(a) Let X and Y be the arrival times of buses A and B respectively, it is given that buses A and B are independent and hence X and Y are independent random variables.
Therefore, X and Y are also degenerate at c.
Since a person arrives at the bus stop at time 0, the arrival times of buses A and B cannot be negative
i.e., X, Y ≥ 0.
Also, both buses cannot arrive at time 0
i.e., P(X = 0, Y = 0) = 0.
Now, suppose that X and Y are not degenerate. T
hen, their joint distribution function is given by:
F(X, Y) = P(X ≤ x, Y ≤ y) > 0, for some x, y ≥ 0.
Using the independence of X and Y, we get:
F(X, Y) = P(X ≤ x)P(Y ≤ y) > 0,
for some x, y ≥ 0.
Since P(XY = 0) = 0,
we have XY ≠ 0 and
hence P(XY = c) > 0,
for some c ≠ 0.
Now, for a fixed ε > 0,
let Bε = {(x, y) : |xy - c| < ε}.
Then, P((X, Y) ∈ Bε) > 0.
Similarly, let B'ε = {(x, y) : x < ε} and
B''ε = {(x, y) : y < ε}.
Then, P((X, Y) ∈ B'ε) > 0
and P((X, Y) ∈ B''ε) > 0.
Now, we have:
Bε ⊆ B'ε ∪ B''ε and (X, Y) ∈ B'ε
if and only if X < ε and (X, Y) ∈ B''ε
if and only if Y < ε.So,
using the union bound and taking ε small enough, we get:
P(X < ε) + P(Y < ε) > P((X, Y) ∈ Bε) > 0.
This contradicts the assumption that P(X = 0, Y = 0) = 0.
Therefore, X and Y must be degenerate.
Now, we will show that if XY is degenerate at c ≠ 0
i.e., P(XY = c) = 1,
then X and Y are also degenerate at the same point.
To see this, note that for any Borel sets A, B ⊆ R, we have:
P(X ∈ A, Y ∈ B) = P(XY ∈ A × B) = P(XY = c)
= 1, if (c ∈ A × B) or (c is an isolated point of A × B).
Therefore, X and Y are also degenerate at c.
This completes the proof of the required statement.
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12 marbles are in a bag; 3 each of red, blue, green, and orange. If 3 marbles are chosen at random, what is the probability that all 3 are green?
Answer: [tex]\dfrac{1}{220}[/tex]
Step-by-step explanation:
Given
There are 3 marbles of red, blue, green and orange
Total marbles are 12
No of ways of choosing 3 green marbles out of 3 green marbles is [tex]^3C_3[/tex]
Total no of ways of selecting 3 marbles out of 12 are [tex]^{12}C_3[/tex]
So, the probability is
[tex]\Rightarrow P=\dfrac{^3C_3}{^{12}C_3}=\dfrac{1\times 3\times 2\times 1}{12\times 11\times 10}\\\\\Rightarrow P=\dfrac{1}{220}[/tex]
You are sailing North across the ocean from towards the port of -4=rs ( City A. Your navigation dashboard displays your ship's location at 4-ras (0,0) and port is at (-4, 4).
a. What is the distance between your ship and the port?
b. What bearing do you need to take to arrive at the port?
The distance between your ship and the port is approximately 8 units. To arrive at the port, you need to take a bearing of 135 degrees. In the given scenario, your ship's location is at coordinates (0,0), and the port is located at coordinates (-4, 4).
To find the distance between these two points, you can use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates. In this case, the difference in x-coordinates is (-4 - 0) = -4, and the difference in y-coordinates is (4 - 0) = 4. Plugging these values into the distance formula, you get the square root of ((-4)²+ 4²) = sqrt(16 + 16) = sqrt(32) ≈ 5.66. Therefore, the distance between your ship and the port is approximately 5.66 units or rounded to 8 units.
To determine the bearing you need to take to arrive at the port, you can use the concept of trigonometry. The bearing is the angle between the direction you need to go and the north direction. In this case, the angle can be calculated using the inverse tangent function (arctan) of the ratio of the difference in y-coordinates to the difference in x-coordinates. The difference in y-coordinates is 4, and the difference in x-coordinates is -4. Taking the arctan(4 / -4), you get an angle of -45 degrees. Since the bearing is typically measured from the north direction in a clockwise manner, you need to add 180 degrees to obtain the bearing of 135 degrees. Therefore, you need to take a bearing of 135 degrees to arrive at the port.
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Point B has coordinates (1,2). The x-coordinate of point Ais - 11. The distance between point A and
point B is 13 units. What are the possible coordinates of point A?
An FBI agent orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel?
Answer:
22.5 pounds
Step-by-step explanation:
The computation of the weight of the block of gel is shown below:
As we know that
Volume = (length) (width) (height)
= (20) (6 ) (6)
= 720 cubic inches
Now we have to convert into cubic foot
As we know that
1 ft = 12 inches
So 1ft^3 = 12 inches^3
= 1728 inches ^3
Now
= 720 × 1 cubic foot ÷ 1728 cubic inches
= 5 ÷ 12
Now the weight is
= 54 × 5 ÷ 12
= 22.5 pounds
Find the measures of the missing angles
Help pleaseee
Answer:
Nwm miałem to dawno powodzenia
What is the surface area of the rectangular prism below
7 7 14
A.496 B.490 C.980 D.248
Answer:
B
Step-by-step explanation:
Formula
SA = 2*L*W + 2*L*H + 2*H*W
Givens
L = 14
W = 7
H = 7
Solution
SA = 2*14*7 + 2*14*7 + 2*7*7
SA = 196 + 196 + 98
SA = 490
Give the characterisations for finito, ineinte, denumwable, cos weak then show that 22 is denumerable
1. Finite: A set is considered finite if it contains a specific number of elements. In other words, a set is finite if you can count its elements and reach a finite number. For example, a set containing {1, 2, 3} is finite because it has three elements.
2. Infinite: A set is considered infinite if it has an uncountable number of elements. This means that the set cannot be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). For example, the set of all integers {..., -3, -2, -1, 0, 1, 2, 3, ...} is infinite.
3. Denumerable: A set is denumerable (also called countable) if its elements can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). In other words, a denumerable set has a countable number of elements. For example, the set of all natural numbers is denumerable.
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I Need Help ..
4. Evaluate the functions,
Let f(0) = 21-1 and 8(x) - 7-4 find
a. /(0)
b. S(1)
c. (-1)
en g(0)
f. 8(-2)
Answer: cos ( 390 ) − 4 cot ( − 45 ) sin (330 )
Step-by-step explanation: MAKE ME BRANLIEST!!!!!!
please help me out here I really appreciate any answers
Answer:
ok
Step-by-step explanation:
Evaluate the indefinite integral as a power series. ∫x^4 In (1 + x)dx [infinity]
f(x) = C + ∑ ____
n=1
what is the radius of convergence R?
R= ?
The indefinite integral of x^4 * ln(1 + x) with respect to x can be expressed as a power series: f(x) = C + ∑(n=1 to ∞) [a_n * x^n]
To find the coefficients a_n, we can differentiate both sides of the power series representation. Using the power rule and the fact that the derivative of ln(1 + x) is 1 / (1 + x), we obtain:
f'(x) = ∑(n=1 to ∞) [n * a_n * x^(n-1)] = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]
Next, we equate the coefficients of the power series representations of f(x) and f'(x):
x^4 * ln(1 + x) = ∑(n=0 to ∞) [(n+1) * a_(n+1) * x^n]
Comparing the coefficients of corresponding powers of x, we can find a_n. By equating the coefficients of x^4 on both sides, we find a_5 = 1 / 5.
To determine the radius of convergence R, we use the ratio test. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.
In this case, as n approaches infinity, the limit of |a_(n+1) / a_n| is 1. Therefore, the radius of convergence R is 1 / 1, which simplifies to R = 1.
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What is the initial value and growth factor of Z = 8•3w and A =6(2.5)t
Answer: The initial value for Z= 8 * 3w is 8 and the growth factor for it is 3. The initial value for A= 6(2.5)t is 6 and the growth factor for it is 2.5.
Step-by-step explanation: Exponential growth equations.
Can we conclude that racial profiling is being used? see es es ts ts. see O A. No, because the P-value is greater than the significance level. OB. Yes, because the P-value is greater than the significance level. O C. No, because the P-value is less than the significance level. OD. Yes, because the P-value is less than the significance level.
We cannot conclude that racial profiling is being used when P-value is greater than the significance level. Therefore, the correct option is A. No, because the P-value is greater than the significance level.
Racial profiling is a biased practice in which someone is targeted or suspected based on their ethnicity, nationality, religion, or race instead of their conduct. The aim of racial profiling is to decide whether someone is suspicious or not based on their racial identity. As a result, this technique frequently leads to unjustifiable detainment, searches, and arrests.
A p-value is a probability value used in hypothesis testing that aids in determining whether or not the null hypothesis should be rejected. The smaller the p-value, the more likely the test result is to be statistically significant. In other words, it is less probable that the null hypothesis is true.
Therefore, we reject the null hypothesis when the p-value is lower than the level of significance. In contrast, we accept the null hypothesis when the p-value is higher than the significance level.In summary, since the p-value is greater than the significance level, we cannot conclude that racial profiling is being used. Therefore, the correct option is A. No, because the P-value is greater than the significance level.
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please help 6th grade math i will give brainliest
Answer:
8
Step-by-step explanation:
First add all the terms together.
[tex]8+7+5+9+6+13=48[/tex], so the total is 48.
Then you divide the total by the number of terms (which is 6) to get the mean.
[tex]\frac{48}{6}=8[/tex], so the mean is 8.
Independent Practice
Which property justifies the step shown in solving this equation? − y−5=11
−y−5+5=11+5
A.
Multiplication Property of Equality
B.
Addition Property of Equality
C.
Subtraction Property of Equality
D.
Division Property of Equality
Answer:
B. Addition Property of Equality
Step-by-step explanation:
B addition property of equality
An engineer designs a structure that is is 21 feet long and 3
yards high. What is the ratio of length to height?
Answer:
7:3
Step-by-step explanation:
Convert one of the measurements to the other before attempting to solve the question.
1 yard = 3 feet
Multiply both sides by 3 to get:
3 yards = 9 feet
Therefore the ratio would be
21:9
Simplify to 7:3 length to height.
NO FILES PLEASE! THANKS!
Answer:
C, A and D
Step-by-step explanation:
4 - dictado audio you will hear a conversation. Listen carefully and write what you hear during the pauses. The entire conversation will then be repeated so you can check your work
According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.
What is the conversation about?To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.
Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.
Note: This question is incomplete. Here is the complete information:
Conversation:
Hello
Hello, How are you?
I am fine, and you?
i am fine too, What are you doing?
I am studing for an exam this week.
Oh, sorry I won´t distract you.
Don´t worry.
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What’s ’ Y = 1/2x + 4
Answer:
see explanation
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 )
y = [tex]\frac{1}{2}[/tex] x + 4 ← is in slope- intercept form
Thus
y = [tex]\frac{1}{2}[/tex] x + 4 is the equation of a straight line
with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = 4
Suppose you waited 10 years to invest in the same retirement fund and have the same $400,000 for retirement at the same 8% interest. What amount will you have to deposit each month to match the value of your annuity?
Answer:
$7,196.42
Step-by-step explanation:
Using the compound interest formula to fins the amount after 10years;
A = P(1+r)^n
Principal P = $400,000
Rate r = 8% = 0.08
Time t = 10 years
Substitute
A = 400,000(1+0.08)^10
A = 400,000(1.08)^10
A = 400,000(2.1589)
A = 863,569.99
A ≈ 863,570
Hence the amount after 10 years is $863,570
Monthly deposit = $863,570/120 (10 years is equivalent to 120months)
Monthly deposit = 7,196.42
Therefore he will have to deposit $7,196.42 into his account monthly
Gerald’s truck is in need of repairs totaling $3,000. Gerald is considering how he will pay for these repairs.
Hello again!
Answer:
The correct answer is B. 18 months.
Step-by-step explanation:
I just typed in "credit card payoff calculator" in g00gle, and it should be the first one you see.
That was the website I used to solve this problem. You can use that for other problems you need to solve too.
Hope this helps :)
Math help me out this is tricky man hurry solve both
Answer:
1) a , b , c , e are ans....
2) a.F b.T c.F d.T
Prove these facts about matrices. (a) The row space of a matrix is isomorphic to the column space of its transpose. (b) The row space of a matrix is isomorphic to its column space.
Therefore, the row space and column space of a matrix are isomorphic for both rectangular and square matrices.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
(b) The row space of a matrix is isomorphic to its column space.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
The isomorphism between row space and column space of a matrix transpose is a significant and helpful concept. The row space of a matrix A is the subspace that is spanned by the rows of A. The column space of a matrix A is the subspace that is spanned by the columns of A. The row space of A is equivalent to the column space of A transpose. The statement is denoted mathematically as row(A) ≅ col(A^T).
(b) The row space of a matrix is isomorphic to its column space.
In the case of a square matrix, it is easy to demonstrate that the row space is identical to the column space. Consider the product of an m x n matrix A and the column vector x of size n, Ax = b, which equals a linear combination of the columns of A with weights given by the entries of x. The solution b lies in the column space of A. Similarly, the equation AT y = c expresses the fact that the solution y lies in the column space of A.
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Solve.
x2=14425
Express your answer as a fraction, using± if necessary.
Enter your answer in the box.
Answer:
x is 120.104121495
Step-by-step explanation:
because you can square out the equation and get x
Answer:
The first one should be right but if you’re from K12 then it’ll be 12/5, and just that again except had a negative.
Step-by-step explanation:
which helps yhu find the total number of flowers
Answer:
what do you mean? is there another part of the problem?
Step-by-step explanation:
Help slove this problem
The new coordinates after the rotation of 270° counterclockwise around the origin are:
J'(8, -10)
K'(3, -10)
L'(9, -5)
What are the coordinates after the transformation?There are different types of transformation of geometry such as:
Translation
Reflection
Rotation
Dilation
The original coordinates before transformation are:
J(10, 8)
K(10, 3)
L(5, 9)
Now, the transformation rule of rotation of 270° counterclockwise around the origin is: (x,y) →(y,-x).
Thus, the new coordinates are:
J'(8, -10)
K'(3, -10)
L'(9, -5)
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NEED HELP ASAP!!! At a movie theater, the price of 2 adult tickets and 4 child tickets is $48. The price of 5 adult tickets and 2 child tickets is $64.
Let x be the cost of an adult ticket and let y be the cost of a child ticket. Write and solve a system of equations to find the ticket price for one adult and for one child.
Answer:
Step-by-step explanation:
2x+4y=48
5x+2y=64
Adult ticket: $10 Child ticket: $7
For 2 adults and 3 children with the given price per ticket, the family having brought $40 as a budget, their budget would not be high enough as the total would come to be $41. They'd be a dollar short.
Please help asaaap number 9
Answer:
The answer is 5 years
Step-by-step explanation:
50+(3x5)=65
75-(2x5)=65
A farmer has 600m of fencing to enclose a rectangular area and divide sections as shown. a) write a equation to express the total area enclosed as a function of the length x. I b) Determine the domain and the range of this area function.
The domain of the area function is 0 < x ≤ 300, and the range is A > 0. The total area enclosed by a rectangular fence, given a fixed amount of fencing, can be expressed as a function of the length of one side.
The domain and range of this area function depend on the constraints imposed by the amount of fencing available.
a) To express the total area enclosed as a function of the length x, we need to consider that the perimeter of a rectangle is twice the sum of its length and width. Since the farmer has 600m of fencing, we can write the equation:
2x + 2y = 600
Solving for y, we can express it in terms of x:
y = (600 - 2x) / 2
The area of the rectangle is given by the product of its length and width:
A = x * y = x * (600 - 2x) / 2
b) The domain of the area function is determined by the values of x that satisfy the constraints of the problem. Since x represents the length of one side of the rectangle, it must be positive (x > 0). Additionally, the sum of the lengths of all four sides must be less than or equal to the available fencing, which gives us the constraint: 2x + 2y ≤ 600.
The range of the area function represents the possible areas of the enclosed rectangle. Since both x and y are positive, the range is also positive.
Therefore, the domain of the area function is 0 < x ≤ 300, and the range is A > 0.
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Complementary of supplementary? Find the value of x
Answer: x=6
The two angles shown in each are complementary because they add up to 90°.
10 & 12 would be supplementary to one another because they would add up to 180°.
Step-by-step explanation:
We know that on both 10 & 12 the angles add up to equal 90° so...
10. 8x+7x=90
15x=90
x=6
12. it's the same in pic as 10
The two angles shown in each are complementary because they add up to 90°.
10 & 12 would be supplementary to one another because they would add up to 180°.
You and your friend decide to conduct a survey at your school to see whether students are in favor of a new dress code policy. Your friend stands at the school entrance and asks the opinions of the first 100 students who came to campus on Monday. You obtain a list of all students at the school and randomly select 60 to survey
Your friend finds 34% of his sample in favor of the new dress code policy, but you find only 16%. Which do you believe us more likely to be representative of the school population? Explain your choice.
Answer:
34% in favor of the new dress code
Step-by-step explanation:
Because it has a higher percentage and when there is only 16% of students that doesn't really prove the claim or statement. But, when there is more participating or voting that claim or statement is supported.