(a) Let A denote the event that heads have not come up by time m. Then A= {T_1= T_2=...=T_m= T}, where T=Tail event and T_i denotes the outcome of the ith toss. By independence of the tosses, T_i=T with probability 2/3 and T_i=H with probability 1/3.
Thus, P(A)=P(T_1=T) P(T_2=T) ...P(T_m=T) = (2/3) ^m. Now, since A is the complement of the event B={X≤m}, i.e., B= {T_1= T_2=...=T_m= H}, so P(B) = 1-P(A) = 1-(2/3) ^m. Thus, P(X>m) =P(A)= (2/3) ^m.
(b) Suppose that heads have not come up by time m, and let A denote the event that it takes at least n more tosses for heads to come up for the first time. That is, A={X> m+n|X> m}. Then A={T_m+1=T_m+2=...=T_m+n=T}, where T_i denotes the outcome of the ith toss.
Since T_1, T_2, …, T_m are all tails, we can ignore them and find that P(A|P (T_m+1=T_m+2=...=T_m+n=T|T_1=T_2=...=T_m=T). By independence of tosses, T_m+1, T_m+2, ..., T_m+n is also independent of the previous tosses,
hence P(A|B) =P(T_m+1=T) P(T_m+2=T) …P(T_m+n=T) = (1/3) ^n.
The formula P(A|B) =P(A) is true, which is known as the memory lessness property of the geometric distribution. Hence, P(X>m+n|X>m) =P(A|B) =P(A)= (1/3) ^n.
Finally, we have P(X>m+n)=P(X>m+n,X>m)/P(X>m) =P(X>m+n)/P(X>m) = ((2/3) ^n)/((2/m) = (2/3) ^{n-m}.
Thus, we can compare the results and see that P(X>m+n|X>m) = P(X>n).
The event that you have waited m time without seeing heads does not change the chance of having to wait time n to see heads.
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PLEASE HELP ASAP!! WILL GIVE BRANLIEST!!!
Answer:
Brand A
Step-by-step explanation:
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )
Brand A
V = [tex]\frac{1}{3}[/tex]π × 6² × 15 = [tex]\frac{1}{3}[/tex]π × 36 × 15 = π × 12 × 15 = 180π in³
Brand B
V = [tex]\frac{1}{3}[/tex]π × 5² × 18 = π × 25 × 6 = 150π in³
Brand A have the largest volume
Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
Answer:
Step-by-step explanation:
Two boys want to balance a seesaw perfectly. One boy weighs 240 pounds and is sitting four feet from the fulcrum. The other boy weighs 160 pounds. Where should the lighter boy sit to balance the seesaw?
We solve using the formula
Distance on the fulcrum × Weight of the boy
= 4 × 240 = x × 160
4 × 240 = 160x
x = 4 × 240/169
Ruth read a total of 14 books over 7 months. After belonging to the book
club for 10 months, how many books will Ruth have read in all? Assume
the relationship is directly proportional.
Answer:
20 books
Step-by-step explanation:
Well 14 books in 7 months.
Find the unit rate
14/7=2
So 2 books each month
We have Ruth here that was in the book club for 10 months.
And since 2 books each month,
2*10=20
20 books
Now consider the so-called random walk with absorbing barriers on 1 = {0, 1, 2, 3, 4}. This is also a Markov chain on N = {0,1,2,3,4} with the following transition probability matrix P =
[1 0 0 0 0]
[1/2 0 1/2 0 0]
[0 1/2 0 1/2 0]
[0 0 1/2 0 1/2]
[0 0 0 0 1]
(a) Draw a graphical diagram that shows how this chain moves. (b) Is this chain irreducible? Why or why not? (c) Find E(X5 | X3 = 1, X0 = 2).
The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.
(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.
(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.
To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.
By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.
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HELP MEEE
Review
Question 11 of 40
11 Which ordered pairs are solutions to the inequality graphed in the coordinate plane?
Select all that apply.
A(-3, -8)
B
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Answer:
this is hard to tell and sorry if I'm wrong but I would say it is only a
Step-by-step explanation:
Aanything in the shaded area is correct if it's not it's wrong
A part manufactured at a factory is known to be 12.05 cm long on average, with a standard deviation of 0.119. One day you suspect that that the part is coming out a little longer than usual, but with the same deviation. You sample 19 at random and find an average length of 12.25. What is the z-score which would be used to test the hypothesis that the part is coming out longer than usual?
Z-score is used to test the hypothesis that the part is coming out longer than usual. Z-score is defined as the number of standard deviations away from the mean.
It is calculated using the formula z = (x - μ) / σ, where x is the sample mean, μ is the population mean, and σ is the population standard deviation. In the given problem, the population mean is μ = 12.05 cm and the population standard deviation is σ = 0.119 cm. The sample mean is x = 12.25 cm. The sample size is n = 19.
Therefore, the formula to calculate the z-score is Z = (x - μ) / (σ / √n) Substituting the values, we get z = (12.25 - 12.05) / (0.119 / √19) ≈ 6.586Therefore, the z-score which would be used to test the hypothesis that the part is coming out longer than usual is approximately 6.586.
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Events A and B are mutually exclusive. P(A) = 0.9 and P(B) = 0.1. Find P(AUB) to one decimal place. P(AUB) =
Since events A and B are mutually exclusive, they cannot occur together. Therefore, the probability of the union of events A and B is equal to the sum of their individual probabilities. P(AUB) = P(A) + P(B) - P(A ∩ B) Where, P(A) = 0.9P(B) = 0.1Since the events are mutually exclusive, P(A ∩ B) = 0Thus,P(AUB) = P(A) + P(B) - P(A ∩ B)= 0.9 + 0.1 - 0= 1 Hence, the value of P(AUB) is 1.
The most common method for distinguishing between integers and non-integers is the decimal numeral system. It is the expansion to non-number quantities of the Hindu-Arabic numeral framework. Decimal notation is the method used to represent numbers in the decimal system.
Decimal spots are places of the digits to one side of a decimal point. The process of reducing a decimal number to a specified degree of accuracy is known as rounding. To do this we find the decimal spot we wish to adjust to and check out at the digit to one side of that number.
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If 3 inches represents 25 feet on a scale
drawing, how long will a line segment be
that represents 15 feet?
Answer:
1.8 inches
Step-by-step explanation:
1. find the # of inches that represents 1 foot.
3/25 = 0.12in
2. to find the length of the line segment that represents 15 feet, multiply 0.12 inches by 15.
0.12*15 = 1.8in
Han and Andre were comparing the miles they ran during one week of cross country practice Hantan 12 which was three times as much as Andre
How many they run together during the one week
Answer:
I don't know.
Step-by-step explanation:
[x-2]/4=[3x-7]/10 its x-2 dived by 4 not 2/4 same with other side
Answer:
x = 4
Step-by-step explanation:
Given
[tex]\frac{x-2}{4}[/tex] = [tex]\frac{3x-7}{10}[/tex] ( cross- multiply )
4(3x - 7) = 10(x - 2) ← distribute parenthesis on both sides )
12x - 28 = 10x - 20 ( subtract 10x from both sides )
2x - 28 = - 20 ( add 28 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
9.20. set s = 2z = {2x : x ∈ z}, the set of even integers. prove that s is equicardinal with z.
To prove that the set S = 2Z = {2x : x ∈ Z}, the set of even integers, is equicardinal with Z, the set of all integers, we need to show that there exists a one-to-one correspondence (bijection) between the two sets.
A one-to-one correspondence between two sets exists if every element of one set is paired with a unique element from the other set, and vice versa.
Let's define a function f: Z -> S such that f(x) = 2x for every x ∈ Z.
This function assigns each integer x from Z to its corresponding even integer 2x in S.
To prove that f is a bijection, we need to show that it is both injective (one-to-one) and surjective (onto).
Injectivity: Suppose f(a) = f(b) for some a, b ∈ Z. Then, 2a = 2b. Dividing both sides by 2, we get a = b. Hence, f is injective.
Surjectivity: For every y ∈ S, y = 2x for some x ∈ Z. Choosing x = y/2, we have f(x) = 2x = y. Therefore, f is surjective.
Since f is both injective and surjective, it is a bijection. Thus, S and Z are equicardinal sets.
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A pool has a length that is 3 times the width. Write the algebra radical value of the corner to corner distance
Answer:
The distance between corner to corner is equal to √10 times the width.
D = √10*W
Step-by-step explanation:
For a rectangle of length L and width W, the distance between two opposite corners can be calculated if we use the Pythagorean's theorem, where we can think on the length as one cathetus, the width as another cathetus and the diagonal as the hypotenuse.
Then the length of the diagonal is:
D^2 = L^2 + W^2
D = √( L^2 + W^2)
In this case we know that the length is 3 times the width, then:
L = 3*W
Replacing this in the equation for the diagonal we have:
D = √( (3*W)^2 + W^2) = √( 9*W^2 + W^2)
D = √( 10*W^2) = √10*√W^2 = √10*W
D = √10*W
The distance between corner to corner is equal to √10 times the width.
Janna is buying a netbook with a flash drive. The total cost c will include the price p of the netbook plus $12.50 for the flashdrive. Which is the dependent variable?
Suppose Lucy want to make sure that when she reaches into her drawer, she is certain to take out enough gloves so that she will have one matching pair to wear. HOW MANY GLOVES MUST SHE TAKE?
Answer:
its 2
Step-by-step explanation:
I have consulted many nice people ( my idiot friends) they all say 2 good luck
Mhanifa please help im almost done :)
Answer:
19)
9/4 = (r - 10)/r9r = 4(r - 10)9r = 4r - 405r = -40r = -820)
(x + 6)/x = 10/710x = 7(x + 6)10x = 7x + 423x = 42x = 1421)
(n - 9)/(n + 5) = 7/47(n + 5) = 4(n - 9)7n + 35 = 4n - 363n = -71n = -71/322)
6/(b + 9) = 4/(b + 5)6(b + 5) = 4(b + 9)6b + 30 = 4b + 362b = 6b = 323)
8/3 = (v - 9)/(7v + 4)8(7v + 4) = 3(v - 9)56v + 32 = 3v - 2753v = - 59v = -59/5324)
8/(5x - 4) = 6/(x + 5)8(x + 5) = 6(5x - 4)8x + 40 = 30x - 2422x = 64x = 64/22x = 32/11I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!I NEED HELP I WILL GIVE BRANLIEST REAL ANSWERS ONLY PLZZZ!!!!!
Answer:
Step-by-step explanation:
To find each probability you will state the probability of the first event happening and multiply it by the chance of the second event happening.
P(2 Nickels): 6/10 x 5/9 = 30/90 (1/3 chance)
P(2 Dimes): 4/10 x 3/9 = 12/90 (4/30 chance)
P(1 nickel and 1 dime): 6/10 x 4/9 = 24/90 (8/30 chance)
I hope this helps :D
A rectangle has a length of 2x + 1 and a width
of 5x - 4. Which expression best describes the
area of the rectangle?
F 7x - 3
H 10x2 – 3x - 4
J 10x2 + 13x - 4
G 14x - 6
Answer:
H
Step-by-step explanation:
The rectangle has a length of (2x + 1) and a width of (5x - 4).
And we want to select the expression that represents the rectangle's area.
Recall that a rectangle's area is simply its length multiplied by its width. Thus:
[tex]A=(2x+1)(5x-4)[/tex]
Expand by distributing:
[tex]A=(2x+1)(5x)+(2x+1)(-4)[/tex]
Distribute:
[tex]A=(10x^2+5x)+(-8x-4)[/tex]
Simplify:
[tex]A=10x^2-3x-4[/tex]
Hence, our answer is H.
please help, tysm if you do
Answer: It’s 3
Step-by-step explanation:
Hoped I help :)
What is the value of x in this equation?
2x + 2 = -52
pls someone help
Answer: x= −27 or x = 27
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Subtract 2 from both sides
2x= -54
Divide both sides by 2
x = -27
For the following regression model Y = α + βX + u
-Explain how we can test if we adopt the wrong functional forms
of independent variables?
In order to test if we have adopted the wrong functional forms of independent variables in a regression model Y = α + βX + u, we can use diagnostic plots of the residuals.
Residuals are the differences between the actual values of the dependent variable and the predicted values of the dependent variable. We can plot the residuals against the independent variables to check if there is any functional form that has not been captured by the model, which would indicate that the model has adopted the wrong functional form of independent variables.
If there is no pattern in the residuals when plotted against the independent variables, then it can be concluded that the model has captured the correct functional form of the independent variables. However, if there is a pattern in the residuals, it would indicate that there is some functional form that has not been captured by the model, and we would need to explore different functional forms of the independent variables to see which one fits the data better. This can be done by using different functional forms of the independent variables, such as polynomial, logarithmic, exponential, etc., and comparing the results using various statistical tests.
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If the residuals are normally distributed, then it suggests that the functional form of the independent variable is correct. If they are not, then it suggests that the functional form of the independent variable is incorrect.Overall, it is important to test for the functional forms of independent variables to ensure that the results of the regression model are unbiased and accurate.
In a regression model, it is important to make sure that the functional forms of the independent variables are correct. If they are not, the results of the model may be biased and incorrect. There are several ways to test if the functional forms are correct or not. Below are some of the methods:Plotting the residuals against the independent variable: If the functional form of the independent variable is correct, then the residuals should be randomly distributed around zero, without showing any patterns. If there are patterns in the residuals, then it suggests that the functional form is incorrect. Testing for linearity: One way to test for linearity is by including the square or cubic terms of the independent variable in the model and testing their significance. If the squared or cubic term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for additivity: One way to test for additivity is by including interaction terms between the independent variables and testing their significance. If the interaction term is significant, then it suggests that the functional form of the independent variable is incorrect. Testing for normality: One way to test for normality is by examining the normal probability plot of the residuals.
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How many four-digit numbers ABCD have the property that ABCDis equal 26 times BCD?
Note that x1x2...xn represents the n-digit number with digits x1x2...xn.
9514 1404 393
Answer:
9
Step-by-step explanation:
There are 9 such numbers:
1040, 2080, 3120, 4160, 5200, 6240, 7280, 8320, 9360
_____
For each ABCD, where BCD = x, we want ...
26x = 1000A +x
25x = 1000A
x = 40A
The digit A ranges from 1 to 9 for a 4-digit number. That means there are 9 such numbers. For A=1, for example, x = 40·1 = 40, so the number ABCD is 1040. 26·BCD = 26·040 = 1040 as required.
Answer:
9 is correct but if you are here from caribou math it is 7
Step-by-step explanation:
don't dislike what they said because it is the right formula. 25x = 1000A
you get 1040 2080 3120 4160 5200 6240 7280 8320 9360. But since caribou asks for bcd, b > 0 because its a 3 digit number. from that we can eliminate 1040 and 2080 getting 7
PLSSS HELP!!!! in need of help immediately! (check whole picture) and pls don’t leave a link.
Answer: C!!!!!!!
Step-by-step explanation:
Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste
You measure a wound to be 2.5 inches long. How many millimetres long is the wound? Round to the nearest tenth.
You measure the depth of a wound to be 0.25 inches. How many millimetres is this? Round to the nearest whole number.
(a) If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is 63.5 mm.
(b) If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is 6.35 mm.
What is the measure of the lengths?If you measure a wound to be 2.5 inches long, the corresponding length in millimeters is calculated as follows;
1 in = 25.4 mm
2.5 in = ?
? = 2.5 x 25.4 mm
? = 63.5 mm
If you measure the depth of a wound to be 0.25 inches, the corresponding length in millimeters is calculated as follows;
1 in = 25.4 mm
0.25 in = ?
? = 0.25 x 25.4 mm
? = 6.35 mm
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A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 2 inches, and a height of 1 1/2 inches. What is the surface area of the box?
Answer:
SA = 157 in²Steps:
SA = 2LW + 2WH + 2LH
SA = 2(9×2) + 2(2×11/2) + 2(9×11/2)
SA = 2×18 + 2×22/2 + 2×99/2
SA = 36 + 22 + 99
SA = 157 in²
The points (x, 3) and (-1, -4) lie on the same line. If the slope of the line is 1, what is
the value of x?
A-3
B 1
C 6
D-6
Answer:
C) 6
Step-by-step explanation:
use slope formula:
(-4 - 3) / (-1 - x) = 1
cross-multiply:
-7 = -1 - x
-6 = -x
6 = x
I need help thank you
Answer: 4x-3
Step-by-step explanation: use the slope formula to calculate the slope, then add the y-int to the equation and ur done hope this helps
Evaluate 3f(2) what is it
Answer:
the eanswer should be 12
Step-by-step explanation:
i took the test
20. Solve for x,
(x-2y) = 12
P
mathemat
I
vision oro
How do you do this?
Answer:
x= 24 and y = 6
Step-by-step explanation:
I think that the right answer
Help wit this? 10m-8m+2+10
Answer:
2m+12
Step-by-step explanation:
add like terms
2m+12
Plz help ASAP !!!!!!!! Plzz
Answer:
option a is the answer to the question