Answer:
A man is viewing the plane from a position. 3000 ft from the base of a radio tower. The airplane is flying horizontally away from the man. If the plane is flying at the rate of 600 ft/sec, at what rate is the distance between ...
Find the perimeter of the figure shown above with aside length 5 unit
The perimeter of the figure with side length of 5 units is 50 units
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
Smaller shapes = squares
Side lengths = 5 units
The perimeter of the figure is calculated as
Perimeter = Number of visible sides * Side length of the square shape
In this case, we have
Number of visible sides = 10
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 10 * 5
Evaluate the products
Perimeter = 50 units
Hence, the perimeter is 50 units
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Multiply. State the product in simplest form..
p²-4p-12
18p
6p+12 p²-9p+18
, p‡ - 2,3,6
The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression is
[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]
Now factories p²- 4p -12, p²-9p+18, and 6p + 12:
p²- 4p -12
= p²- (6 - 2)p -12
= p²- 6p + 2p -12
= p(p - 6) + 2(p - 6)
=(p - 6)(p + 2)
p²- 9p + 18
= p²- (6 + 3)p + 18
= p²- 6p -3p + 18
= p(p - 6) -3(p -6)
=(p - 6)(p - 3)
6p + 12
=6(p+2)
Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:
[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]
Multiply the denominator with denominator and numerator with numerator:
= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)
Now cancel out (p+2)(p - 6) from denominator and numerator:
= 18p/ 6(p - 3)
Divide denominator and numerator by 6:
= 3p/ (p - 3)
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Maximum revenue Imagine this scenario: You are trying to fulfill you dream of opening your own business, designing and selling coffee mugs. After many years and hours of studying for college, you feel that there is a big demand for coffee mugs. You are trying to get a contract with a local store to be the sole provider of coffee mugs. You and your company partner are researching how many coffee mugs must be produced and sold for maximum revenue. After extensive research, you concluded that you could give away 50 coffee mugs without charging anything. If you charge $10.00, nobody will buy the coffee mugs. Your job is to find the maximum possible revenue from selling the coffee mugs. Answer the following questions:
1. Graph the linear relationship between the price of coffee mugs p, and the number of coffee mugs sold S . Hint: To give away 50 coffee mugs means when the price p=0 , S(0) = 50. Plot that point on the graph. Find one more point using the other given condition. Keep in mind S(p) is a linear function.
2. Find the equation of the linear function S(p) that describes the situation.
3. The revenue is determined by R = S p. Express the revenue as a function of the price p.
4. Graph the revenue function. Make sure to label the x - and the y - axis with the appropriate units.
5. At which price per coffee mug do you not make any money?
6. Find the price per coffee mug that makes the most revenue.
7. How many coffee mugs must be made to maximize the revenue?
8. What is the maximum revenue? 9. How many coffee mugs must be sold to make at least $50 in revenue?
Therefore at $5 you selling 15 mugs will generate the maximum revenue.
What is a graph?In discrete mathematics, a graph is made up of points called vertices, and the connecting lines between them are called edges. Simple graphs, linked and unconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and linked and unconnected graphs are only a few of the numerous varieties of graphs.
Here,
For $0 for , 50 mugs be sold
For $10 for , 0 mugs be sold
Thus, from graph
1) Slope= 50/-10 =-5
2) m(p)= -5(p-10) =-5p +10
=> m(p) =10 -5p
3)Revenue R(p) = m(p)
R(p) = 10 -5p
4) point(5,15)
5) at price p =0 , p=5 , we do not make any money
6)At $5 most revenue is made
7)when p=5
R(p) = 10 -5(5)
R(p) = 15
Thus , 15 coffee mugs will yield max revenue
8)Max revenue = $45
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A cat gave to 3 kittens who each had a different mass between 147 znd 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.
Kitten Mass (in grams)
Archer 147
Nate 153
Lisa 159
Bob 57
How will the birth of the 4th kitten affect the mean and median?
Choose 1 answer
A. Both the mean and median will increase, but the median will increase by more than the mean.
B. Both the mean and median will increase, but the mean will increase by more than the median.
C. The mean will increase, and the median will decrease.
The affect of mean and median due to the birth of the 4th kitchen is B. Both the mean and median will increase, but the mean will increase by more than the median.
The median is the middle value when the values are ordered from smallest to largest. In this case, the median of the first 3 kittens is 153 because it is the middle value of (147, 153, 159). The median of all 4 kittens is 153 because it is the middle value of (57, 147, 153, 159). The median does not change because the addition of the 4th kitten does not change the position of the middle value.
The mean is calculated by adding up all the values and dividing by the number of values. In this case, the mean of the first 3 kittens is:
(147 + 153 + 159) / 3 = 153
The mean of all 4 kittens is:
(147 + 153 + 159 + 57) / 4 = 128
The mean increases because the addition of the 4th kitten with a lower mass pulls the overall average down.
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Which line is an irregular line of blank verse?
“He only says, ‘Good fences make good neighbours.’”
“If I could put a notion in his head:”
“And on a day we meet to walk the line”
“And set the wall between us once again.”
THE ANSWER IS THE FIRST ONE
Identify the irregularity in the line.
THE ANSWER IS THE SECOND ONE
The line that is an irregular line of a blank verse is A . “ He only says , ‘Good fences make good neighbours. ”
The irregularity of the line is that it has 11 syllables while other lines have 10 syllables .
What is a blank verse ?Unrhymed but metric poetry with usually always iambic pentameter is referred to as "blank verse" in literature.
Going by the definition, the three bottom lines are regular lines in a blank verse as they have 10 syllables. However, the first line, has 11 syllables, thereby making it irregular.
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PLEASE HELP WILL GET BRAINLIEST!!
Answer:
235.5
Step-by-step explanation:
cylinder volume formula
V = pi * r^2 * h
V = 3.14 * 5^2 * 3
V = 3.14 * 25 * 3
V = 3.14 * 75
V = 235.5
one urn, u1, contains one blue ball (labeled b1) and three red balls (labeled r1, r2, and r3). a second urn, u2, contains two red balls (labeled r4 and r5) and two blue balls (labeled b2 and b3). an experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement.
Two urns contains different numbers of different colour balls. Two balls are randomly chosen from both of urns. The probability that two red balls are choosen is 1/3..
We have given that
First Urn, u₁ contains 3 Red( labelled r₁,r₂,r₃) ; 1 blue ball ,(labelled b₁).
Total number of balls in urn, u₁ = 4 balls
Second Urn, u₂ contains 2 red (labelled r₄,r₅) and 2 blue (labelled b₂, b₃) .
Total number of balls in urn, u₂ = 4 balls
Assume , A = first urn , u₁ is selected
Assume, B = Second urn u₂ is selected
Assume , R = selected balls are red
Case 1 : Urn u₁ is choose and two balls without replacement are withdraw.
Probability to choose the first urn, P(A) = 1/2
Probability that the two withdraw without replacement balls are red in colour, P(A/R)
= 3/4 × 2/3 = 1/2
Case 2 : Urn u₂ is choose and two balls without replacement are withdraw.
Probability to choose the second urn, P(B) = 1/2
Probability that the two without replacement withdraw balls are red in colour, P(B/R)
= 2/4 × 1/3 = 1/6
The required probability= P(A) P(A/R) + P(B)P(B/R) = 1/2(1/2) + 1/2(1/6) = 1/4 + 1/12
= 4/12 = 1/3
Hence, the required probability is 1/3..
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Complete question:
One urn u1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn u2 contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. Probability that two red balls are choosen.
a random sample of 100100 observations from a population with standard deviation 17.037078307720517. yielded a sample mean of 93.1). Given that the null hypothesis is μ≤90 and the alternative hypothesis is μ>90 using α=.05, find the following:(a) Test statistic(b) P-value:(c) The decision for this test is:i. Reject the null hypothesis.ii. Fail to reject the null hypothesis.
1)Test Static: 1.82
2)P-Value: < 0.05
3)Decision: i. Reject the null hypothesis.
To test the claim that the population mean is greater than 90, we can use a one-sample t-test.
(a) The test statistic for the one-sample t-test is calculated as:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))Plugging in the values, we get:
t = (93.1 - 90) / (17.037078307720517 / sqrt(100)) = 3.1 / (17.037078307720517 / 10) = 3.1 / 1.7037078307720517 = 1.82(b) To find the p-value for the test, we can use a t-table or a statistical software package to find the probability of observing a t-value as extreme or more extreme than the one we obtained, given that the null hypothesis is true. For a one-tailed test with α = 0.05 and df = 99 (the sample size - 1), the critical value for t is approximately 1.65. Since our test statistic (1.82) is greater than the critical value, the p-value is less than 0.05.
(c) Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that the population mean is indeed greater than 90. Therefore, the decision for this test is: i. Reject the null hypothesis.
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c) If the gradient of a line, C, is a 2/3 , what is the gradient of the line which is perpendicular to C?
Any line perpendicular to line C must have a slope equal to -3/2.
Which is the slope of a line perpendicular to line C?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the slopes is -1, then if the slope of the line perpendicular to line C is x, then we can write:
x*(2/3) = -1
Solving for x we get:
x = -3/2
That is the slope of the perpendicular line.
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Express 2678 as a product of prime numbers
Answer:
2, 13, 103
Step-by-step explanation:
These prime numbers are the ones.
2678 = 2 * 13 * 103
A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example, 3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.
So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.
A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.
The answer is -
2678 = 2 * 13 * 103
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Estimate y when x = 8 from the best fitted straight line y = 13.06 + 0.6x.
Answer:
17.86
Step-by-step explanation:
You want to find y when x=8 using the equation y = 13.06 +0.6x.
EvaluationPut the value of the variable in place of the variable in the equation, and do the arithmetic.
y = 13.06 +0.6x
y = 13.06 +0.6·8 . . . for x=8
y = 13.06 +4.8
y = 17.86
The estimated value of y for x=8 is 17.86.
PLEASE HELP ASAP
A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?
Answer:
D
Step-by-step explanation:
slope of the given line :
(-4-2)/(-1-4)
-6/-5
6/5
slope of a perpendicular line : -5/6
y-7 = -5/6 (x-(-3)
y -7 = -5/6 (x+3)
y -7 = -5/6 x - 5/2
5/6 x + y - 7 + 5/2 = 0
5/6 x + y + (-14 + 5)/2 = 0
5/6 x + y - 9/2 = 0
5x + 6y - 27= 0
5x + 6y = 27
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )
m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then
y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 3, 7 ) into the partial equation
7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]
y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form
multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions
6y = - 5x + 27 ( add 5x to both sides )
5x + 6y = 27 ← equation of perpendicular line in standard form
DIG DEEPER You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and ( 45w + 25) dollars in checking account. how much money do you save each week?
The sum of both accounts' expression in its most basic form is 55w + 145.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the instructions given in the question,
Amount in savings account = 10w + 120
Amount in checking account = 45w + 25
Then, total money shaved each week will be,
(10w + 120) + (45w + 25)
10w + 45w + 120 + 25
= 55w + 145
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This bar chart shows the numbers of pets owned by people
questioned in a survey. Note that the scale on the vertical
axis is missing.
The total number of pets
owned by the respondents
is 92.
How many people owned
exactly 2 pets?
Answer: C. The width of the bar representing dogs is more than the widths of the other bars.
Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.
Find the value of x in the following equation:
1.2(3x + 5) = 3.6x + 6
A:Infinite solutions
b: No solution
c: x = 1.8
d: x = 0
Answer:
A:Infinite solutions
Step-by-step explanation:
1.2 ( 3x + 5 ) = 3.6x + 6
1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6
3.6x + 6 = 3.6x + 6
Answer: A
Step-by-step explanation:
Abdul was scuba diving 76 feet below the surface of the ocean. To get a closer look at a school of fish, he swam up 28 feet.
What is Abdul's position now relative to the surface of the ocean?
Answer:
-48 ft.
Step-by-step explanation:
-76+28= -48
Hope this helps! Had this on one of my quizzes
Answer:
-48 espero te sirva perdon por llegar tarde
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
point
vertex
one
face
face
circular
length
area
volume
what is answer to 3/7 x 5/2?
Answer:
15/14 or 1 1/14
Step-by-step explanation:
multiple the numerators and deno
3x5=15
7x2=14
15/14 or 1 1/14
Answer:
Step-by-step explanation:
Exact form
15/14
Decimal Form:
1.07142857........
mixed number is
1, 1/14
What is the slope of linear relationship?
Photo goes with qustion
A. 1/4
B. -4/1
C. 4/1
D. -1/4
5. (8.51) What is the equation of the line shown?
HELP PLEASE!!
Answer:
D
Step-by-step explanation:
D. If it's not D, C. It's a negative slope with a negative y-intercept of -1
If you are given an equation of a line
and a set of points, and are asked to find
an equation that is perpendicular to Line
#1, what do you need to do?
If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.
How to determine an equation of this line?Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:
m₁ × m₂ = -1
Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;
m₁ × m₂ = -1
2 × m₂ = -1
Slope, m₂ = -1/2.
In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.
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In the figure below, R is between Q and S, and S is between R and T. If QS = 12, RT=9, and QT=17, find RS.
In the given figure QT is of 16 units.
What is a line segment ?A line segment has two end points unlike a line which can extend indefinitely in both the directions.
According to the given question S is between Q and T and R is the midpoint of QS. RS=4 And RT= 12 we have to find QT.
As R is the midpoint of QS It will be twice of RS which
= 8 units.
And if RS is 4 units then QR is also 4 unit as R is the midpoint.
QT = QR + RT.
QT = 4 + 12
QT = 16 units.
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As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by
y = 8 x^2
x=0
x=4
y=0
As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?
The volume of the solid you (the region) create by spinning about the x-axis is V = 225units³
How is the volume of a solid object calculated?Depends whether it is a solid with sides, height, and depth. In this case it is the multiplicarion of the three to get the volume.
If it is an irregular shaped object it is done by water displacement. Fill a container with a known amount of water, immerse the object, and the difference in volume in the water is the volume of the object.
How do I find the volume of an irregular shape?Break the volume down into prisms and pyramids that you can calculate the volume of and sum the pieces up to get the total volume. If the shape has curved surfaces, it gets much more complicated.
This gives a y = 15
x = 3
The straight line equation will be y = 5x
The volume of a pyramid is given by the following equation:
where r = radius of the base
h= height of the cone
from the graph, roating about the x - axis gives h = 3, r = 15
Volume =
= 225 units³
Volume of cone formed is 225 units³.
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Suppose your PRNG uses the following formula: X = X * 3 - 2. And suppose that X is 5. What are the next three numbers that would be generated?
The next three numbers that would be generated are 13, 37, and 109.
What is formula?Formula is a mathematical expression that is used to calculate the value of a particular quantity, such as a number, a quantity of a certain type of material, or a number of elements. The most common form of a formula is an equation, which contains two or more variables and is written in the form of a mathematical expression. Formulas are used in many disciplines, including physics, chemistry, engineering, and economics, to solve problems and determine relationships between quantities.
This is because the formula applies the operation of multiplying the current number by 3 and then subtracting 2. Applying this formula to 5 gives 13, and then applying the formula to 13 gives 37, and so on. The resulting sequence is 5, 13, 37, 109, and so on. This is a simple PRNG that can be used to generate sequences of random numbers.
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If you wanted to make $798 by investing $6139 for 3 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
Answer:
Below
Step-by-step explanation:
6139 * x * 3 = 798
x = 798/(3*6139) = .0433= 4.33%
How many miles are in 54.74 kilometers? Round to the nearest whole
number, if necessary.
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles.
So to convert 54.74 kilometers to miles, you can multiply 54.74 by 0.621371:
54.74 kilometers * 0.621371 miles/kilometer = 34.09 miles
Rounded to the nearest whole number, this is 34 miles.
Step-by-step explanation:
Answer:
To convert kilometers to miles, you can use the conversion factor that 1 kilometer is equal to 0.621371 miles. To convert 54.74 kilometers to miles, you can multiply the number of kilometers by the conversion factor:
[tex]54.74 kilometers * 0.621371 miles/kilometer = 34.08 miles[/tex]
Rounded to the nearest whole number, there are approximately 34 miles in 54.74 kilometers.
Step-by-step explanation:
Evaluate the expression when c=4 and d=5.
d+6 c
Answer:
29 is the correct answer
NO LINKS!!
Write an expression for the apparent nth term a_n of the sequence. (Assume that n begins with 1).
1, 1/2, 1/6, 1/24, 1/120, . . .
a_n =
Answer:
The apparent nth term of the given sequence is given by the formula:
a_n = 1 / n!
where n! is the factorial of n, defined as the product of all positive integers less than or equal to n.
For example, the first term of the sequence is 1/1! = 1/1 = 1, the second term is 1/2! = 1/2 = 1/2, the third term is 1/3! = 1/6, and so on.
Therefore, the expression for the apparent nth term of the sequence is:
a_n = 1 / n!
Answer:
[tex]a_n=\dfrac{1}{n!}[/tex]
Step-by-step explanation:
Given sequence:
[tex]1,\; \dfrac{1}{2},\; \dfrac{1}{6}, \; \dfrac{1}{24}, \; \dfrac{1}{120}, \; ...[/tex]
Analyse each term in the sequence:
[tex]a_1=\dfrac{1}{1}=\dfrac{1}{1 \times 1}=\dfrac{1}{1!}[/tex]
[tex]a_2=\dfrac{1}{2}=\dfrac{1}{2 \times 1}=\dfrac{1}{2!}[/tex]
[tex]a_3=\dfrac{1}{6}=\dfrac{1}{3 \times 2 \times 1}=\dfrac{1}{3!}[/tex]
[tex]a_4=\dfrac{1}{24}=\dfrac{1}{4 \times 3 \times 2 \times 1}=\dfrac{1}{4!}[/tex]
[tex]a_5=\dfrac{1}{120}=\dfrac{1}{5 \times 4 \times 3 \times 2 \times 1}=\dfrac{1}{5!}[/tex]
The exclamation mark "!" placed after a number means factorial.
It means to multiply all whole numbers from the given number down to 1. Example: 4! = 4 × 3 × 2 × 1
Therefore, the equation for the nth term of the given sequence is:
[tex]a_n=\dfrac{1}{n!}[/tex]
What is the measure of ZE, in degrees? D 48 5 O A. Cannot be determined OB. 48° O C. 96° D. 84°. :)
Answer:
84
Step-by-step explanation:
EFD is an iscosilies triangle therefore angle F = angle D = 48
and therefore angle E= 180-48-48=84
X1,..., X are i.i.d. standard normal variables. Denote by An the sample mean of the squares of these variables: 1.:- x - - * - }(x2 + x3 + .. + x2). 1 Recall An= = x. For very large n, the distribution of (An-a) is approximated best by ... (In the choices below, the parameter for the normal distributions N (4,0") are the mean w and the variance o?.) O N (0,1) O N (0,2) O N (0,n) O N (0,2n) O x x. Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
Answer:
Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
Step-by-step explanation:
Define a sequence of random variables B, Does the sequence of random variables Bre n converge in probability to a constant b? If yes, enter the value of b below, if no, enter "DNE". (Enter e for the constant e)
B6- As above, let a be the limit in probability of An, ie. An a, and b be the limit in probabiity of Bn = 4, i.e. Br*b, if these limits exist. Does the sequence of random variables (Br-b) converge in distribution? Choose the correct characterization of the limit distribution: O N (0,1) O N 0, "Var (X2) O N (0, "Var (x2)) O N (0, 24Var (X²)) O N 0, e?Var (An)) O Does not converge in distribution
The correct characterization of the limit distribution and other Questions are answered in the following steps.
For the first question, the distribution of (An-a) is approximated best by N(0, n) because the variance of the sample mean of i.i.d. standard normal variables is 1/n.
For the second question, since An converges in probability to a constant, Bn = 4An also converges in probability to 4a. Therefore, the sequence of random variables (Bn-b) does converge in distribution.
For the third question, the limit distribution of (Bn-b) is N(0, 4^2 * n) because the variance of the product of a random variable and a constant is the constant squared times the variance of the random variable.
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