a. Show that if a random variable U has a gamma distribution with parameters a and ß, then E[]=(-1) b. Let X₁, ‚X₁ be a random sample of size n from a normal population N(μ₂o²), -[infinity] 3, the
Answers
The expected value of a random variable U, following a gamma distribution with parameters a and ß, is E[U] = a/ß. We start by acknowledging that the gamma distribution is defined as:
f(x) = (1/Γ(a)ß^a) * x^(a-1) * e^(-x/ß)
where x > 0, a > 0, and ß > 0. The expected value E[U] is given by:
E[U] = ∫[0,∞] x * f(x) dx
To calculate this integral, we can use the gamma function, Γ(a), which is defined as:
Γ(a) = ∫[0,∞] x^(a-1) * e^(-x) dx
Now, let's substitute the expression of f(x) into E[U] and evaluate the integral:
E[U] = ∫[0,∞] (x^a/ß) * x^(a-1) * e^(-x/ß) dx
= (1/Γ(a)ß^a) * ∫[0,∞] x^(2a-1) * e^(-x/ß) dx
Using the property of the gamma function, we can rewrite the integral as:
E[U] = (1/Γ(a)ß^a) * Γ(2a)ß^(2a)
= (Γ(2a)/Γ(a)) * ß^a * ß^a
= (2a-1)! * ß^a * ß^a / (a-1)!
= (2a-1)! / (a-1)! * ß^a * ß^a
= (2a-1)! / (a-1)! * ß^(2a)
Note that (2a-1)! / (a-1)! is a constant term that does not depend on ß. Therefore, we can write:
E[U] = C * ß^(2a)
To make E[U] independent of ß, we must have ß^(2a) = 1, which implies that ß = 1. Thus, we obtain:
E[U] = C
Since the expected value is a constant, it is equal to a/ß when we choose ß = 1:
E[U] = a/ß = a/1 = a
Therefore, the expected value of a random variable U following a gamma distribution with parameters a and ß is E[U] = a.
To know more about the gamma distribution refer here:
https://brainly.com/question/23837265#
#SPJ11
Related Questions
Which statement best analyzes the role this event plays in the plot?
In "The Necklace" Mathilde realizes too late that the necklace is a fake.
Answers
The statement that best analyzes the role this event plays in The Necklace plot is A. It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
How to illustrate the information?There are both planned and unplanned events, and the start and end times may be noted. Event types include accidents, celebrations, natural disasters, and rallies. The event is the occurrence of the event.
Loisel is well-liked and adored by all. As she walks away, she searches for the pendant and discovers it has gone missing. After days of searching, she and her husband decide to replace it with something similar. It takes her ten decades to pay for the successor, which costs the same as your salary.
In this case, it best analyzes the role this event plays in leading to the resolution where Mathilde learns a lesson about the downfall that can come from vanity and greed The plot of The Necklace.
Therefore, the correct option is A.
Learn more about the necklace on:
https://brainly.com/question/18922838
#SPJ1
Complete question
Which statement best analyzes the role this event plays in The Necklace plot?
“Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!”
It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
It is the climax of the story since the reader is most excited at this point.
It serves as a complicating incident because Mathilde will have to suffer the consequences of her actions.
It serves as the falling action because it shows that Mathilde will have to get used to her place in life.
Solve: (4x-1) divided by 2 =x+7
Answers
Answer:
x=5/2
Step-by-step explanation:
4x-1/2=x+7
4x-x=7+1/2
3x=14/2+1/2
3x=15/2
x=15/2×1/3
so
x=5/2
probability 30%, 25%, 10% and 35%
value $100, $70, $30 and $1
You find an old coin. You know it is worth one of four possible amounts, according to this table. What is its expected value? Please express your answer to the nearest cent (1.e. $11.38).
Answers
The probability and value of a coin are given in the table. Using the table, the expected value is found to be $50.85.
Expected values (E(X)) are values that are considered as the result of the next repeated trial in an experiment. This value is calculated by multiplying the probability and each outcome value. The formula to used to calculate this expected value is given by, \(E(X)=\mu=\sum^{n}_{i=1}x_iP(x_i)\).
Here, the probability of each outcome is denoted by \(P(x_i)\), the outcome is denoted by \(x_i\), the mean is denoted by μ and the expected value is denoted by E(X).
In the given table, first, convert the given probability in terms of decimals, then multiply each probability with each value. Now, we have to add all the values of x. P(x) to get the expected value,
E(X)=ΣxP(x)
=30+17.5+3+0.35
=50.85
The required answer is $50.85
To know more about expected value:
https://brainly.com/question/29574962
#SPJ4
The complete question is -
You find an old coin. You know it is worth one of four possible amounts, according to this table. What is its expected value? Please express your answer to the nearest cent (i.e. $11.38).
Ocean depth is usually measured in fathoms, but that is not a relatable unit and is often converted. Echosounding determined the depth of an area off the coast of Bermuda to be 780 fathoms. How many meters is this
Answers
Ocean depth is commonly measured using the unit of fathoms, which represents a specific length underwater. However, since fathoms may not be a familiar or relatable unit for many people, it is often converted to more commonly used units such as meters.
In this case, the depth of an area off the coast of Bermuda was determined to be 780 fathoms. To convert this measurement to meters, we use the conversion factor that one fathom is equal to 1.8288 meters. By multiplying the number of fathoms (780) by the conversion factor (1.8288 meters/fathom), we can calculate the depth in meters.
The calculation would be: 780 fathoms * 1.8288 meters/fathom = 1425.984 meters.
Therefore, the depth of the area off the coast of Bermuda is approximately 1425.984 meters. This conversion allows for a more relatable and commonly used unit of measurement when discussing ocean depths.
Learn more about ocean depth, brainly.com/question/14141884
#SPJ11
Factor: x2 + 30x – 70
Answers
Answer:
x=
295
−15≈2.175564037
x=−
295
−15≈−32.175564037
Step-by-step explanation:
Answer:
x^2+30x−70
Step-by-step explanation:
Let's simplify step-by-step.
x^2+30x−70
There are no like terms.
A contractor is building a wheelchair ramp for a doorway that is 12 feet above the ground. To meet ADA guidelines, the ramp will make an angle of
with the ground to the nearest tenth of an inch, what is the length of the ramp? "hint-how many inches in a foot?"
The distance of AC is
B
4.8
inches
A
1.2 ft
B
Answers
The length of the ramp is approximately 14.3 inches.
We can use trigonometry to determine the length of the ramp. Let's name the ramp's length "x."
We know that the height of the doorway is 1.2 feet, and we want the ramp to make an angle of 4.8 degrees with the ground.
From trigonometry, we know that as per the tangent function,
tan(4.8) = opposite/adjacent
where "opposite" is the height of the doorway (1.2 feet) and "adjacent" is the length of the ramp (x).
Now we can solve for x:
tan(4.8 ) = 1.2 / x
x = 1.2 / tan(4.8 )
x ≈ 14.3 inches
To learn more about the tangent function;
https://brainly.com/question/22043858
#SPJ1
A sauce recipe calls for 3/4 cup of chicken broth. To make enough sauce for a party, Marcy needs to triple the recipe.
2 (3) = (*) (6)
cups of chicken broth,
She estimates that the tripled recipe will need
The exact amount of chicken broth needed is
cups.
Answers
Answer:
less than 3
9/4
Step-by-step explanation:
Answer:
less than 3
9/4
Step-by-step explanation:
boom!!!
A pair of angles is supplementary if the sum of their measures is 180 degrees. A pair of angels is complementary if the sum of their measures 90 degrees. the supplement of a given angel is 10 degrees more than twice its complement. Let 90-x equal the degree measure of its complement and 180-x equal the degree measure of its supplement. Write and solve an equation to find the measure of the given angel.
Answers
Answer:
The measure of the complement =
= 80°
The measure of the supplement=
= 170°
Step-by-step explanation:
Let
90-x equal the degree measure of its complement
180-x equal the degree measure of its supplement.
We are told in the question that: the supplement of a given angle is 10 degrees more than twice its complement.
Hence, the Equation is;
(180 - x) = 10° + 2(90 - x)
180 - x = 10 + 180 - 2x
Collect like terms
-x + 2x = 10 + 180 - 180
x = 10°
Hence,
The measure of the complement =
90 - x
= 90 - 10
= 80°
The measure of the supplement=
180 - x
= 180 - 10
= 170°
Robert is moving and must rent a truck. In addition to an initial fee, the rental company charges a fee of $1.50 per mile driven. If Robert were to drive 4 miles, the total cost would be $26. Write an equation for C, in terms of m,m, representing the total cost of renting the truck if Robert were to drive mm miles.
Answers
Answer:
son $23.345 creo que si espero que si sea
which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?h=6, k=36h=−6, k=−36h=6, k=30h=−6, k=−30
Answers
The values of h and k used to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. To rewrite the given function in vertex form, we need to complete the square.
Starting with the function f(x) = x^2 + 12x + 6, we can rewrite it as f(x) = (x^2 + 12x + 36) - 36 + 6. Notice that we added and subtracted the square of half the coefficient of x, which is (12/2)^2 = 36.
Simplifying further, we have f(x) = (x + 6)^2 - 30. Comparing this form with the vertex form, we can see that h = -6 and k = -30.
Therefore, the correct values for h and k to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.
Learn more about function here
https://brainly.com/question/30721594
#SPJ11
PLEASE HELP I WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!
Use mathematical induction to prove that 1 + 2 + 3 + … + n = (1/2) n (a1 + an).
Use the result to find the sum of 1 + 2 + 3 + ... + 500.
Answers
Answer:
See below for proof.
\(S_{500}=125250\)
Step-by-step explanation:
Given arithmetic series:
1 + 2 + 3 + … + nTherefore:
\(S_n=1+2+3+...+(n-2)+(n-1)+n\)
\(S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)\)
\(S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))\)
Let:
a = first term = 1d = common difference = 1n = nth termTherefore:
\(S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)\)
Reverse the order:
\(S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a\)
Add the two expressions for Sₙ:
\(2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)\)
Therefore, the term (2a + (n – 1)d) has been repeated n times:
\(2S_n=n(2a+(n-1)d)\)
Divide both sides by 2:
\(S_n=\dfrac{1}{2}n(2a+(n-1)d)\)
\(S_n=\dfrac{1}{2}n(a+a+(n-1)d)\)
Replace a with a₁ (first term) and a + (n – 1)d with aₙ (last term):
\(S_n=\dfrac{1}{2}n(a_1+a_n)\)
To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:
a₁ = 1aₙ = 500n = 500Therefore:
\(\implies S_{500}=\dfrac{1}{2}(500)(1+500)\)
\(\implies S_{500}=250(501)\)
\(\implies S_{500}=125250\)
if a = 1 3 5 and b equals to 1 3 5 find a into B and Plot the co-ordinate in graph paper
Answers
To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.
Given:
a = [1, 3, 5]
b = [1, 3, 5]
To find a · b, we multiply the corresponding components and sum them:
\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)
So, a · b equals 35.
Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.
On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.
First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.
Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).
The graph paper would show a single point labeled 35 on the number line.
Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.
For more such questions on vector
https://brainly.com/question/3184914
#SPJ8
Please help!
Much appreciated if anyone would help x
Answers
B) 1/9
HOPE THIS HELPS :)
The average length of time that three computers operate on a given day is 960 minutes. None of the computers operate for less than 930 minutes. What is the greatest possible length of time any one of the computers operates
Answers
The greatest possible length of time will be "1020 min".
Given:
The average length of time,
= 960
For all 3 computers,
The minimum length of time,
= 930
Let,
The length of time of 2 computers will be "930".The 3rd one be "930+x".Now,
→ \(\frac{930+930+930+x}{3} = 960\)
→ \(\frac{930+930+930}{3} +\frac{x}{3} =960\)
→ \(\frac{3\times 930}{3} +\frac{x}{3} =960\)
→ \(930+\frac{x}{3}=960\)
→ \(\frac{x}{3} = 960-930\)
→ \(x = 30\times 3\)
→ \(x = 90\)
hence,
The greatest possible length of time will be:
= \(930+x\)
= \(930+90\)
= \(1020 \ min\)
Thus the above is the appropriate answer.
Learn more:
https://brainly.com/question/7994890
Two continental tectonic plates move apart at about 3 cm/year. How wide will the gap between those continents be in 15 years?
Answers
Answer:
45 cm in 15 years
here you go.
You are going to paint one side of a building. The wall is 105 feet long and 35 feet high. One gallon of paint covers 317 square feet with a single coat of paint. Find how many gallons should be purchased to apply one coat of paint to the side of the building.
Answers
Amount of paint that should be purchased to apply one coat of paint to the side of the building is 12 gallons.
What is area?Area is the amount of space occupied by a two-dimensional shape. That is, it is a quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is the square unit, commonly expressed in square inches, square feet, and so on.
Given,
length of the wall = 105 feet
height of the wall = 35 feet
Area of the wall
= length × height
= 105 × 35
= 3675 square feet
One gallon paints 317 square feet
Number of gallons to paint 3675 square feet
= 3675/317
= 11.59 ≈ 12
Hence, 12 gallons should be purchased to apply one coat of paint to the side of building.
Learn more about area here:
https://brainly.com/question/27683633
#SPJ1
E is the midpoint of DF, DE=6x+8, and EF=7x-5
Find DE, EF, and DF
Answers
6x+8=7x-5
+5 +5
6x+13=7x
-6x -6x
13=x
Now substitute 13 for x in 6x+8 to find DE.
6(13)+8 = 86
We already know since both sides are equal that EF also equals 86, but you can still substitute 13 again in 7x-5 to get EF.
7(13)-5 = 86
Now that we have both halves of DF, we can add 86+86 to get our total length of 172.
Find the volume of the shape with the given dimensions 8 in by 5 in by 3 in
Answers
Answer:
V = (8 in)(5 in)(3 in) = 120 in^3
Step-by-step explanation:
The likeliest name for this shape is "rectangular prism." Let's assume that the length, L, is 8 in; the width, W, is 5 in; and the height, H, is 3 in.
Then the volume of this rectangular prism is V = L * W * H, or
V = (8 in)(5 in)(3 in) = 120 in^3
Find the area of a right triangle that has one leg with a length of 8cm and a hypotenuse length of 17cm.
*Need it ASAP!!
Answers
Answer:
Step-by-step explanation:
\(b^2=h^2-a^2\\ \\ b^2=17^2-8^2\\ \\ b^2=225\\ \\ b=15\\ \\ A=15(8)/2\\ \\ A=60cm^2\)
How many equal sections divide a directed line segment if it is to be partitioned with a 2:7 ratio? 2, the least number given in the ratio
2, the least number given in the ratio
14, the least common multiple of the numbers given in the ratio
9, the sum of the numbers given in the ratio
5, the difference of the numbers given in the ratio
7, the greatest number given in the ratio
Answers
9514 1404 393
Answer:
9, the sum of the numbers given in the ratio
Step-by-step explanation:
The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.
It is convenient to think of the line segment as being divided into 9 equal parts.
_____
Additional comments
It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.
It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.
Tax is paid on meals in a restaurant.
The price of a meal is $65.35 this includes the tax of $11.45.
What is the percentage tax?
Answers
Answer:
17.52%
Step-by-step explanation:
65.35/11.45 = 0.1752
.1752 * 100
= 17.52
6. suppose that x is an exponential random variable with mean 1. give another random variable that is negatively correlated with x and that is also exponential with mean 1.
Answers
If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.
Let Y = 2 - X, where X is an exponential random variable with mean 1.
To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.
Cov(X,Y) = E[XY] - E[X]E[Y]
Since X and Y are both exponentially distributed with mean 1, we have:
E[X] = 1, E[Y] = 2 - E[X] = 1
E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)
Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0
Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.
Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.
Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.
Learn more about variable here:
https://brainly.com/question/29696241
#SPJ11
Given j(-8,-5) and l(6,-11) if k(r-4,2s) is the midpoint of jl which correctly gives the values of r and s?
Answers
The values of r and s is -1 and -4 respectively.
Given that:-
coordinates of j are (-8,-5)
coordinates of l are (6,-11)
coordinates of k are (r-4,2s)
Also, k is the mid-point of jl.
We have to find the values of r and s.
We know that, for (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).
Here,
(x,y) = (-8.-5)
(z,w) = (6,-11)
(r-4,2s) = ((x+z)/2,(y+w)/2)
Hence,
(r-4,2s) = ((-8+6)/2,(-5-11)/2)
(r-4,2s) = (-1,-8)
Comparing the coordinates, we get:-
r - 4 = -1
r = -1+4 =3
2s = -8
s =-8/2 = -4
To learn more about mid-point, here:-
https://brainly.com/question/11302835
#SPJ4
Communication in Gaussian noise. In a communication system, a transmitter wants to send some signal to a receiver over a noisy medium. Suppose the signal ΘΘ is a Gaussian distributed random variable Θ∼N(0,1)Θ∼N(0,1). The noise in the medium is modeled as a Gaussian distributed random variable W∼N(0,49)W∼N(0,49) independent of the signal. The receiver observes X=2Θ+WX=2Θ+W. Give your answers to at least 4 decimal places.
Answers
The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49). The probability of X being greater than 10 is very small, less than 0.001%.
In this communication system, the signal Θ is a Gaussian distributed random variable with a mean of 0 and standard deviation of 1. The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49).
The receiver observes X, which is the sum of 2Θ and W. Since Θ and W are independent, we can calculate the mean and variance of X as follows:
E[X] = E[2Θ + W] = 2E[Θ] + E[W] = 0 + 0 = 0
Var[X] = Var[2Θ + W] = 4Var[Θ] + Var[W] = 4(1) + 49 = 53
Therefore, X is also a Gaussian distributed random variable with a mean of 0 and standard deviation of √53 = 7.2801.
To find the probability of X taking a certain value, we can use the formula for the Gaussian probability density function:
f(x) = (1/√(2πσ^2)) * e^(-(x-μ)^2/(2σ^2))
where μ is the mean and σ is the standard deviation. For example, the probability that X is equal to 0 can be calculated as:
f(0) = (1/√(2π*53)) * e^(-(0-0)^2/(2*53)) = 0.0494
To find the probability of X being greater than a certain value, we can use the cumulative distribution function (CDF) of the Gaussian distribution. For example, the probability that X is greater than 10 can be calculated as:
P(X > 10) = 1 - Φ((10 - μ)/σ)
where Φ is the standard normal CDF. Substituting the values for μ and σ, we get:
P(X > 10) = 1 - Φ((10 - 0)/7.2801) = 0.00002
So the probability of X being greater than 10 is very small, less than 0.001%.
In the given communication system with Gaussian noise, the signal Θ is a Gaussian distributed random variable Θ∼N(0,1), and the noise W is also a Gaussian distributed random variable W∼N(0,49), independent of the signal. The receiver observes X = 2Θ + W. To provide accurate information, answers should be given to at least 4 decimal places.
Learn more about cumulative distribution function at: brainly.com/question/30402457
#SPJ11
Serena paid $24.60 for 7 and 1/2 gallons of gasoline. What is the cost per gallon of gasoline?
Answers
Answer:
The cost would be $3.28 for each gallon.
what does the phase line for x'=xsinx look like
Answers
Answer:
sm like this hope this helps your welcome
In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
Answers
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
For similar question on population proportion.
https://brainly.com/question/29516589
#SPJ8
The Jacksons and the Simpsons were competing in the final leg of the Amazing Race, which was 240240240 kilometers long. In their race to the finish, the Jacksons immediately took off traveling at an average speed of vvv kilometers per hour. The Simpsons' start was delayed by an hour. When they eventually took off, they traveled at an average speed that was 404040 kilometers per hour faster than the Jacksons' speed. Sadly for them, that didn't help, and the Jacksons won. Write an inequality in terms of vvv that models the situation.
Answers
Answer:
240/(v+40) + 1 > 240/v
Step-by-step explanation:
Both parties traveled a distance of 240 km.
Simpsons took off at average speed of 40 km/h & 1 hour later: 240/(v+40) + 1
Jacksons took off at average speed of v km/h: 240/v
An inequality in terms of v that models the situation is; [240/(v + 40)] + 1 > 240/v
How to write an inequality?We are told that distance travelled by both Jackson and Simpson is 240 km each.
Jacksons took off at average speed of v km/h. Thus, their time taken is 240/v
The Simpsons took off at an average speed of 40 km/h faster than Jacksons Speed. Since their start was delayed by an hour, then;
Time taken = [240/(v + 40)] + 1
Thus, the inequality that models the situation is; [240/(v + 40)] + 1> 240/v
Read more about Inequality at; https://brainly.com/question/25275758
#SPJ6
Which function in cryptography takes a string of any length as input and returns a string of any requested variable length?
Answers
The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.
According to the statement
we have to explain about the function in which cryptography takes a string of any length as input and returns a string of any requested variable length.
So, For this purpose,
we know that the
A sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length.
So from definition and its working process it is clear that for this purpose the sponge function is used.
this function returns the string of any variable length.
So, The sponge function in cryptography takes a string of any length as input and returns a string of any requested variable length.
Learn more about sponge function here
https://brainly.com/question/2328150
#SPJ4
A common belief among doctors, nurses and other medical professionals is that lunar cycle influences human behavior, such as the quality of sleep. In a recent study, a scientist was interested in investigating whether there is a significant difference in the number of sleeping hours in different moon phases: waxing crescent, full moon, and waning crescent. Participants’ number hour of sleep were recorded in the table below.
Quality of sleeps (in number of hours)
Waxing Crescent Full Moon Waning Crescent
7 4 5
8 5 7
9 4 8
7 3 9
8 6 6
With α = .05, determine whether there are any significant mean differences among your groups.
Answers
reject the null hypothesis and conclude that there is a significant difference in the mean number of sleeping hours among the three groups.
In order to investigate whether there is a significant difference in the number of sleeping hours in different moon phases: waxing crescent, full moon, and waning crescent, the scientist could use one-way analysis of variance (ANOVA) because it is a statistical method that is used to compare three or more groups of data from different populations. In the present case, three groups of data and each group has a sample size of 5.To perform one-way ANOVA State the null hypothesis and the alternative hypothesis:
Null hypothesis: There is no significant difference in the mean number of sleeping hours among the three groups.
µ1 = µ2 = µ3
Alternative hypothesis: There is a significant difference in the mean number of sleeping hours among the three groups.
µ1 ≠ µ2 ≠ µ3
Set the level of significance α. The level of significance is set to
α = 0.05
Calculate the total variation (SS)The total variation is given by:
SST = SSW + SSB
where SSW is the sum of squares within groups and SSB is the sum of squares between groups.
Calculate the sum of squares between groups (SSB)The sum of squares between groups is given by:
\(SSB = \frac{T^2}{n} - \sum_{i=1}^k \frac{X_i^2}{n_i}\)
\(SSB = \frac{(7+4+5+8+5+7+9+4+8+7+3+9+8+6+6)^2}{15} - \frac{7^2+4^2+5^2+8^2+5^2}{5} - \frac{9^2+4^2+8^2+7^2+3^2}{5} - \frac{8^2+6^2+6^2}{5}\)
SSB = 236.8
Calculate the sum of squares within groups (SSW)The sum of squares within groups is given by:
\(SSW = \sum_{i=1}^k \sum_{j=1}^{n_i} (X_{ij} - \bar{X}_i)^2\)
\(SSW = (7-7.4)^2 + (8-7.4)^2 + (9-7.4)^2 + (7-6.8)^2 + (8-6.8)^2 + (4-4.6)^2 + (5-4.6)^2 + (4-5.4)^2 + (8-5.4)^2 + (5-6)^2 + (7-6)^2 + (9-7.4)^2 + (6-6.8)^2 + (6-5.4)^2 + (3-4.6)^2\)
SSW = 30.4
Calculate the degrees of freedom (df)The degrees of freedom are given by:
df1 = k - 1 = 3 - 1 = 2 (between groups)df2 = N - k = 15 - 3 = 12 (within groups)
Calculate the mean square between groups (MSB)The mean square between groups is given by:
\(MSB = \frac{SSB}{df1}\)
\(MSB = \frac{236.8}{2} = 118.4\)
Calculate the mean square within groups (MSW)The mean square within groups is given by:
\(MSW = \frac{SSW}{df2}\)
\(MSW = \frac{30.4}{12} = 2.533\)
Calculate the F statistic The F statistic is given by:
\(F = \frac{MSB}{MSW}\)
\(F = \frac{118.4}{2.533} = 46.7\)
Determine the critical value of F The critical value of F is found using an F distribution table with α = 0.05, df1 = 2, and df2 = 12.The critical value of F is 3.89. The calculated F value is 46.7, which is much greater than the critical value of 3.89.
Therefore, we reject the null hypothesis and conclude that there is a significant difference in the mean number of sleeping hours among the three groups.
To learn more about null hypothesis
https://brainly.com/question/28042334
#SPJ11