Answer:
Step-by-step explanation:
We first examine a simple hidden Markov model (HMM). We observe a sequence of rolls of a four-sided die at an "occasionally dishonest casino", where at time t the observed outcome x_t Element {1, 2, 3, 4}. At each of these times, the casino can be in one of two states z_t Element {1, 2}. When z_t = 1 the casino uses a fair die, while when z_t = 2 the die is biased so that rolling a 1 is more likely. In particular: p (x_t = 1 | z_t = 1) = p (x_t = 2 | z_t = 1) = p (x_t = 3 | z_t = 2) = p (x_t = 4 | z_t = 1) = 0.25, p (X_t = 1 | z_t = 2) = 0.7, p (X_t = 2 | z_t = 2) = p (X_t = 3 | z_t = 2) = p (X_t = 4 | z_t = 2) = 0.1. Assume that the casino has an equal probability of starting in either state at time t = 1, so that p (z1 = 1) = p (z1 = 2) = 0.5. The casino usually uses the same die for multiple iterations, but occasionally switches states according to the following probabilities: p (z_t + 1 = 1 | z_t = 1) = 0.8, p (z_t = 2) = 0.9. The other transition probabilities you will need are the complements of these. a. Under the HMM generative model, what is p (z1 = z2 = z3), the probability that the same die is used for the first three rolls? b. Suppose that we observe the first two rolls. What is p (z1 = 1 | x1 = 2, x2 = 4), the probability that the casino used the fair die in the first roll? c. Using the backward algorithm, compute the probability that we observe the sequence x1 = 2, x2 = 3, x3 = 3, x4 = 3 and x5 = 1. Show your work (i.e., show each of your belief for based on time). Consider the final distribution at time t = 6 for both p (z_t = 1) = p (z_t = 2) = 1.
ANSWER:
Let say we have that the first state of the die is state 1. Therefore the probability of this is p(z1=1)=0.5.
Also the probability that the same die is used(i.e. casino would be in the same state) is p(z2=1|z1=1)=0.8.
Again, suppose the first state of the die is state 2. So, p(z1=2)=0.5 and p(z2=2|z1=2)=0.9.
Other transition probabilities can be written as
p(zt+1=2|zt=1)=1-p(zt+1=1|zt=1)=.2
p(zt+1=1|zt=2)=1-p(zt+1=2|zt=2)=.1
p(z3=1|z1=1) = [p(z3=1|z2=2)*p(z2=2|z1=1)]+[p(z3=1|z2=1)*p(z2=1|z1=1)] = 0.1*0.2+0.8*0.8 = 0.66
p(z3=2|z1=2) = [p(z3=2|z2=2)*p(z2=2|z1=2)]+[p(z3=2|z2=1)*p(z2=1|z1=2)] = 0.9*0.9+0.2*0.1 = 0.83
With this, the total probability that the same die is used for the first three rolls (i.e. casino would be in the same state) is given thus;
{p(z1=1)*p(z3=1|z1=1)}*{p(z1=2)*p(z3=2|z1=2)}
= 0.5*0.66+0.5*0.83 = 0.745
Prob = 0.745
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
A homeowner wants to build a fence to enclose a 320 square yard rectangular area in his backyard. Along one side the fence is to be made of heavy-duty material costing $9 per yard, while the material along the remaining three sides costs $1 per yard. Determine the least cost to the homeowner.
Answer:
Determination of the least cost of fence enclosure:
= cost of heavy-duty one side of the length plus cost of remaining three sides of the fence
= $416 ($360 + $56)
= $416
Step-by-step explanation:
Rectangular Fence Area = 320 square yard
Since fence is rectangular, the two sides are length and width
Length of rectangular is always greater than the width
Length cannot be 20 yard with width as 16 yard
Therefore, length = 40 yard and width = 8 yard.
Proof: Area of a rectangular = 40 x 8 = 320 square yard
Since, parameter = 2 (Length + Width)
= 2 x (40 + 8)
= 96 yards
Therefore, along one side with heavy-duty material is one length side of the fence = 40 yard
Cost of the one length with heavy-duty material = 40 x $9 = $360
Remaining three sides = 96 - 40 = 56 yard
Cost of remaining three sides = 56 x $1 = $56
Total cost of fencing = $416 ($360 + $56)
Find y when x = 4 (30 points)
Answer:
y = 54/25
Step-by-step explanation:
y = p×q^(x-1)
when x = 1 then y = 10
so,
10 = p×q^(1-1)
or, 10 = p×1
or, p = 10
when x = 6 then y = 0.7776
0.7776=p×q^(6-1)
or, 0.7776=p×q^5
or, 0.7776=10×q⁵
[0.7776 = 7776/10000 = 486/625]
or, 486/625 = 10×q⁵
or, 486/6250=q⁵
or, [tex] \frac{ \sqrt[5]{486} }{ \sqrt[5]{6250} } = q[/tex]
or, [tex]q = \frac{3 \sqrt[5]{2} }{5 \sqrt[5]{2} } [/tex]
or, q = 3/5
so, when x = 4
y = p×q^(x-1)
y = 10×(3/5)^(4-1)
y = 10×(3/5)^3
y = 10×27/125
y = 54/25
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). y= [tex]\frac{2}{x^2}[/tex]+3
Answer:
One possible answer is:
f(x) = (2/x) + 3 and g(x) = x².
Step-by-step explanation:
Explanation:
We are to write this equation as y = f(g(x)). This means we want it to be a composite of functions; in f(x), we take the value of g(x) and use in place of x.
If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x². To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.
someone please help it's Multiple Coordinate Transformations
Answer:
Step-by-step explanation:
Coordinates of the vertices of the given rectangle are,
A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).
If the given rectangle ABCD is translated by 1 unit right and 4 units down,
Rule for the translation will be,
(x, y) → [(x + 1), (y - 4)]
Therefore, coordinates of A, B, C and D after translation will be,
A(-4, 5) → A'(-3, 1)
B(-2, 5) → B'(-1, 1)
C(-2, 1) → C'(-1, -3)
D(-4, 1) → D'(-3, -3)
Then A', B', C' and D' are reflected about the y-axis.
Rule for the reflection about y-axis will be,
(x, y) → (-x, y)
New coordinates after the reflection will be,
A'(-3, 1) → A"(3, 1)
B'(-1, 1) → B"(1, 1)
C'(-1, -3) → C"(1, -3)
D'(-3, -3) → D''(3, -3)
Finally these points are rotated 270° clockwise about the origin,
Rule to be followed,
(x, y) → (-y, x)
Therefore, new coordinates will be,
A"(3, 1) → A"'(-1, 3)
B"(1, 1) → B'"(-1, 1)
C"(1, -3) → C"'(3, 1)
D"(3, -3) → D"'(3, 3)
Write the equation in standard form.
x2 + 6 = 5x
Answer:
Step-by-step explanation:
x2 + 6 = 5x
2x-5x = -6
3x = -6
x = -6/3
x = -2
Answer:
[tex]x^{2} -5x + 6 =0[/tex]
Step-by-step explanation:
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
Find the value of angle X. x = 40 x = 55 x = 109 x = 130 I will mark as Brainliest
Answer:
130 degree
Step-by-step explanation:
Interior angles of the triangle:
81, 49, (180-x)
and by sum of all angles of triangle is 180 degree,
therefore,
81 + 49 + 180 - x = 180
x = 130 degree
Help me please I dont know what to do
Answer:
It's option A. ± √60
Step-by-step explanation:
x^2 = 60
here ^2 will move to the other side and when it does it'll become a square root to 60.
so, x = √60
now, the answer in its simplified form would be 2√15 and -2√15.
The answer of this square root will be negative as well as positive, so, ±√60.
Answer:
±√60
You'll have to remove the square from the x by squaring the 60, hence the ±60 as the answer
Find the value of x.
Answer:
x=3
Step-by-step explanation:
I guessed and checked which x value would make ABC proportional to DBE. If x=3, than DB=8 which is double BE. If x=3, than AB=14 which is double BC. Since it is proportional, It should be correct. I don't remember the actual way you solve this with a formula but this makes sense to me.
Answer:
x=3
Step-by-step explanation:
We can use ratios to solve since the triangles are similar
x+5 4
------------ = ---------------
x+5 +2x 4+3
Simplifying
x+5 4
------------ = ---------------
3x+5 7
Using cross products
7(x+5) = 4(3x+5)
Distribute
7x+35 = 12x+20
Subtract 7x from each side
35 = 5x+20
Subtract 20 from each side
15 = 5x
Divide by 5
3 =x
V= pi r2h rectangular prism cylinder cone sphere
Answer:
Step-by-step explanation:
rectangular prism=lwh
cylinder=πr²h
cone=1/3 πr²h
sphere=4/3 πr³
An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected
Answer:
The standard error decreases and the width of the confidence interval also decreases.
Step-by-step explanation:
The standard error of a distribution (E) is given as:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }[/tex]
Where n is the sample size, [tex]z_{\frac{\alpha}{2} }[/tex] is the z score of he confidence and [tex]\sigma[/tex] is the standard deviation.
The sample size is inversely proportional to the standard error. If the sample size is increased and everything else is constant, the standard would decrease since they are inversely proportional to each other. The confidence interval = μ ± E = (μ - E, μ + E). μ is the mean
The width of the confidence interval = μ + E - (μ - E) = μ + E - μ + E = 2E
The width of the confidence interval is 2E, therefore as the sample size increase, the margin of error decrease and since the width of the confidence interval is directly proportional to the margin of error, the width of the confidence interval also decreases.
Christopher has $1947 in his savings account. This weekend he will deposit another $99 in the account. How much money will be in Christopher savings account after this weekend
Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]
[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]
= 1.1489
XW : XY ≈ 1.15 : 1
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]
XY : WY = 1 : 0.7342
XW : XY : WY = 1.15 : 1 : 0.7342
Therefore, WX > XY > WY
Option (D). will be the correct option.
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
-50 POINTS- (5/5) Which scatter plot represents the following data?
Answer:
B is plotted correctly
Step-by-step explanation:
A point (1,2) is plotted at (1,3)
B is plotted correctly
C point (1,2) is plotted at (1,3)
D point (1,2) is plotted at (1,3)
Answer:
B.
Step-by-step explanation:
According to the table, there is a point at (0, 5), and a point at (1, 2).
A: The scatterplot has a point at (0, 5), but a point at (1, 3).
B: The scatterplot has points at (0, 5) and (1, 2).
C: The scatterplot has a point at (0, 5), but a point at (1, 3).
D: The scatterplot has a point at (0, 5), but a point at (1, 3).
Hope this helps!
The seventh-grade class is raising money
to have a class trip at the end of the year.
They began the year with $1,500. Now they
have $1,650 in the account.
What is the percent of increase for the
money the class has raised? I
a.
b.
Make Sense and Persevere The
class figured out that if the percent
increase is 99% from the beginning of
the year, the class will have enough
money for every student to go on the
field trip. How much money will the
class need to raise for every student to
go.
Answer:
The percent of the increase for the money the class raised is 10 %
Step-by-step explanation:
Because if you divide 1500 by 10 you get 150 that means 150 is 10 % of 1500 and if you add 150 to 1500 you get 1650 so the increase of money the class raised is 10 %
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
I NEED HELP ASAP
191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students. Calculate the Margin of Error, rounded to the nearest tenth of a percent. Is it reasonable that the state education department claims the percentage for the entire state is 73%? Justify your answer.
Answer:
It is not reasonable that the state education department claims the percentage for the entire state is 73%.
Step-by-step explanation:
We are given that 191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of high school students who went outside more during school hours as elementary school students than they do now as high school students = [tex]\frac{191}{288}[/tex] = 0.66
n = sample of high school students = 288
p = population percentage for the entire state
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
The margin of error is given by;
M.E. = [tex]2 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
= [tex]2 \times \sqrt{\frac{0.66(1-0.66)}{288} }[/tex]
M.E. = 0.056 or 5.6%
So, the confidence interval so formed = [tex]\hat p \pm \text{Margin of error}[/tex]
= [[tex]0.66 - 0.056 , 0.66 + 0.056[/tex]]
= [0.604, 0.716]
Since the above interval does not include 0.73 or the population proportion of 73% falls outside the above interval. So, it is not reasonable that the state education department claims the percentage for the entire state is 73%.
What is the constant of proportionality between y and x in the graph?
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
find the perimeter of a square of sides 10.5cm
Answer:
Perimeter = 42 cm
Step-by-step explanation:
A square has all equal sides so you would just add 10.5 + 10.5 + 10.5 + 10.5 to get 42 cm.
Answer:
42 cm
Step-by-step explanation:
Side of square = 10.5 cm (given)
Perimeter of square = Side X 4
= 10.5 X 4
= 42 cm
HOPE THIS HELPED YOU !
:)
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.
Answer: 669
Step-by-step explanation:
Given, In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft.
i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66
Sample size : n= 1013
Then , Mean for the sampling distribution of sample proportion = np
= (1013) × (0.66)
= 668.58 ≈ 669 [Round to the nearest whole number]
Hence, the mean of those who do not worry about identify theft is closest to 669 .
there are 12 eggs in one box and 12 boxes in one crate. how many eggs are in a shipment of 24 crates
Answer:
Step-by-step explanation:
12 eggs in one box
12 boxes = 1 crate
12 x 12 = 144 eggs
144 x 24 crates = 3456 eggs
Answer:
3,456 eggs
Step-by-step explanation:
There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12
12*12=144
144 eggs in one crate.
We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.
144*24=3,456
There are 3,456 eggs in 24 crates.
Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit
Answer:
A. 10%
B. Lower limit= 21
Upper limit = 39
Step-by-step explanation:
Mean = 30
SD = 3
a. COV = SD/|x| × 100
= 3/30 × 100
= 10%
= 0.1
B. For 88.9 chevbychev interval:
= (1 - 1/K²) = 0.889
= 1/K² = 1 - 0.889
= 1/K² = 0.111
= K² = 1/0.111
= K² = 9
= K = √9
K = 3
Lower limit = 30 - 3(3)
Lower limit = 21
Upper limit = 30 + 3(3)
Upper limit = 39
Therefore lower limit is 21 and upper limit is 39
Which numbers are 9 units from −5 on this number line?
Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
-14,-5 -4 4 5 9
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
PLEASE HELP!!! Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending. *
Answer:
155.00-65.50-23.25-26.45+165.30
Step-by-step explanation:
Answer:
155 + 165.3 - 65.5 - 23.25 - 26.45
Step-by-step explanation:
She had $155 dollars in the starting = +155
She withdrew $65.5 = -65.5
She withdrew another $23.25 = -23.25
She withdrew another $26.45 = -26.45
She deposited $165.3 = +165.3
The expression looks like:
155 + 165.3 - 65.5 - 23.25 - 26.45
We could solve the expression:
155 + 165.3 - 65.5 - 23.25 - 26.45
=> 320.3 - 88.75 - 26.45
=> 320.3 -115.2
=> 205.1
At the end of the week, she had a total of $205.10.
1+3^2⋅2−5 order of operations
Answer:
Below
Step-by-step explanation:
● 1 + 3^2 × 2 -5
Start by calculating 3^2 wich is 9
● 1 + 9 × 2 -5
Multiply 2 by 9 (9×2=18)
● 1 + 18 -5
Add 1 to 18 (1+18 = 19)
● 19 -5
Substract 5 from 19 (19-5 = 14 )
● 14
While organizing the magazines at the doctor's office, Camille put 12 magazines in the first pile, 15 magazines in the second pile, 18 magazines in the third pile, 21 magazines in the fourth pile, and 24 magazines in the fifth pile. If this pattern continues, how many magazines will Camille put in the sixth pile?
Answer:
27
Step-by-step explanation:
since you are adding 3 to the pile each time, on the 6th pile you would have 27 because 24 + 3 = 27