Answer:
Follows are the solution to the given points:
Step-by-step explanation:
Given value:
[tex]\to f_X (x) \ \ xe^{-x} \ , \ x>0[/tex]
For point a:
Moment generating function of X=?
Using formula:
[tex]\to M(t) =E(e^{tx})= \int^{\infty}_{-\infty} \ e^{tx} f(x) \ dx[/tex]
[tex]M(t) = \int^{\infty}_{-\infty} \ e^{tx}xe^{-x} \ dx = \int^{\infty}_{0} \ xe^{(t-1)x} \ dx[/tex]
integrating the values by parts:
[tex]u = x \\\\dv = e^{(t-1)x}\\\\dx =dx \\\\v= \frac{e^{(t-1)x}}{t-1}\\\\M(t) =[\frac{e^{(t-1)x}}{t-1}]^{-\infty}_{0} -\int^{\infty}_{0} \frac{e^{(t-1)x}}{t-1} \ dx\\\\[/tex]
[tex]= \frac{1}{t-1} (0) - [\frac{e^{(t-1)x}}{(t-1)^2}]^{\infty}_{0}\\\\=\frac{1}{(t-1)^2}(0-1)\\\\=\frac{1}{(t-1)^2}\\\\[/tex]
Therefore, the moment value generating by the function is [tex]=\frac{1}{(t-1)^2}[/tex]
In point b:
[tex]E(X^n)=?[/tex]
Using formula: [tex]E(X^n)= M^{n}_{X}(0)[/tex]
form point (a):
[tex]\to M_{X}(t)=\frac{1}{(t-1)^2}[/tex]
Differentiating the value with respect of t
[tex]M'_{X}(t)=\frac{-2}{(t-1)^3}[/tex]
when [tex]t=0[/tex]
[tex]M'_{X}(0)=\frac{-2}{(0-1)^3}= \frac{-2}{(-1)^3}= \frac{-2}{-1}=2\\\\M''_{X}(t)=\frac{(-2)(-3)}{(t-1)^4}\\\\M''_{X}(0)=\frac{(-2)(-3)}{(0-1)^4}= \frac{6}{(-1)^4}= \frac{6}{1}=6\\\\M''_{X}(t)=\frac{(-2)(-3)}{(t-1)^4}\\\\M''_{X}(0)=\frac{(-2)(-3)}{(0-1)^4}= \frac{6}{(-1)^4}= \frac{6}{1}=6\\\\M'''_{X}(t)=\frac{(-2)(-3)(-4)}{(t-1)^5}\\\\M''_{X}(0)=\frac{(-2)(-3)(-4)}{(0-1)^5}= \frac{24}{(-1)^5}= \frac{24}{-1}=-24\\\\\therefore \\\\M^{K}_{X} (t)=\frac{(-2)(-3)(-4).....(k+1)}{(t-1)^{k+2}}\\\\[/tex]
[tex]M^{K}_{X} (0)=\frac{(-2)(-3)(-4).....(k+1)}{(-1)^{k+2}}\\\\\therefore\\\\E(X^n) = \frac{(-2)(-3)(-4).....(n+1)}{(-1)^{n+2}}\\\\[/tex]
One step inequalities
15<-5x
Solve for x
I think 3 would be the answer if not I'm sorry
I'm having struggles with this, it would be much appreciated for assistance (:
I would be happy to help, but there is no problem
Step-by-step explanation:
3t + 7 = 2 +5t , then find the value of t.
Answer:
t = 5/2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3t + 7 = 2 + 5t
Step 2: Solve for t
[Subtraction Property of Equality] Isolate t terms: 7 = 2 + 2t[Subtraction Property of Equality] Isolate t term: 5 = 2t[Division Property of Equality] Isolate t: 5/2 = tRewrite: t = 5/2Answer:
t = ⁵⁄₂ or 2.5Explanation:
3t + 7 = 2 + 5t
Simplify both sides of the equation3t + 7 = 5t + 2
Subtract 5t from both sides3t + 7 − 5t = 5t + 2 − 5t
−2t + 7 = 2
Subtract 7 from both sides−2t + 7 − 7 = 2 − 7
−2t = −5
Divide both sides by -2
−2t / -2 = −5 / -2
Simplifyt = ⁵⁄₂
Turn the fraction into a decimalt = 2.5
t = ⁵⁄₂ or 2.5
Pls help extra points and mark brainlist
Answer:
x-4=19
Step-by-step explanation:
Hope that helps!
Answer:
x-4 is equal to 19
may be this is answer of your questions
Please help me with this work
Answer:
1. (5y) = 35
2. (6y) = 1
3. (4y) = 2
4. (11y) = 15
5. 18, 24, 42, 60
The number of miles Henry rides his bike in 10 days is 60miles
Step-by-step explanation:
Determine if the following is discrete or continuous data: The function c =
12p gives the cost c based on the number of pizzas p.
Answer:
Step-by-step explanation:
Remember, discrete data is separate, by itself, but continuous data goes on and can have numbers in between. So this problem is c = 12p is the cost of pizzas, you can have 1 pizza, 2 pizzas, 10 pizzas, 30 pizzas, etc., but you can't have 2.1314552 pizzas or 4.5, etc., so the data is discrete. Think of the graph, you would not connect the dots if you were graphing this data.
A line passing through the point (-8,-3) and has a slope of 5/4
Answer:
y=5/4x+7
Step-by-step explanation:
Honestly, I just guessed and checked, but here is a picture of evidence.
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
Answer:
where are the choices?
Step-by-step explanation:
Where are the choices?
An apple has 80 calories. This is 12 less than 1/4 the number of calories in a package of candy. How many calories are in the candy.
Pls helpp
Answer:
368 calories are in the candy.
Step-by-step explanation:
80 + 12 = 92.
92 x 4 = 368.
Ethan earns 64.00 in a day. If a month has 22
work days, then what is Ethan's monthly pay?
Answer:
$1408
Step-by-step explanation:
64 * 22 = 1408
Answer:
1408
Step-by-step explanation:
22x64=1408
Hope this helps!!!!
Simplify completely*****
Answer:
[tex]\displaystyle x - 3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{x^2 + 7x - 30}{x + 10}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{(x - 3)(x + 10)}{x + 10}[/tex][Fraction] Divide: [tex]\displaystyle x - 3[/tex]Factor and simplify
sec⁴x-tan⁴x÷sec²x + tan²
X
Verify the identity
Answer:
1
Step-by-step explanation:
sec⁴x-tan⁴x÷sec²x + tan²X
= sec⁴x-tan⁴x/sec²x + tan²X
= (sec²x)²-(tan²x)²/sec²x + tan²X
Using the difference of two square
a² - b² = (a+b)(a-b)
(sec²x)²-(tan²x)² = (sec²x + tan²X)(sec²x - tan²X)
= (sec²x)²-(tan²x)²/sec²x + tan²X
= (sec²x + tan²X)(sec²x - tan²X)/sec²x + tan²X
= sec²x - tan²X
Also sec²X = 1 + tan²X
Substitute
= 1 + tan²X- tan²X
= 1
Hence the value of the expression is 1
What is the answer to 2x+3=7?
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
2x + 3 = 7
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 3 on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Evaluate x + 12 when x=5
Answer:
17
Step-by-step explanation:
5+12
Answer:
the answer is 17.
Step-by-step explanation:
x + 12 when x = 5.
so x = 5.
5 + 12 = 17
11 is the quotient of a number y and 6.
Answer:
y/6=11
Step-by-step explanation:
y ÷ 6 = 11
Quotient means the end result of the division. So, this is a division problem.
y = 66.
Because 66 / 6 = 11
Have a beautiful day!
97 inches = how many yards?
Answer:
8 yards
Step-by-step explanation:
97 divided by 12
Use the images above to answer the question
0.05 is blank of 0.5
0.05 × 10 = 0.5
PLEASE MARK ME AS BRAINLIEST
The decimal 0.05 is 10 times the decimal number 0.5.
What is a decimal number?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A number is a numerical unit of measurement and labeling in mathematics. The first examples are the numbers 1, 2, 3, and 4.
The given decimals are 0.05 and 0.5. The expression will be solved as below:-
When the number 0.05 is multiplied by 10 then it will become 0.5.
0.05 x 10 = 0.5
Therefore, the decimal 0.05 is 10 times the decimal number 0.5.
To know more about decimal numbers follow
https://brainly.com/question/1827193
#SPJ2
if x+y=5, then what does y-5 equal?
Answer:
-x
Step-by-step explanation:
rearrange the terms by adding or subtracting the same thing from both sides:
[tex]x+y=5\\y = 5 - x\\y - 5 = -x[/tex]
A full-time employee who works 40 hours per week earns $27.50 per hour. Estimate that person's income. Round 52 weeks to 50 weeks per year, and round the hourly wage to the nearest dollar for the estimate. what is the estimated of annual income?
fifty five thousand 55,000
Marcy goal was to collect 10 cans of food for a local food bank. She collected 160 cans use the grid to model to understand how to write this as a ratio, a fraction
Answer:
We're told that Marcy collected 160 out of 10 cans. That could be expressed as 160/10, but given that the numerator and denominator are both divisible by 10, we can factor that out and express it as 16/1. You can also express it as ratio of 16:1 cans collected to cans intended.
Answer:
As a ratio, this is expressed as
✔ 160 to 100
As a fraction, this is expressed as
✔ 160/100
As a percent, this is expressed as
✔ 160%
Step-by-step explanation:
I just did it!
A metal strip is being installed around a workbench that is 7 feet long and 2 feet wide. Find how much stripping is needed
25.000.016 - 13.812.318
Answer:
11.187898
Step-by-step explanation:
In ΔOPQ, o = 5.2 inches, p = 8.4 inches and q=8.7 inches. Find the measure of ∠Q to the nearest 10th of a degree.
Answer:
75.475667
Step-by-step explanation:
Answer:75.5
Step-by-step explanation:
This is due soon help
Answer:
What where I can't see it...
Answer:
there is nothing bro .
A pizzeria charges $8 for a large cheese pizza plus $2 for each additional topping.
m = ______ b = ______
Answer:
m = 2
b = 8
Step-by-step explanation:
m, the slope, will be 2. This is because $2 is charged for each topping.
b, the y intercept, will be 8. This is because there is a standard charge of $8 for a cheese pizza without any toppings.
The y intercept can be represented by the point (0, 8), where 0 represents the amount of toppings and 8 represents the price of $8.
So, m = 2 and b = 8
A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has a scale of 1 inch to 500 feet. True or false: the map with a scale of 1 inch to 500 feet will be smaller
Line DCE is parallel to line AB
a) Find the size of angle ABC
b) Find the size of angle DCA
c) Calculate the size of angle ACB
Answer:
Angle DCA = Angle CAB. (Alternate Interior Angle)
Angle DCA = 68°
Angles(DCA + ACB + BCE) = 180°. (Linear Pair)
Angle ACB + 68° + 33° = 180°
Angle ACB = 79°
Therefore,
Angle ABC = 33°. (Alternate Interior Angle)
cos 48 degrees in fraction
Kylie and Matt are driving out of town, leaving from the same house in
different cars. Matt drives at a rate of 40 miles per hour. Matt drives 50
miles before Kylie begins traveling. Kylie drives at a rate of 50 miles per
hour. .
Answer:
They will meet in 5 hours.
Step-by-step explanation:
This question should ask how long until they meet.
Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie begins traveling.
So the total distance for Matt is given by:
[tex]M(t) = 40t + 50[/tex]
Kylie drives at a rate of 50 miles per hour.
When he starts(at position 0), Matt will be already at 50. So Kylie's equation is given by:
[tex]K(t) = 50t[/tex]
How many hours until they meet?
This is t for which:
[tex]K(t) = M(t)[/tex]
So
[tex]50t = 40t + 50[/tex]
[tex]10t = 50[/tex]
[tex]t = \frac{50}{10}[/tex]
[tex]t = 5[/tex]
They will meet in 5 hours.
