of y doubles its previous value.
Whenever x changes by 1.7, the value of y becomes 1 unit larger than its previous value.
Whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.7)ˣ------>equation(1)
1.7=1- unit growth factor.
When ever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.7ˣ⁺¹
y'=1.7ˣ×1.7----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ
y'=(1.7)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
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i need help on this! i did the first part though
Answer:
Winning jump = 5.474
Her best jump = 4.76
Step-by-step explanation:
4.25×1.12=4.76
4.76×1.15=5.474
OM
C2022
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Question 14
II Pause
Use this situation to answer the problem
A river in one part of the Rocky Mountains has a flow rate of 250 cubic meters of
water per second. The flow of the water can be modeled mathematically with the
function, w(t) = 250t, where w(t) represents the volume of the water in cubic
meters, at time t, in seconds.
zoom
Iluminate Education, Inc.
Type here to search
ii
C
Find the number of cubic feet of water that have flowed down the river in 5 minutes
58°F Clear
2648625 cubic feet of water that have flowed down the river in 5 minutes
How to find the number of cubic feet of water that have flowed down the river in 5 minutes?Given that:
The flow of the water can be modeled mathematically with the
function, w(t) = 250t, where w(t) represents the volume of the water in cubic meters, at time t, in seconds.
In order to find the number of cubic feet of water that have flowed down the river in 5 minutes. We'll first convert the time t = 5 minutes into seconds and then substitute it into the function. That is:
t = 5 minutes = 5 × 60 = 300 seconds
w(t) = 250t
w(300) = 250 × 300
w(300) = 75000 cubic meters
To convert to cubic feet multiply by 35.315:
w(300) = 75000 × 35.315 = 2648625 cubic feet
Therefore, the number of cubic feet of water that have flowed down the river in 5 minutes is 2648625 cubic feet
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alyssa finds the measurement of a rock sample to be 16 grams. what does she now know about the rock?
Alyssa knows the mass of the rock is 16 grams.
Measurement is a method in which the property of an object are determined by comparing them to the standard quantity.
It is important metric to express any quantity of object , things.
Some basic type of measurement are:
Time = Seconds , minutes and hours are some units which are used to represent timeLength = units are meter , centimeter etc.Weight = units included grams , kilogram , tons etc.Temperature = units for temperature is centigrade , FahrenheitAccording to the question
It is given that Alyssa finds the measurement of a rock sample to be 16 grams
Here, 18 grams is the mass of the rock
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The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
The error of type I is Despite the fact that the median age is 34, we get to the conclusion that it is not. The appropriate response to this question is option C.
A Type I error is rejecting the null hypothesis when it is actually true. It involves making inferences from statistically significant outcomes even though they might have happened by chance or for other reasons.
The probability of error will depend on the significance level (alpha or) that you choose. In order to determine the statistical likelihood of receiving your results, you established that number at the outset of your investigation (p-value).
The usual level of significance is 0.05 or 5%. The likelihood that the null hypothesis is true is only
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question a 15-foot ladder is leaning against a wall. the top of the ladder is sliding down the wall at a rate of 2 ft/sec. how fast is the bottom of the ladder moving when it is 12 feet away from the wall?
Speed the top of the ladder is sliding down = 1.6ft/sec when it is 12 feet away from the wall
15-foot ladder is leaning against a wall.
the top of the ladder is sliding down the wall at a rate of 2 ft/sec.
how fast is the bottom of the ladder moving when it is 12 feet away
Using equivalent proportion
15 ft -------------------2ft/sec
12 ft-------------------X ft/sec
Hence X = (12 x 2) ÷ 15 =1.6 ft/sec
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the national center for health statistics has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall? (round to the nearest hundredth of a percent)
If there is a 0.41% chance that an American citizen will die from falling, then the probability that you will not die from a fall is 99.59%
The chances of an American citizen will die from falling = 0.41%
The probability is the ratio of number of favorable outcomes to the total number of outcomes
The equation will be
The probability = Number of favorable outcomes / Total number of outcomes
The probability that you will not die from a fall = 1 - The chances of an American citizen will die from falling
Substitute the values in the equation
The probability that you will not die from a fall = 1 - 0.41
= 99.59%
Therefore, the probability that you will not die from a fall is 99.59%
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golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. the ratio of the length to the width for these rectangles is called the golden ratio. find the value of the golden ratio using a rectangle with a width of 1 unit
golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. The value of this golden ratio = 1/2 (1 + √5) = 1.618
Ratio:
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
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suppose i want to represent the following set of words using a phone lattice: {cattle, battle, cattles,battles}. what is the minimum number of states that i require?
⇒We can represent this phone lattice in two minimum number of ways and states to represent it.
What is phone lattice?
A state diagram, or directed network in which each node stands for a state of a system, is what is known as a phone lattice. Each edge of a phone lattice has exactly one letter. A word is represented by each route from the start node to the final/end node.
The minimum no. Of states in using a phone lattice to the given requirement is two.
We can represent this phone lattice in two minimum number of ways and states to represent it.
A dual lattice may be defined as the inclusion on the extents. We represent a lattice using a Hasse diagram of the given partial ordering on all the maximal rectangles, transitivity and reflexivity arcs that are omitted. Concepts in the given system are often known as elements of this lattice.
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Dilate A(-1,-1),D(0,2),I(3,1) by scale factor of 2 from the origin
The points after dilation will be A'(-2, -2), D'(0, 4), L'(6, 2) if the points are A(-1,-1),D(0,2),I(3,1)
What is dilation?The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.
It is given that:
Dilate A(-1,-1),D(0,2),I(3,1) by scale factor of 2 from the origin
After dilation:
A (-1,-1) --> ( -1x2 , -1x2 ) --> (-2, -2)
D (0,2) --> ( 0x2 , 2x2 ) --> (0, 4)
L (3,1) --> ( 3x2 , 1x2 ) --> (6, 2)
Thus, the points after dilation will be A'(-2, -2), D'(0, 4), L'(6, 2) if the points are A(-1,-1),D(0,2),I(3,1)
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when constructing a confidence interval for a population mean from a sample of size 10, the number of degrees of freedom for the critical value is
the Degree of freedom is 9.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
We have given,
Sample size =n=10
Degree of freedom =n-1=10-1=9
Hence the Degree of freedom is 9
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