the limit will go to infinity or negative infinity (depending on the sign of the function).
How do you know if a limit is infinity or negative infinity?
The limit as x approaches zero would be negative infinity, since the graph goes down forever as you approach zero from either side: As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity (depending on the sign of the function).
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x² = 5x + 6 = 0 if and only if x = 2. True False
Answer:
Did you mean x^2 + 5x + 6?
Step-by-step explanation:
If so, then the answer would be x=-2 or x=-3
Step 1: Factor left side of equation.
(x+2)(x+3)=0
Step 2: Set factors equal to 0.
x+2=0 or x+3=0
x=−2 or x=−3
suppose you want to distribute 10 candies among 5 kids such that each kid gets atleast one candy. in how many ways can you distribute the candies? (all 10 pieces of candies are identical, but the kids are distinct.)
There are a total of 126 ways to distribute the 10 identical candies among the 5 distinct kids.
A combination is also called a selection. A combination corresponds to a selection of things from a given set of things. It is Denoted by
ⁿCᵣ = n!/r!(n-r)!
the number of unique r selections fromaset of n objects.
We have given that,
Total number of candies for distribution = 10
number of kids who take the candies = 5
Candies are distributed among the kids such that each kid has atleast one candy.
Here, candies are identical and kids are distinct.
Number of ways in which 10 identical candies can be divided among 5 kids if each kid must get at least one candy. The problem can be solved using the combination formula with
n = 5, k = 10.
= ⁽ᵏ⁻¹⁾Cₙ₋₁· = ⁹C₄ = 126 ways to do this.
So, there are 126 ways to distribute the candies among the five kids.
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Solve the following exponential equation by first writing it in the logarithmic form and then using a calculator to solve it to 2 decimal places. 6 = 170 2 = log T =
The value of x from the exponential equation is 2.866.
Logarithm:
A logarithm is a power to which a number must be raised to get some other number.
Here we have to find the value of x.
The equation is given:
[tex]6^{x}[/tex] = 170
Taking logarithms on both sides, we have:
log [tex]6^{x}[/tex] = log 170
x log 6 = log 170
x = log 170 / log 6
= 2.230/ 0.778
= 2.866
Therefore the value of x is 2.866.
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How do you prove the SSS congruence theorem?.
When one triangle's three sides are equal to the corresponding three sides of another triangle, two triangles are said to be congruent.
Triangle ABC and triangle PQR, where AB = PQ, BC = QR, and AC = PR.
Triangle ABC is comparable to PQR, therefore proving
Assuming triangle ABC's longest side is BC, triangle PQR's longest side is QR.
As a result, the angles RQS = angle CBA, QRS = angle BCA, and they combine at SQ and SR.
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In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California. In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem. PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34. The standard error for the difference in proportions is 0.011.
Researchers want to decrease the margin of error by adjusting the confidence level. Which confidence interval will have the smallest margin of error (MOE)?
a) 90% confidence interval
b) 95% confidence interval
c) 99% confidence interval
90% confidence interval will have the smallest margin of error.
What is global warming?
Long-term changes in temperature and weather patterns are referred to as climate change. These changes may be organic, but since the 1800s, human activity has been the primary cause of climate change. This is primarily because burning fossil fuels, such as coal, oil, and gas, releases gases that trap heat.
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California.
In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem.
PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34.
The standard error for the difference in proportions is 0.011.
The correct option is (a).
As the confidence level decreases margin of error decreases.
So 90% confidence interval will have the smallest margin of error.
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Alex competes in 100 m wheelchair races. He calculates the information
below using his last 4 race times.
His minimum race time was 18.9 s.
The range of his race times was 5.2 s.
The median of his race times was 22.3 s.
The mode of his race times was 24.1 s.
If Alex includes a new race time of 24.9 s in his calculations, how much will
the mean change by?
Give your answer in seconds (s).
With including a new race time of 24.9s the mean will change from 21.9s to 22.5s by 0.6s
What is mean?
The mean is the average or the most common value in a collection of numbers.
In statistics, it is a measure of central tendency of a probability distribution along median and mode.
It is also referred to as an expected value.
According to the given question:
His initial mean would be calculated by:
His minimum race time = 18.9s
The maximum race time = 18.9 + 5.2 = 24.1s
Since the mode is also 24.1, there are two 24.1s races.
Since the median is 22.3s and the number of race times is even, the final race time can be calculated by:
24.1 - 22.3s = 1.8s
22.3 - 1.8 = 20.5s
So the race times are 18.9s, 20.5s, 24.1s and 24.1s.
This means that his initial mean was ( 18.9 + 20.5s + 24.1 + 24.1)/4 = (87.6)/4 = 21.9s
With the new race time, the equation will change to (87.6 + 24.9)/(4+1)= 112.5/5= 22.5s
So the mean change would be 22.5 - 21.9 = 0.6 s
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Alton estimated that 230 people attended the band concert. The actual count for attendance was 200 people. Find the percent of error.
The percentage of error in the estimation of Alton is:
13.04%
Given:
Alton estimated that 230 people attended the band concert.
The actual count for attendance was 200 people.
we are asked to determine the percent of error = ?
Percent error
Using this formula
Percent error=Actual attendance -Estimated attendance/Actual attendance
Let plug in the formula
Percent error=230-200/230
Percent error=30/230
Percent error=0.1304×100
Percent error=13.04%
Hence we get the percentage error as 13.04%.
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which of the following is correct about a probability distribution? a. sum of all possible outcomes must equal 1 b. outcomes must be mutually exclusive c. probability of each outcome must be between 0 and 1 inclusive d. all of the above
The option that is correct about a probability distribution is D. All or the above.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
In this case, the sum of all possible outcomes must equal 1, the outcomes must be mutually exclusive and the probability of each outcome must be between 0 and 1 inclusive
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I think I fixed it. anyway please HeLp
Answer:
the answer would be 3 and the power that is being compose is 2
A race track has a diameter of 350 ft. How far does a car drive if it completes one lap
around the track?
1) 843 ft
2) 1,099 ft
3) 1,653 ft
4) 2,198 ft
The required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.
Given that,
A race track has a diameter of 350 ft. how far a car drive if it completes one lap is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
Diameter = 350 ft
Circumference = πD
Circumference = 3.14 × 350 = 1099ft
Thus, the required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.
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Between which two consecutive whole numbers does v87 lie?
The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.
Given that,
The number is square root of 87 which is√87.
We have to find the two consecutive whole numbers does √87 lies.
We know that,
What is an whole number?In the category of numbers known as "whole numbers," all natural numbers and 0 are included. They are a subset of "real numbers," which are those that don't contain fractions, decimals, or negative numbers.
The √87 lies between √81 and √100
Which we can write as
√81<√87<√100
9<√87<10
Therefore, The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.
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in multiple regression analysis, there can be any number of dependent variables but only one independent variable there must be only one independent variable the coefficient of determination must be larger than 1 there can be several independent variables, but only one dependent variable
In multiple regression analysis, there can be several independent variables, but only one dependent variable
The link between several independent or predictor variables and one dependent or criterion variable is typically explained using multiple regression. The constant term, along with a number of independent variables and their corresponding coefficients, are used to model a dependent variable. Thus, it refers to a regression model that uses two or more predictor variables.
It is a statistical method that can be used to examine the relationship among a single dependent variable and a number of independent variables. The variables are quantified because an equation is used to represent the model. Although the independent variables are almost always positive, their coefficients occasionally aren't.
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Annie was given two pieces of information and must write the equation of a line. She knows the line crosses the y-axis at the point (0,6) and has a slope of 7. What is the equation of the line?.
The correct answer is the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.
We know a point which is (0,6) and a slope which is 7. It's a unique point, where we have to find its equation. Firstly, it is the y intercept because
x = 0. We can use the equation for a line in the form of slope-intercept
The required equation of line formula is y= mx+c where m is the slope that is 7 and c is the y intercept that is 6.
where y = 7x + 6
The general equation of a straight line is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept, it represents the equation of a straight line with gradient m and intercept c on the y-axis.
Hence, the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.
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What does a higher mean absolute deviation mean?.
Higher mean absolute deviation is an example of a measure of variability and range. It give us some information about how spread out the data in a data set is. When used together with measures of center like the mean and median, they can give us a useful overview of the data set.
For an example,
A chef wants to hire someone to work in his kitchen. There are two candidates: Sally and Nader. To test their abilities, he times how long it takes them to make each of four meals and records the data in two tables.
He decides to calculate the mean time it took each candidate to make the four meals; he is planning to hire the candidate with the lower (quicker) mean time.
The mean time it takes Sally to make a meal is
= 3+5+7+9 / 4
=24/6
= 6 minutes
The mean time it takes Nader to make a meal is
= 5+6+5+8 / 4
=24/4
= 6 minutes
After having mean times same he doesn't classify which one is best he used their statical graphs.
For Sally, the mean absolute deviation of her times is the mean of the distances,
=4+1+2+3 / 4
=2.5
For Nader, the mean absolute deviation of his times is
= 1+0+1+2 / 4
=1
The chef sees that the mean absolute deviation of Nader’s times is lower than the mean absolute deviation of Sally’s times. This shows that Nader is more consistent in his cooking times and agrees with what we observed from the bar graphs.
Which means that the higher mean absolute deviation occurs less consistency in the mean absolute deviation.
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Does the altitude of an isosceles triangle bisect the vertex angle?.
Yes, the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.
Given, an isosceles triangle ABC
now, the two sides are equal
AB = AC
now, drawing an altitude AD in the triangle.
So, in triangles ADB and ADC
AB = AC (given)
AD = AD (common)
∠ADB = ∠ADC (90°)
So, by RHS congruence rule
ΔADB ≅ ΔADC
and therefore ∠BAD = ∠CAD (by CPCT)
Hence, Yes the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.
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SOMEONE PLEASE HELP ☹️
Answer: A is the answerrrrrr
Step-by-step explanation:
How do you find the length and width of a rectangle when given the area?.
if you additionally recognize the perimeter of the rectangle, you could use that data to locate possible values for length and width. The area of a rectangle (A) is related to the length (L) and width (W) of its facets by the following relationship: A = L × W
ShapeIn Euclidean aircraft geometry, a rectangle is a quadrilateral with four right angles. it may additionally be defined as an equiangular quadrilateral, given that equiangular method that all of its angles are identical (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with 4 facets of an equal period is a square. The term rectangular is sometimes used to refer to a non-square rectangle. A rectangle with vertices ABCD might be denoted as Rectangle ABCD.
The phrase rectangle comes from the Latin rectangles, which is a mixture of rectus (as an adjective, right, proper) and angelus (attitude).
A crossed rectangle is a crossed (self-intersecting) quadrilateral that consists of two opposite aspects of a rectangle in conjunction with the two diagonals (consequently simplest aspects are parallel). it's miles a special case of an antiparallelogram, and its angles aren't right angles and now not all same, although opposite angles are the same. different geometries, along with spherical, elliptic, and hyperbolic, have so-called rectangles with opposite facets same in the period, and the same angles that aren't right angles.
Rectangles are worried in many tiling issues, including tiling the aircraft by means of rectangles or tiling a rectangle through polygons.
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A 5. 5% 20-year municipal bond is currently priced to yield 7. 2%. For a taxpayer in the 33% marginal tax bracket, this bond would offer an equivalent taxable yield of:.
Using the Equivalent Taxable yield formula ,
the equivalent Taxable yield for a taxpayer is 10.75%.
Equivalent Taxable yield :
Tax-equivalent yield is determined by taking the yield of a tax-exempt bond and dividing it by one minus an investor's federal income tax bracket.
Tax-equivalent yield is a way to measure the return on a taxable bond or other investment to make it equal to the return associated with a tax-exempt bond or investment.
Formula:
Tax-equivalent yield = interest rate ÷ (1 – tax rate)
We have given that
Marginal tax bracket or tax rate = 33%
currently priced yield = 7.2 %
Equivalent taxable yield = Yield / ( 1 - Tax% )
= 7.2% / ( 1 - 33% )
= 0.072 /(1-0.33)
= 0.072/0.67
= 0.10746
= 10.75%
Hence, total equivalent Taxable yield for taxpayer is 10.75%.
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A baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground. How tall is the building? [neglect friction. ].
After solving, the height of the building is 15.19 m tall.
In the given question, a baseball dropped from the roof of a tall building takes 3. 1 seconds to hit the ground.
We have to find the height of the building.
Initial Velocity, denoted as u, is the velocity at time interval t = 0. It is the speed at which motion first occurs.
Initial velocity u=0
Time t=3.1 seconds
Let height of the cliff is h.
So s=ut+at^2/2
Now putting the value
s = 0+(9.8×3.1)/2
s = 30.38/2
s = 15.19 m
Hence, the height of the building is 15.19 m tall.
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the short-run quantity of output supplied by firms will exceed the natural level of output when the actual price level the price level that people expected.
The price level that people expected rise above.
What is the term for price increases?
The rate at which prices rise over a given time is called inflation. A country's cost of living or overall increase in prices are two examples of broad measures of inflation.
What happens when the price level rises above expectations?
The economy's leading indicators are price levels; Inflation occurs when prices rise in response to increased demand, while deflation occurs when prices fall in response to decreased demand.
What happens when the price rises?
The average price of all goods and services sold rises when an economy's price level rises. The percentage increase in a nation's price level over some time, typically a year, is what is used to calculate inflation. This indicates that inflation is taking place during the time when prices rise.
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Which set of data has a mean of 15 a range of 22 a median of 14 and a mode of 14?.
3,14,19,25,14 is set of data has a mean of 15 a range of 22 a median of 14 and a mode of 14.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
First, arrange the given set in ascending order.
3,14,19,25,14
Ascending order = 3, 14, 14, 19, 25
Mean = sum of observations/total observations
(3+14+14+19+25)/5
75/5
15
Median is the middle number of the data.
3, 14, 14, 19, 25
14 is the median
The Mode is the number that occurs most number of times.
3, 14, 14, 19, 25
In the given data, 14 occurs two times. so, 14 is the mode.
Range:
Range is highest value - lowest value
3, 14, 14, 19, 25
=> 25 - 3 =22
so, range is 22.
Hence, the required set of data is 3,14,19,25,14
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The equation of the graph
is y = pqx where p and q are
positive constants.
Find the values of p and q.
a)
p=
b)
q=
The values of p and q are 3 and 2.
Given:
The equation of the graph is y = pq^x where p and q are positive constants.
From the graph:
curve linear course points are:
(0,3) and (1,6)
substitute points in y = pq^x
3 = pq^0
3 = p*1
p = 3
y = pq^x
6 = pq^1
6 = p*q
6 = 3*q
divide by 3 on both sides
6/3 = 1
q = 2
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No matter which brand he chooses, gareth will pay for the freezer on his credit card, which has an apr of 9. 31%, compounded monthly. It takes gareth eighteen months to pay off a brand s freezer and four years to pay off a brand r freezer. Assuming that gareth makes no other purchases or payments with his credit card, over the next ten years, which brand of freezer will have a lower lifetime cost, and how much lower will it be? (round all dollar values to the nearest cent. ).
The correct option is (a) Gareth will choose the Brand R credit card for the freezer because it is $548.18 less expensive than the Brand S.
An annual percentage rate, or APR, is used to express the interest rate that is applied to the principal amount of a loan.
The credit card's yearly percentage rate is 9.31%.
Gareth takes four years to pay off a Brand R freezer compared to just 18 months for a Brand S freezer.
Overall, ten years have gone.
To determine which credit card has the lowest lifetime cost for a freezer, we must compare the APRs of the two cards.
Let's say there are 1000 freezers. As a result, the APR for 18 months will be lower because the interest rate's duration is shorter.
The B and R will therefore be $548.18 less expensive than Brand S, according to a comparison of the APR.
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How many prime numbers are multiples 3?.
Answer:
the only positive multiple of 3, which is a prime number is 1×3=3 itself.
hope this helps! :)
Step-by-step explanation:
quadrilateral $abcd$ is a square. let $a,$ $b,$ $c$ be parallel lines passing through $a$, $b$, $c$, respectively. the distance between lines $a$ and $b$ is $12,$ and the distance between lines $b$ and $c$ is $17$. find the area of square $abcd$.
The area of square abcd is be parallel lines passing through $a$, $b$, $c$, respectively is the 433.
Squares are quadrilaterals with four congruent aspects and four proper angles, and additionally they have units of parallel aspects. Parallelograms are quadrilaterals with units of parallel aspects. Since squares have to be quadrilaterals with units of parallel aspects, then all squares are parallelograms.
Here we have the values the distance between lines a and b is 12, and the distance between lines b and c is 17.
The distance is 12 and 17
x^2 = 12^2 + 17^2 = 144 +289 = 433
433 is the total that is the area of square of abcd.
Thus the area = 433.
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If you are conducting a survey to determine the public opinion on whether hockey is too dangerous, which of the following samples would be the least biased and most not useful ?
B: shoppers at the mall
The shoppers at the mall would be the least biased and the hockey fans would be most not useful for the survey
For avoiding bias the best option would be one that most diverse individuals. If we are evaluating violence in hockey we should avoid hockey fans, as the probably would think that violence is something bad and they do not want their sport to be bad.
The hockey fans would be most not useful for the survey
If there is a correlation between football fans and hockey fans, for example, that most of hockey fans also watch football games (which is very likely because sports fans tend to watch more than one sport), we will have the same kind of bias than above.
A similar reasoning can be thought with sportscasters, as they are peole that are very interested in sports and their opinion can be biased. Also, as mos sportscasters are men, you got a gender bias.
However, in a shopping mall we can have the most random sample. There will be interviewed people that love hockey, people that do not love hockey. we avoid age bias, as in a shopping there are people of every age. we can expect to find women and men, differently to the other options. So, this is the best option to run a survey about violence/danger in hockey.
Therefore, the shoppers at the mall would be the least biased and the hockey fans would be most not useful for the survey.
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Dylan buys 2 sodas and 3 teas for £2.
Caroline buys 5 sodas and 3 teas for £2.75.
Work out the cost of one soda and one tea.
Answer:
.4
=soda,
0.5=tea
Step-by-step explanation:
Answer:
one soda costs 0.25 euros
One tea costs 0.5 euros
Step-by-step explanation:
we make a system of equations
S- soda
t- tea
2s+3t=2
5s+3t=2.75
we have to isolate a variable because I like to use substitution method best
2s+3t=2
-3t. -3t
2s=2-3t
/2. /2. /2
s=1-1.5t
5(1-1.5t)+3t=2.75
5-7.5t+3t=2.75
5-4.5t=2.75
-5. -5
-4.5t=-2.25
/-4.5. /-4.5
t=0.5
One tea is 0.5 euros
Now to find one soda we just fill it in
2s+3(0.5)=2
2s+1.5=2
-1.5. -1.5
2s=0.5
/2. /2
s=0.25
One side cost 0.25 euros
Hopes this helps please mark brainliest
Ciphers, such as the enigma machine, that rearrange the sequence of characters based on a fixed rule are known as ______________.
Ciphers, such as the enigma machine, that rearrange the sequence of characters based on a fixed rule are known as substitution cipher.
A type of encryption known as a replacement cypher employs a key to substitute certain plaintext chunks with the ciphertext in a predetermined manner.
Single letters, pairs of letters, triplets of letters, combinations of the aforementioned, etc. are all acceptable "units." The receiver decodes the text using the inverse substitution technique to ascertain what the original message was.
Cyphers for transposition and substitution are similar. In a transposition cypher, the plaintext's units are not changed; instead, they are rearranged in a brand-new, frequently extremely complex pattern. A substitution cypher modifies the units themselves while preserving the order of the units from the plaintext in the ciphertext.
The substitution cypher can take many different shapes. If a cypher only functions with single letters, it is referred to as a simple substitution cypher; a polytrophic cypher, on the other hand, functions with larger groups of letters.
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If she made the last free throw; then her probability of making the next one is 0.7 . On the other hand, If she missed the last free throw, then her probability of making the next one is 0.3. Assume that state is Makes the Free Throw and that state 2 is Misses the Free Throw: (1) Find the transition matrix for this Markov process_
The transition matrix for Markovian is,
[ 0.7 0.3 ]
[ 0.3 0.7 ]
What is meant by probability?Probability is an area of mathematics that deals with numerical descriptions of the likelihood of an event happening or a proposition being true. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.
Probability is simply the possibility of something happening. When we are confused about the outcome of an event, we might discuss the probabilities of certain outcomes—how likely they are. Statistics is the study of occurrences based on probability.
Let [tex]S_{i}[/tex], i = 1, 2, is denoted for state i.
If [tex]T_{ij}[/tex] is denoted for the transition from [tex]S_{j}[/tex] to [tex]S_{i}[/tex],
The transition probabilities are given by:
Probability(T₁₁) = 0.7
Probability(T₂₁) = 1- Probability(T₁₁) = 1 - 0.7 = 0.3
Probability(T₁₂) = 0.3
Probability(T₂₂) = 1- Prob(T₁₂) = 1 - 0.3 = 0.7
So, the transition matrix for Markovian is,
[ 0.7 0.3 ]
[ 0.3 0.7 ]
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What is a central angle part of?.
In Circles the central angle is the angle measures between two radii of the circle.
As shown in the figure:
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