The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).
Therefore the answer is exp(m + k²/2).
The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.
The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.
The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.
For log-normal distribution, the expectation of X is calculated as follows:
E(X) = exp(m + k²/2)
where m is the mean of log(X) and k is the standard deviation of log(X).
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If b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
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1. From the information given in the triangles, are these triangles always, sometimes, or never congruent?
A. always
B. sometimes
C. never
D. cannot be determined
On solving the provided question, we can say that - the both triangle similar triangle ABC and triangle DEF
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
here,
AB = DE
BC = EF
AC = DF
so, by SSS both triangles are similar
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Given sin(- 0) = - 1/4 and tan 0 = √15/15
What is the value of cos 0?
A. √15/60
B. -√15/4
C. √15/4
D. -√15/60
im bord yallllllll ahhh :)
Answer:
You are bord and I'm stuck in a Geometrie assignment because I have a lot of missing work so I have to submit them before June 05 :(
Step-by-step explanation:
Answer:
same
Step-by-step explanation:
- listen to music
- if u have a sibing brag to them that u have freands and they dont
- go get Starbucks
- listen to true crime stores
thats what i do
What the answer too 3(-8+f)=57
The Answer is ...
f = 27
PLEASE HELP BETS ANSWER GETS CROWN THERE ARE 2 QUESTIONS
ANSWER LIKE THIS
Q1. ANSWER
Q2. ANSWER.
NO LINKS OR FILES PLEASEEEE. (btw this is my last one)
Answer:
I am sorry but I can not answer as you have forgotten part of the question. Please repost and make sure you have everything there before you post the question!
What is an equation of the line that passes through the points (-4,-3) and (3,-3)
Answer:
y=-3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-3-(-3))/(3-(-4))
m=(-3+3)/(3+4)
m=0/7
m=0
y-y1=m(x-x1)
y-(-3)=0(x-(-4))
y+3=0(x+4)
y+3=0
y=0-3
y=-3
what is the volume of the cylinder below
A. 175π units
Wyatt says that 0.6 has the same value as 0.600 do you agree explain
Answer:
Yes, the zeros can be used as place holders. When using place holders, the value does not change.
-1.8 × (-9.3)
How do I find this with the whole equation written out show your work of how you do this please
Answer:
16.74
Step-by-step explanation:
-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum
-1.8
x -9.3
---------
5 4
1 6 2 0
---------
1 6 7 4 ||| add two decimal spaces
16.74
Peter has 30 pencils and Tony has 14,how many pencils must Tony give Peter so that peter shall have 3 times as many as Tony
Tony must give 3 pencils to Peter,
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let Peter has x pencils and Tony has y pencils.
Then, we have equation x=3y (Peters pencils are 3 times as Tony).
Total pencils = 30+14
= 44 pencils.
So, x + y=44
Put x= 3y we get
3y+ y= 44
4y= 44
y= 11
Thus, Tony must give 3 pencils to Peter,
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A= v-u/ t
v = 37. 6 correct to 3 significant figures.
u = 11. 3 correct to 3 significant figures.
t = 8. 4 correct to 2 significant figures.
Work out the upper bound for the value of a.
Show your working clearly
The upper bound of a is 3.13.
Upper Bound
The smallest amount that would round up to the following anticipated value is the upper bound.
Significant FiguresThe number of digits that contribute to a value's level of precision is known as significant figures and is typically found in measurements. As soon as a digit is non-zero, we begin calculating significant numbers.
Given in the question
v = 37. 6
u = 11. 3
t = 8. 4
To find:- a = (v - u)/t
Solution: -
Since finding the upper boundary for a
Upper boundary = (upper v - lower u) / (lowest t)
So putting the value values of v, u, t in we get the value
a = (37.6 - 11.3) / 8.4
Therefore the value of a = 3.13
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Select all of the following 2D shapes that may be formed by slicing a square pyramid?
A square
B rectangle
C circle
Dtriangle
Answer:
A and D
Step-by-step explanation:
Ok so first, if you slice parallel to the base, you can get a square.
If you slice parallel to a face, you get a triangle.
helpp pleaaaaaaaaaseee
The linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
and the solution would be x = 8, y = 6.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that describe a relationship between multiple variables. The variables in each equation are related to each other, and the solution of a system of linear equations is the set of values that satisfy all of the equations in the system.
In this case, since Kent and Rew each bought the same amount of boondins and hopts, we can use the same variable names (x for boondins and y for hopts) for both of them. We can use this information to write two equations to model the relationship between the amounts of boondins and hopts that Kent and Rew bought:
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
This system of linear equations is called a system of two equations in two variables.
Hence, the linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
and the solution would be x = 8, y = 6.
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Is ∆MHT ≈ ∆TMA? If so, state the congruence property you used to make the determination and fully explain your reasoning. Be sure to cite all properties, definitions, or theorems used in your reasoning. You may use a flowchart if you wish. If they are not congruent, explain why they are not.
Please help
Answer:
Triangle MHT and Triangle TMA are congruent.
If you reflect over the dotted line, point H and A will be on the same point. The triangles are also the same shape and same size.
HELP ME PLEASEE !!!!
Answer:
y=179
Step-by-step explanation:
the statement is true.
you need to replace (x) for 4 and solve
y= 40(4) + 19
y=160 + 19
y=179
it costs 179$ for 4 weeks so the statement is true
Solve this system of equations. Explain how you determined your answer.
2x−4y=−14
−8x+4y=−4
Answer:
(3, 5 )
Step-by-step explanation:
Given the 2 equations
2x - 4y = - 14 → (1)
- 8x + 4y = - 4 → (2)
Adding (1) and (2) term by term will eliminate the y- term
- 6x + 0 = - 18
- 6x = - 18 ( divide both sides by - 6 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (2)
- 8(3) + 4y = - 4
- 24 + 4y = - 4 ( add 24 to both sides )
4y = 20 ( divide both sides by 4 )
y = 5
solution is (3, 5 )
I need help.
professional?
- needed
The equation of the linear function after a translation down 9 units is given as follows:
f(x) = x - 11.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value of y at which the graph cross the y-axis.The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:
b = -2.
When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:
m = 2/2.
Then the function is of:
y = x - 2.
After the translation down 9 units, 9 is subtracted from the function, hence:
f(x) = x - 2 - 9
f(x) = x - 11.
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One way to compute a 15% tip for a bill is to multiply it by 0.15. A restaurant bill was $36.20. Calculate the tip.
What is Destiny's hourly wage?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
or in this case, hourly wage :)
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{200}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{200}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{0}}} \implies \cfrac{ 200 }{ 10 } \implies \cfrac{20}{1}\cfrac{dollars}{hour}\qquad \textit{\$20 per hour}[/tex]
ILL BRAINLIEST YOU PLEASE HELP ME
Remember SohCahToa
For this let's use sine.
SinA = opposite/adjacent
SinA = x/c
We know c = 8 and A = 21
Sin21 = x/8
x = (sin21)8
Put that in the calculator:
x = 2.87 (rounded)hope this helps :D
if you don’t help I could possibly die.
What is a truth table in logic gate?
The Truth Table in logic gate is used to specify the output of the logic gate for all possible combinations of the input signals. , it is the breakdown of all the possible truth values returned by the logical expression.
What is Truth Table ?
The truth table is a tabular representation of all combinations of values for inputs and their respective outputs.
It can be called as a mathematical table which shows all possible outcomes that would occur from all the possible scenarios that are considered as factual.
Truth tables are generally used for the logic problems as in Boolean algebra and electronic circuits.
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Answer:
Step-by-step explanation:
A truth table for a logic gate is the table that specifies the logic value/state of the output of the gate for all possible combinations of the logic states of all inputs.
Let's take the example of the AND gate with two logic inputs A and B and one output Y.
A B Y
0 0 0
0 1 0
1 1 1
1 0 0
This is the truth table for the AND gate.
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
15 20
30
40
45
Town B
15 20 25 30
58
0
5
10
15
20
SO
55 60
25 30 35 40 45
Degrees (F)
Which statement is the most appropriate comparison of the centers?
A. The median temperature for both towns is 30°
B. The mean for town A, 30°, is greater than the mean for town B, 25
ОО O
C. The median temperature for both towns is 20°
D. The median for town A, 30°, is greater than the median for town B.
Answer: D
Step-by-step explanation:
A rectangle has an area of 266 square centimeters. If it's length is 19 cm, find its width
Answer: w=14 cm
Step-by-step explanation: w=A
l=266
19=14cm
Answer:
Area = length x width
so you do 266/19 = 14
hope that answers your question
Don't hesitate to comment if you don't understand something.
Step-by-step explanation:
A map of a playground can be represented on the coordinate plane below. The swings are located at (5, 7), the slide is located at (2, –4), and the sandbox is located at (0, 5). Jenny left the swings and walked 3 yards west and 2 yards south. Kent left the sandbox and walked 5 yards east and 4 yards north. If each square of the coordinate plane is equal to one square yard, how many yards north of the swings is Kent located? Help PLS
Answer:
2 yards
Step-by-step explanation:
The coordinates of the location of the swings = (5, 7)
The coordinates of the location of the slides = (2, -4)
The coordinates of the location of the sandbox = (0, 5)
The path through which Jenny walked = 3 yards west and 2 yards south from the swing
The path through which Kent walked = 5 yards east and 4 yards north from the sandbox
The coordinates of Kent's final location = (0 + 5, 5 + 4) = (5, 9)
Given that the coordinate of the location of the swing = (5, 7)
Kent is located at the coordinate (5 - 5, 9 - 7) = (0, 2) relative to the swing
Therefore, Kent is located 2 yards north of the swing.
Lesson 1. 12
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.
Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.
Assume at x= O the buoy is at normal ocean depth.
Find the following:
Period =
Equation of the mideline:
Amplitude =
Maximum =
Minimum =
For the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
What is the sine function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Asin(Bx)+C is the usual sine function formula.
A buoy bobs 6 meters up and down.
That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.
A=6 Amplitude
The x-axis distance that constitutes one complete oscillation is known as the period.
We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).
20 seconds make up the complete oscillation period.
⇒ 20 (B) = 2π
B=2π /20
= π/ 10
Given that the buoy is 10 meters under the ocean's surface, C equals –10.
Using the formula's whole range of values:
⇒y = 6sin ( (π/ 10) x ) - 10
The midline is the initial point.
x=0 is the first point.
⇒y=6sin(0)-10
y= -10
The line is drawn from the origin at y = -10.
Either the highest or smallest value is at the second point.
Therefore, (5,-4) and (15, -16.)
Therefore, for the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
''By taking log'' on both side Mike solve this equation.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 37ˣ = 12
Now,
Since, The expression is,
⇒ 37ˣ = 12
Solve this expression as;
⇒ 37ˣ = 12
Taking log both side, we get;
⇒ log 37ˣ = log 12
⇒ x log 37 = log 12
⇒ x = log 12 / log 37
⇒ x = 1.08 / 1.57
⇒ x = 0.69
Thus, The value of x = 0.69
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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
BC = 205.8 feet
Step-by-step explanation:
We only have one side, DB, so we have to use the given angles rather than the Pythagorean theorem.
Answer:
BC ≈ 205.8 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BD}{BC}[/tex] = [tex]\frac{67}{BC}[/tex] ( multiply both sides by BC )
BC × cos71° = 67 ( divide both sides by cos71° )
BC = [tex]\frac{67}{cos71}[/tex] ≈ 205.8 ft ( to the nearest tenth )
42 kg in the ratio 4 : 2
Answer:
28 : 14
Step-by-step explanation:
4 : 2
4 + 2 = 6
42 ÷ 6 = 7
7 × 4 = 28
7 × 2 = 14