A linear recurrence relation is homogeneous if f(n) = 0. The order of the recurrence relation is determined by k. We say a recurrence relation is of order k if an = f(an−1,...,an−k).
Given: a) an = 3an-1 + 4an-2 +5an-3
We note that the given recurrence relation is linear, because the right-hand side is a linear combination of previous terms. We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms. The degree of the recurrence relation is the largest value k for which are occurs in the recurrence relation.
k=3
Given: b) an = 2nan-1 + an-2
We note that the given recurrence relation is not linear, because the right-hand side is not a linear combination of previous terms (due to the
fact that 2n is not a constant). We note that the given recurrence relation is homogeneous, because the recurrence relation does not contain any constant terms.
Given: c) an = an-1 + an-4
Because the right-hand side is a linear combination of the prior terms, we observe that the provided recurrence relation is linear. Given that there are no constant terms in the recurrence relation, it is important to observe that it is homogenous. The biggest value k for which are k appears in the recurrence relation is the recurrence relation's degree.
Degree of linear homogeneous recurrence are k=3 .
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-10 (x+3) - 6x + 5
O -41x
0 -16x - 25
O 3x + 5
O 4x + 35
A population numbers 12,000 organisms initially and grows by 17.5% each year.
Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a â‹… b t where
P =
A population numbers 12,000 organisms initially and grows by 17.5% each year. The growth function of the population is P = 12,000 x 1.175^t
An exponential growth function can be written as:
P = A (1 + r)ⁿ
Where:
P = quantity after n periods
n = number of periods
r = growth rate per period
A = initial quantity
In the given problem, the period is the number of years t
A = 12,000
r = 17.5% = 0.175
Hence, the growth function:
P = 12,000 (1 + 0.175)^t
P = 12,000 x 1.175^t
Your question is incomplete, but most probably your question was:
A population numbers 12,000 organisms initially and grows by 17.5% each year. Suppose P represents population, and t the number of years of growth, write the function in terms of t.
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the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago. if the sample has a mass of today, find the initial mass of the sample. round your answer to two decimal places.
The initial mass of the sample is =2.39 kg
Radioactivity=Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.Radioactive describes something that exhibits or is caused by radioactivity. If something is radioactive, it emits radiation, which usually takes the form of electromagnetic waves or fast-moving elementary particles, such as protons or neutrons.
M(t)= Mo E =2.546 M(3)=2.54-02(3)
=2.54e -0.06
=2.39 kg (initial mass of the sample)
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How do I solve this problem?
5 + 2/3 ( 2p - 6 ) = 9
Answer:
p = 6
Step-by-step explanation:
5 + 2/3 (2p - 6) = 9
5 + 4/3p - 4 = 9
1 + 4/3p = 9
4/3p = 8
p = 6
Answer:
p= 6
Step-by-step explanation:
Solve for p:
(2 (2 p - 6))/3 + 5 = 9
Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:
(15/3 + (2 (2 p - 6))/3) = 9
15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:
((2 (2 p - 6) + 15)/3) = 9
2 (2 p - 6) = 4 p - 12:
((4 p - 12) + 15)/3 = 9
Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):
(4 p + (15 - 12))/3 = 9
15 - 12 = 3:
(4 p + 3)/3 = 9
Multiply both sides of (4 p + 3)/3 = 9 by 3:
(3 (4 p + 3))/3 = 3×9
(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:
(4 p + 3) = 3×9
3×9 = 27:
4 p + 3 = 27
Subtract 3 from both sides:
4 p + (3 - 3) = 27 - 3
3 - 3 = 0:
4 p = 27 - 3
27 - 3 = 24:
4 p = 24
Divide both sides of 4 p = 24 by 4:
(4 p)/4 = 24/4
4/4 = 1:
p = 24/4
The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:
Answer: p = 6
Sorry I’m slow I need my mathematicians. If I make $11 and hour work 9 hours Sunday-Friday and get paid bi weekly how much would my check be?
Your's check would be $198 for two weeks with 9 hours of work from Sunday-Friday.
Word problems:In a word problem, the mathematical operations are written in text format. To solve such a problem, the text should be understood and simple basic arithmetic operations are applied.
Calculation:It is given that,
He/She makes $11 for 1 hour and works for 9 hours from Sunday to Friday.
For 9 hours of work, he/she gets, $11 × 9 = $99
Then, for two weeks, the payment = $99 + $99 = $198
So, he gets a biweekly check with $198.
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Suppose That A Vector Y Is Orthogonal To Vectors U And V. Show That Y Is Orthogonal To The Vector U + V.
A vector Y is orthogonal to vectors U and V, so Y is orthogonal to the vector (U+V).
In the given question,
Suppose that a vector Y is Orthogonal to vectors U And V.
We have to show that Y is orthogonal to the vector U + V.
As to vectors are orthogonal if and only if their dot product is zero.
So Y∙U = 0 and Y∙V = 0.
To prove that Y is orthogonal to the vector(U+V), we have to show that Y∙(U+V) = 0.
As dot product is distributive. Now
Y∙(U+V) = Y∙U + Y∙V
As Y∙U = 0 and Y∙V = 0. So
Y∙(U+V) = 0 + 0
Y∙(U+V) = 0
Hence, Y is orthogonal to the vector (U+V).
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Part A:
Describe two possible financial goals for which you may require $12,000. Classify each as a want or need. Do research to ensure that amount is enough for your goal.
Part B:
Create and describe three possible investments to reach your goal within five (5) years. Investment 1 is a simple interest investment with 3% annual interest. How much would you need to invest at the beginning? Investment 2 is a compound interest investment, with 3% annual interest compounded monthly. How much would you need to invest at the beginning?
Investment 3 is a regular deposit in an account that earns 3% compound interest, compounded once per year. How much do you need to deposit, and how often will you deposit it, to reach it Part C:
Calculate and describe the total interest earned on each of your three investments. Explain your thinking and show your work.
Part A: Two possible financial goals that may require $12,000 is to save for home ownership and education.
Part B: Three possible initial investments to reach the goal of having a future value of $12,000 in 5 years are:
Investment 1: initial investments of $10,435Investment 2: initial investments of $10,330.43Investment 3: Annual Deposit of $2,194.42.Part C: The total interest earned on each investment is as follows:
Investment 1: $1,565Investment 2: $1,669.57Investment 3: $1,027.90.How are the total interests computed?The total interest for investment 1 is a product of simple interest formula, which multiplies the principal, interest rate, and time.
The total interests for investments 2 and 3 are the results of the online finance calculator., which inputs the future value, compound interest rate, and compounding period.
Investment 1:Future value = $12,000
Investment Period = 5 years
Simple interest rate = 3% or 0.03
Initial investment, P = A/(1 + rt)
Where P = principal
A = Future Value
r = interest rate
t = time
P = $12,000/(1 + 0.03 x 5)
= 12,000/(1.15)
= $10,435
Total Interest = $1,565 ($12,000 - $10435) or ($10,435 x 3% x 5)
Investment 2:Future value = $12,000
Investment Period = 5 years
Compound interest rate = 3% or 0.03 monthly
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $0
FV (Future Value) = $12,000
Results:
Present Value (PV) = $10,330.43
Total Interest = $1,669.57
Investment 3:Future value = $12,000
Investment Period = 5 years
Compound interest rate = 3% or 0.03 annually
N (# of periods) = 5 years
I/Y (Interest per year) = 3%
PV (Present Value) = $0
FV (Future Value) = $12,000
Results:
Periodic Deposits = $2,194.42
Sum of all periodic payments = $10,972.10
Total Interest = $1,027.90
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the post offices calculate shipping costs based on the weight of the item in addition to a fee. The cost to ship a 2 pound item is 6.09, while the cost to ship a 7 pound item is
8.84. Find the rate of change of the cost with respect to the weight of the item
The rate of change of the cost with respect to the weight of the item is equal to 0.55.
What is the rate of change?Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the shipping costs (y) with respect to the weight of the item (x), with the following data points (2, 7) and (6.09, 8.84):
Rate of change, m = (8.84 - 6.09)/(7 - 2)
Rate of change, m = 2.75/5
Rate of change, m = 0.55.
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what should i write blank can someone help pls
The blanks are completed as follows:
s/(s² - 18s + 81) = s/(s - 9)².F(s) = s/(s - 9)².Then the inverse Laplace transform is given as follows:
f(t) = e^(9t) + 9te^(9t).
How to obtain the inverse Laplace transform?The function for this problem is given as follows:
F(s) = s/(s² - 18s + 81).
Completing the squares at the denominator, we have that:
F(s) = s/(s - 9)².
Applying partial fraction decomposition, the function can be defined as follows:
s/(s - 9)² = A/(s - 9) + B/(s - 9)²
Expanding the right side, we have that:
s/(s - 9)² = [A(s - 9) + B]/(s - 9)²
Hence:
As - 9A + B = s.
Then the system for the coefficients is given as follows:
A = 1.-9A + B = 10-> B = 9A -> B = 9.Thus the function in the transform domain is of:
F(s) = 1/(s - 9) + 9/(s - 9)².
Applying the inverse Laplace transform, the function in the time domain is given as follows:
f(t) = e^(9t) + 9te^(9t).
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se green's theorem to evaluate the line integral along the given positively oriented curve. c 5y 7e x dx 10x 9 cos(y2) dy c is the boundary of the region enclosed by the parabolas y
By using Green's Theorem, it can be calculated that
[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] = [tex]\frac{5}{3}[/tex]
What is Green's Theorem?
Green's Theorem gives a relationship between a line integral along a closed curve C and surface integral around plane region D bounded by C
By Green's Theorem,
[tex]\int_c Pdx+ Qdy = \int\int_D (\frac{\partial P}{\partial y} - \frac{\partial Q}{\partial x})dxdy[/tex]
To evaluate [tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex] using Green's Theorem,
Region is between the parabola [tex]y = x^2[/tex] and [tex]x = y^2[/tex]
To find point of intersection,
[tex]x = y^2\\x = (x^2)^2\\x = x^4\\x^4 - x = 0\\x(x^3 - 1) = 0\\x = 0 \ or \ x^3 - 1 = 0\\x = 0 \ or \ x^3 = 1\\x = 0 \ or \ x = 1[/tex]
Along y- axis the limit of integration is from y = [tex]x^2[/tex] to y = [tex]\sqrt{x}[/tex]
P = [tex]5y + 7e^x[/tex]
[tex]\frac{\partial P}{\partial y}[/tex] = 5
Q = [tex]10x + 9(cos(y^2))[/tex]
[tex]\frac{\partial Q}{\partial x}[/tex] = 10
By Green's Theorem,
[tex]\int_c(5y+7e^x)dx+(10x+9cos(y^2))dy[/tex]
= [tex]\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}(10 -5)dxdy\\\\\int_{x = 0}^1\int_{y = x^2}^{\sqrt{x}}5dxdy\\\\\int_{x = 0}^1 5(\sqrt{x} - x^2)\\\\5[(\frac{2}{3})x^{\frac{3}{2}} - \frac{x^3}{3}]_0^1\\\\5(\frac{2}{3} -\frac{1}{3})\\\\\frac{5}{3}[/tex]
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you flip a weighted coin that comes up heads 40% of the time and tails 60%. if you flip this coin 5 times, what is the probability that you see at least 3 tails, rounded to the nearest percent? please input your answer as a decimal rounded to the nearest hundreth
The probability that in 5 flips, at least 3 tails will come will be 0.36.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that you flipped a weighted coin that comes up heads 40% of the time and tails 60%.
The coin shows up heads 40% of the time and tails 60%, this means that the probability of turning to tails would be 0.6 . For 5 flips that, the probability that at least 3 tails will come will be -
P{A} = (0.6 + 0.6 + 0.6)/5 = 1.8/5 = 0.36
P{A} = 0.36
Therefore, the probability that in 5 flips, at least 3 tails will come will be 0.36
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Which statements are true regarding the sequence below? Check all that apply.
20.4, 24, 244.
It can be represented using the formula f(x + 1) = (f(x)) when f(1) = 10.
It can be represented using the formula x=4
It can be represented using the formula fox)=
The domain of the sequence is all real numbers.
The range of the sequence is all natural numbers.
The statements that are true regarding the sequence below are
It can be represented using the formula f(x) = 10/3 (6/5)ˣ⁻¹The domain of the sequence is all real numbers.How to find the true statementsThe given sequence include 10/3, 4, 24/5, 244/25
Applying the formula f(x) = 10/3 (6/5)ˣ⁻¹ to it
for x = 1, f(x) = 10/3 (6/5)¹⁻¹ = 10/3
for x = 2, f(x) = 10/3 (6/5)²⁻¹ = 4
for x = 3, f(x) = 10/3 (6/5)³⁻¹ = 24/5
This shows that the formula works for it hence a correct statement
Real numbers include all positive and negative numbers, fractions and decimals alike and the domain are natural numbers which are part of real numbers
The range are also all real numbers and this go beyond natural numbers
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c.96 test to see if there is evidence that the lie detector says a person is lying more than 50% of the time, regardless of what the person reads.
It is not possible for a lie detector, or any other type of technology, to accurately determine whether a person is lying more than 50% of the time. Lie detectors, also known as polygraph machines, measure physiological responses such as changes in heart rate, blood pressure, and respiration to determine if a person is telling the truth or not. However, these responses can be affected by many factors, such as anxiety or stress, and are not always reliable indicators of deception. In addition, people can learn how to manipulate their physiological responses in order to deceive the polygraph machine. Therefore, it is not accurate to say that a lie detector can determine whether a person is lying more than 50% of the time
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Use the diagram to answer the questions.
What is the value of x?
x =
What is the measure of angle B?
B =
What is the measure of the exterior angle ACD?
ACD =
The value of x is 21
The measure of angle B is 28°
The measure of exterior angle ACD is 63°
Calculating the measure of anglesFrom the question, we are to determine the measure of the angles.
From the given diagram, we can write that
35° + (x + 7)° = 3x° (Exterior angle theorem)
Solve for x in the equation
35° + (x + 7)° = 3x°
35° + x° + 7° = 3x°
35° + 7° = 3x° - x°
42° = 2x°
Divide both sides by 2
42°/2 = 2x°/2
21° = x°
Therefore,
x = 21
The measure of angle B is
Measure of angle B = (x + 7)°
Measure of angle B = (21 + 7)°
Measure of angle B = 28°
The measure of exterior angle ACD
Measure of exterior angle ACD = 3x°
Measure of exterior angle ACD = 3(21)°
Measure of exterior angle ACD = 63°'
Hence, the measure of the exterior angle is 63°
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In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at $220 before tax.
How much sales tax does Yuki pay for her handbag purchase?
Answer:
$18.15 of taxes
Step-by-step explanation:
based on the givens: 220 (4.6% + 3.65% )
calculate the sum or difference: 220 x 0.0825
calculate the product: 18.15
2
2
2
18. 1. The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total
of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many
two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.
How to find the number of two and three points made?The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.
Therefore, the number of two-points and three-points the cruiser scored is as follows:
let
x = number of two-points
y = number of three-points
Hence, using equation
x + y = 43
2x + 3y = 105
Multiply equation(i) by 2
2x + 2y = 86
2x + 3y = 105
subtract equation(i) from equation(ii)
y = 19
Let's find x as follows:
x = 43 - 19
x = 24
Therefore,
number of two points = 24
number of three points = 19
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Please read both questions first, and guess whether the two answers would be the same, except one is positive and one is negative. Check whether you guessed correctly after you have done the calculations.
a) A company has increased its sales team from 40 people to 50 people. What is the percent change?
b) A company has reduced its management team from 50 people
to 40 people, what is the percent change?
PLEASE HELP
Answer:
Step-by-step explanation:
Please help:
89345+7899-5/2*8=?
Answer:
97224
Step-by-step explanation:
BODMAS
B ×
O ×
Division (5/2)
Multiplication (5/2*8)
Addition (89345+7899)
S ×
Do it in this order
What are the vertex and range of y = |2x + 6| + 2? 1 (0, 2); 2 < y < ∞ 2 (0, 2); −∞ ≤ y < ∞ 3 (−3, 2); 2 < y < ∞ 4 (−3, 2); −∞ ≤ y < ∞
Answer: The vertex is at (-6, 2). The range is 2 < y < ∞.
Step-by-step explanation:
y = |2x + 6| + 2 is almost in vertex form, which is y = |x - h| + k. We will divide both values by 2, so the 2 coefficient is on the outside, y = 2|x + 3| + 2.
After this, we can see that the vertex is at (-h, k). This means the vertex is at (-3, 2).
For the range, since this V (the shape of an absolute value graph) opens upwards, it will be everything greater than and equal to the y value of the vertex, in this case, 2. That means our range is;
2 < y < ∞
Answer:
The answer is c, or (3, 2), 2 less than y is greater than infinity
Step-by-step explanation:
I got it right on the test
Have a good day and hope it helps!
use implicit differentiation to find the derivative dy dx. b. find the slope of the curve at the given point. cos(y)
The slope of the curve at the given point is approximately -28
What is the derivative of a function?
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
To find the derivative of y with respect to x using implicit differentiation, we need to take the derivative of both sides of the equation cos(y) = 7x^4 - 7.
On the left side of the equation, we can use the chain rule to find the derivative of cos(y) with respect to x:
d/dx[cos(y)] = -sin(y) * dy/dx
On the right side of the equation, we can use the power rule to find the derivative of 7x^4 - 7 with respect to x:
[tex]d/dx[7x^4 - 7] = 28x^3[/tex]
Substituting these expressions into the original equation, we get:
[tex]-sin(y) * dy/dx = 28x^3[/tex]
To solve for dy/dx, we can divide both sides of the equation by -sin(y):
[tex]dy/dx = -(28x^3)/sin(y)[/tex]
To find the slope of the curve at the given point, we need to substitute the values of x and y into the expression for dy/dx.
The slope at (1, π/2). would be
slope = -(28((1)^3))/sin(π/2) = -28.
Hence, the slope of the curve at the given point is approximately -28.
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HELP THERS MORE OF THESE
Answer:
y=5x
Step-by-step explanation:
intercept is 0
Slope is 5
A photograph is 8 centimeters wide. After Kari enlarges the photograph, it is 3 times as wide as the original. How wide is the photograph in millimeters?
answer: should be
8 *3 =24 centimeters
1cm = 10mm
24cm = 240mm
the photograph is 240 mm
The width of the photograph in millimeters is 240 mm.
How to illustrate the scale?It should be noted that a scale factor simply shows the relationship between a shape abd the original value given.
In this situation, the photograph is 8 centimeters wide and after Kari enlarges the photograph, it is 3 times as wide as the original.
The photograph in millimeters will be:
= 8 × 3 × 10
= 240 millimeters.
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Please help!! Solve x^2 = 36 for x. I think it may be A not so sure tho.
Answer: You are correct
Step-by-step explanation:
For a company picnic, Kylie ordered a box of fresh-baked gingerbread cookies and sugar
cookies. She got 60 cookies in all. 54 of the cookies were gingerbread. What percentage of
the cookies were gingerbread?
Write your answer using a percent sign (%).
Consider the matrices
A= 4 7 , B= -2 3 . C= 3 4 -1, and D= 6
-3 8 0 5 2
-5 -2
What are the dimensions of the product matrix of two of these matrices?
Drag the matrix dimensions to each box to match the product.
BD 2 x 1
CA 3 x 3
DC 2 x 3
The dimensions of the product matrix of two of these matrices is BD = 2 * 1 , CA = 1 * 3 and DC = 2 * 3 .
Given :
The dimension of BD :
B dimensions = ( 2 * 2 )
D dimensions = ( 2 * 1 )
Product of BD dimensions = Numbers of rows of B * number of columns in D
= 2 * 1
The dimension of CA :
C dimensions = ( 1 * 3 )
A dimensions = ( 3 * 3 )
Product of CA dimensions = Numbers of rows of C * number of columns in A
= 1 * 3
The dimension of DC :
D dimensions = ( 2 * 1 )
C dimensions = ( 1 * 3 )
Product of CA dimensions = Numbers of rows of D * number of columns in A
= 2 * 3
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Graph: y > 6
Is (-2,7) a solution? yes or no
Is ( 2,6) a solution? yes or no
Answer:(-2,7) is a yes
(2,6) is no pls mark brainiest
Step-by-step explanation: did a question like this and i mastered this subject
cash received from long-term notes payable $ 67,000 purchase of investments 16,900 cash dividends paid 54,200 interest paid 27,100 compute cash flows from financing activities using the above company information. (amounts to be deducted should be indicated by a minus sign.)
cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300
With regards to the above, information, the amount of cash dividends paid that should be recorded is computed as;
= Cash dividends payable at the beginning of the year + Cash dividends declared for the year - Cash dividends payable at the end of the year
= $27,100 + $67,000 - $54,200
= $ 148 300
Therefore, cash dividends paid that should be recorded in the financing section of the statement of cash flow is $ 148300
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Peter deposited some money in a new checking account. Over time, he withdrew the same
amount of money each week to spend on movies and music. The table shows the balance in
Peter's checking account, in dollars, over time.
Time (t)
4 weeks
8 weeks
10 weeks
15 weeks
Balance (B)
$537
$449
$405
$295
How much money did Peter deposit in his checking account?
Complete the equation to represent the situation.
B =
t+
625 is the total amount deposited by Peter in his checking account.
1) According to question
Balance after 4 weeks= 537 (equation 1)
Balance after 8 weeks= 449 (equation 2)
Each week Peter withdraws same amount.
Let the same amount be x.
From equation 1 and 2
Money spent in 4 weeks = 537-449=88
Therefore money spent in one week = 88/4=22
So the amount deposited by Peter=537 +22x 4 weeks
=537+88=625
2) B=625-22t
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Evaluate the line integral, where C is the given plane curve. 1649 (x®y + sin(x)) dy, C is the arc of the parabola y = x2 from (0, 0) to (1, x2)
Line integral will be ∫c(x²y + sinx )dy = 1/3π²×π³ + 2π
Given:
C is the arc of parabola y = x² from (0,0) to (π,π²)
Let x be the parameter ; since the parabola is given as function of x
the parametric equations are
x=x,y=x², for 0≤x≤π
By using concept
∫c(x²y + sinx)dy = [tex]\int\limits^0_x {(x^2(x^2) + sinx} \, ).2xdx[/tex]
by applying the limits of integration we get ,
= 2 [ π².π³/6 + [ -πcosπ + sinπ - (0 + sin0)] ]
by calculating,
= 2 ( π².π³/6 + π )
= 1/3 π².π³ + 2π
Thus,
∫c(x²y + sinx )dy = 1/3π²×π³ + 2π
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assume that x is uniformly distributed on [0,3]. using the central limit theorem, find the shortest interval (around hn) that has 95% probability of containing the true value of h. (such an interval is known as 95% confidence interval for h).
The probability density function (pdf) for the uniform distribution has the basic formula: f(x) = 1/ (B-A) for A x B.
A continuous probability distribution, the uniform distribution is concerned with equally likely outcomes. It is referred to as having a rectangular distribution on the interval [a,b] or having a uniform distribution for the continuous random variable X. Above is a representation of the probability density function of a continuous uniform distribution. The probability of drawing a heart, club, diamond, or spade is equally likely; hence, the area under the curve is 1, which makes sense given that the total of all probabilities in a probability distribution is 1.
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