integrate by parts xInx
Answer:
[tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
Integrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {x \ln x} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = \ln x[/tex][u] Logarithmic Differentiation: [tex]\displaystyle du = \frac{1}{x} \ dx[/tex]Set dv: [tex]\displaystyle dv = x \ dx[/tex][dv] Integration Rule [Reverse Power Rule]: [tex]\displaystyle v = \frac{x^2}{2}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \int {\frac{x}{2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2 \ln x}{2} - \frac{1}{2} \int {x} \, dx[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \int {x} \, dx \bigg)[/tex][Integral] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x \ln x} \, dx = \frac{1}{2} \bigg( x^2 \ln(x) - \frac{x^2}{2} \bigg) + C[/tex]Factor: [tex]\displaystyle \int {x \ln x} \, dx = \frac{x^2}{2} \bigg( \ln(x) - \frac{1}{2} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
and Mandy takes 3.9 percent of jimmy chocolate jimmy has 5000 pieces of chocolate chocolate how much does jimmy have left
Answer:
Jimmy has 4805 left
Step-by-step explanation:
3.9% = 0.039
5000(0.039) = 195
Mandy took 195 pieces
5000 - 195 = 4805
Jimmy has 4805 left
Cody has $1400 in a savings account that earns 4 % annually. How much will he have total after 3 years?
Use the formula = , where is the interest earned, is the principal (starting amount), is the interest rate expressed as a decimal, and is the time in years.
Answer:
$1,574.81Steps:
total after 1 year = (1400/100 × 4) + 1400 = (14 × 4) + 1400 = 56 + 1400 = $1456total after 2 years = (1456/100 × 4) + 1456 = (14.56 × 4) + 1456 = 58.24 + 1456 = $1,514.24total after 3 years = (1,514.24/100 × 4) + 1,514.24 = (15.14 × 4) + 1,514.24 = 60.57 + 1,514.24 = $1,574.81In a lottery game, three winning numbers are chosen uniformly at random from {1...100}, sampling without replacement. Lottery tickets cost $1 and allow a player to pick 3 numbers. If a player matches the three winning numbers they win the jackpot prize of $1,000. For matching exactly two numbers, they win $15. For matching exactly one number they win $3.
Required:
Find the distribution of net winnings for a random lottery ticket. Show that the expected value of the game is -70.8 cents.
Which postulate or theorem proves △SQY∼△PTY?
A. SAS Similarity Theorem
B. SSS Similarity Theorem
C. AA Similarity Postulate
Check the picture below.
[tex]\stackrel{ \textit{\LARGE S} }{\cfrac{8}{4}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{12}{6}}~~ = ~~\stackrel{ \textit{\LARGE S} }{\cfrac{4}{2}}\implies \text{\LARGE 2}\qquad \textit{similar triangles by SSS}[/tex]
A fish aquarium is 3 ft long, 2 ft wide, and 2 ft high. What is the volume of the aquarium?
ANSWER ASAP I DONT HAVE MUCH TIME
A lie detector is known to be 4/5 reliable when the person is guilty and 9/10 reliable when the person is innocent. If a suspect is chosen from a group of suspects of which only 1/100 have ever committed a crime, and the test indicates that the person is guilty, what is the probability that he is guilty?
Answer:
0.0748 = 7.48% probability that he is guilty
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Tests indicates guilty
Event B: Person is guilty
Probability that the test indicates that the person is guilty:
4/5 = 0.8 of 1/100 = 0.01(person is guilty)
1 - 0.9 = 0.1 of 1 - 0.99(person is not guilty). So
[tex]P(A) = 0.8*0.01 + 0.1*0.99 = 0.107[/tex]
Test indicates guilty and the person is guilty;
0.01 of 0.8. So
[tex]P(A \cap B) = 0.01*0.8 = 0.008[/tex]
What is the probability that he is guilty?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.008}{0.107} = 0.0748[/tex]
0.0748 = 7.48% probability that he is guilty
The required value is [tex]\simeq0.925 \ or \ 92.5[/tex]%.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]T_G[/tex] and [tex]T_I[/tex] denote the test result being guilty or innocent respectively.
And, [tex]G[/tex] and [tex]I[/tex] denote that the person is guilty or innocent respectively.
Given that: [tex]P\left ( T_G\mid I \right )=\frac{4}{5}[/tex]
[tex]P\left ( T_I\mid I \right )=\frac{9}{10}\Rightarrow P\left ( T_G\mid I \right )=1-\frac{9}{10}=\frac{1}{10}[/tex]
[tex]P(G)=\frac{1}{100} \\ \therefore P(I)=1-P(G) \\ =1-\frac{1}{100} \\ =\frac{99}{100}[/tex]
Now, the required probability is,
[tex]P(I\mid T_G)=\frac{P\left ( T_G\mid I \right )\times P(I)}{P(T_G\mid I)\times P(I)+P\left ( T_G\mid G \right )\times P(G)}[/tex]
[tex]=\frac{\frac{1}{10}\times\frac{99}{100}}{\left ( \frac{1}{10}\times \frac{99}{100}\right )+\left ( \frac{4}{5}\times\frac{1}{100} \right )} \\ =\frac{0.099}{0.099+0.008} \\ =\frac{0.099}{0.107} \\ =0.92523 \\ \simeq 0.925 \\ or \ 92.5%[/tex]
Learn more about the topic of Probability: brainly.com/question/26959834
79%
3rd
Her monthly salary is twice the sum of her husband's salary and four. Her monthly
salary is also equal to four more than four times his salary. How much does the
husband make a month? Note the husband's monthly salary is in terms of thousand
dollars.
9514 1404 393
Answer:
0
Step-by-step explanation:
The two expressions for her salary can be equated:
2h +4 = 4 +4h
0 = 2h . . . . . . . . subtract 2h+4 from both sides
h = 0 . . . the husband's salary is zero dollars per month
Answer:
$2000
Step-by-step explanation:
question is in picture please help!
Answer:
I’m not 100% sure but I think 120°.
Step-by-step explanation:
This is because, angles on a straight line add up to 180°. Because there is 60 degrees on one side of line B, this means the other section is 120° (120°+60°=180°) The angle labelled (3x) is alternate to the angle of 120°. Alternate angles are always equal, meaning that 3x is equal to 120°.
I hope this is right.
The following quadrilateral is a parallelogram. Solve for x, y, and z.
Answer:
X = 44Y = 31Z = 105Step-by-step explanation:
The measurements of a quadrilateral will add up to be 360. Additionally, we know these two triangles created within the parallelogram will be congruent, so their corresponding angles will also be congruent by CPCTC.
(44 * 2) + (105 * 2) + (31 * 2) = 360
Have a nice day, fam. Spread The Love.
Which is the greater decimal?
.721 or .72
Answer:
.721 is bigger because Il earned that the decimal that has a larger number as there last number is the greatest decimal.
Step-by-step explanation:
Joe needs to get to his house,which is 106 miles away in 2 hours.How fast does he need to drive
Answer:
53
Step-by-step explanation:
106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.
Use the scale to find the actual area of Janets bedroom in square feet!
Answer: 17 feet long 14 feet wide
The model has a scale of 1 : 16 so you can use a calculator like this one to find the exact length. https://www.ginifab.com/feeds/cm_to_inch/scale_converter.html
Having Problems With This Question
Answer:
f+g(2)=10
f-g(4)=-4
F/G(2)= 7/3
(f)(g)(1)=0
Step-by-step explanation:
1. (f+g)=2x+3+x^2-1 2(2)+2=10
2. (f-g)=(2x+3)-(x^2-1)=-x^2+2x+4= -16+8+4=-4
3. f/g= 2x+3/x^2-1 4+3/3= 7/3
4. f*g= (2x+3)(x^2-1)= 2x^3+3x^2-2x-3= 2(1)^3-2(1)+3(1)^2-3=0
We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 10 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 2 minutes. What is the smallest sample size that we should consider
Answer:
The smallest sample size that we should consider is 68.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 10 minutes.
This means that [tex]\mu = 10[/tex]
What is the smallest sample size that we should consider?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.645\frac{10}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.645*10[/tex]
[tex]\sqrt{n} = 1.645*5[/tex]
[tex](\sqrt{n})^2 = (1.645*5)^2[/tex]
[tex]n = 67.7[/tex]
Rounding up:
The smallest sample size that we should consider is 68.
Giving brainliest to someone who answers this :D plus points too
Answer:
13) 27 units³
14) 160 units³
15) 189 units³
Step-by-step explanation:
To find the volume of a rectangular prism, we need to multiply the length, width, and height of the figure together.
The dimensions of figure 13 are 9, 3, and 1
9 · 3 · 1 = 27
The volume of the figure is 27 units³.
-------------------------------------------------------------
The dimensions of figure 14 are 5, 8, and 4
5 · 8 · 4 = 160
The volume of the figure is 160 units³.
-------------------------------------------------------------
The dimensions of figure 15 are 3, 9, and 7
3 · 9 · 7 = 189
The volume of the figure is 189 units³.
-------------------------------------------------------------
I hope this helps ^^ Good luck :]
Please help me please
Answer:
486 square inches
Step-by-step explanation:
find sin(b) in the triangle
Answer:
We need the triangle, please
Explanation:
Can't find anything about a triangle without the triangle
Answer:
0
Step-by-step explanation:
Sin(undefined) reports 0.
If the value is not undefined, please provide the triangle.
I’m unsure how to do this statistics problem I believe it has to do with the bell curve
you don't have to answer them all but help me out !!
Answer:
1. 10n
2. 3x^2z^2
3. 2(9n^3 - 3n^2 + 3n - 1)
4. (Put the same thing)
5. There are no common factors so it is completely factored out.
Step-by-step explanation:
For 1, you gotta find the gcf of the numbers and the variables. So, the common factor of 90, 70, 70, and -80 is 10. Nothing else greater than 10 divides these numbers. For the variables, only "n" is the GCF, as there is one "n" and all the other numbers have n^2 and etc.
For 2, same thing, you have to find the gcf for the numbers and the variables.
3. same thing ;-; (gcf is 2 btw, nothing divides the variables because 2 has no "n".
4. theres nothing that divides the numbers or the variables. So, the gcf is just 1.
Of all of the individuals who develop a certain rash, suppose the mean recovery time for individuals who do not use any form of treatment is 30 days with standard deviation equal to 8. A pharmaceutical company manufacturing a certain cream wishes to determine whether the cream shortens, extends, or has no effect on the recovery time. The company chooses a random sample of 100 individuals who have used the cream, and determines that the mean recovery time for these individuals was 28.5 days. Does the cream have any effect
Answer:
z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time
Step-by-step explanation:
Sample information:
Size n = 100
mean x = 28,5
Population information
μ₀ = 30
Standard deviation σ = 8
Test Hypothesis
Null Hypothesis H₀ x = μ₀
Alternative Hypothesis Hₐ x < μ₀
We assume CI = 95 % then α = 5 % α = 0,05
As the alternative hypothesis suggest we should develop a one tail-test on the left ( we need to find out if the cream have any effect on the rash), effects on the rash could be measured as days of recovery
A z(c) for 0,05 from z-table is: z(c) = - 1,64
z(s) = ( x - μ₀ ) / σ/√n
z(s) = ( 28,5 - 30 ) / 8/√100
z(s) = - 1,5 * 10 / 8
z(s) = - 1,875
Comparing z(s) and z(c)
|z(s)| < |z(c)| 1,875 > 1,64
z(s) is in the rejection region. We reject H₀. We dont have enought evidence to support that the cream has effect over the recovery time
help me plsssssssss asap
Answer:
B
Step-by-step explanation:
All you have to do is count, and you'll see 5 faces, 6 vertices, and 9 edges
its easy to do.
list at least 4 attributes that are shared by all of the shapes in the rectangle group
Answer:
All of the figures have 4 sides and 4 vertices
They have opposite sides parallel and congruent.
They have four right angles.
They also have perpendicular line segments.
Step-by-step explanation:
Hope this helps!!!
A sector has angle 2.5 radians and perimeter of 18cm. find the radius of the sector
(The answer is 10.5, but how?) pls help
Answer:
4 cm
Step-by-step explanation:
Perimeter = 18cm
θ = 2.5 radian
s = rθ, s = Arc length
Perimeter of Sector, P = arc length, s + 2r
Perimeter = rθ + 2r
r = Radius
18cm = r(2.5) + 2r
18cm = 2.5r + 2r
18cm = 4.5r
r = 18 /4.5
r = 4
The length of the arc which subtends an angle 60° at
the centre of a circle of radius 3 cm is approximately
Answer:
π cm
Step-by-step explanation:
The formula for arc length (s) as a function of radius (r) and central angle Ф (in radians) is s = rФ.
In this problem r = 3 cm and Ф = 60°, and so the arc length subtended is
s = (3 cm)(π/3) = π cm
Write and equation and solve it for the following:
Seven more that twice a number is 25. What is the number?
Answer: Equation: 2n+7=25 Number: n=9
Step-by-step explanation: Twice a number is 2 × n= 2n. 7 more is +7. Hence we get 2n+7=25. Subtract 7 from both sides then divide by 2 and we get 9!
Answer:
9
Step-by-step explanation:
Work backwards
25 - 7 = 18
18 ÷ 2 = 9
You can solve the problem normally to check.
9 × 2 = 18
18 + 7 = 25
That proves that the answer is right. Hope this helps you! Let me know how you did!
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
Answer: $1500 + 3% + $82,975= 84475.03
Step-by-step explanation:
n exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval
The exponential grows at half the rate of the quadratic.
The exponential grows at the same rate as the quadratic.
The exponential grows at twice the rate of the quadratic.
The exponential grows at four times the rate of the quadratic.
https://brainly.com/question/4184462
Answer:
the answer is B)
Step-by-step explanation:
edg2021 :>
The graph represents the gallons of water (y) per minute (x) dispensed by a shower head. Which statements are correct?
The relationship has been analysed using the property of straight line.The correct options are (C), (D) and (E) respectively.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given options are examined one by one as follows,
(a) The point (0, 0) on the graph represents the zero number of gallons dispensed at the beginning.
(b) The point (5, 1) does not lie on the graph.
(c) The point (1, 5) represents 5 gallons dispensed during 1 minute which is equivalent to the unit rate.
(d) The point (1.5, 7.5) lies on the graph which represents 7.5 gallons dispensed in 1.5 minutes.
(e) The point (0, 0) shows no gallons dispensed at t = 0.
Hence, the correct information inferred from the graph are the point (1, 5) represents the unit rate, 7.5 gallons for 1.5 minutes and the point (0, 0) represents zero minutes for zero gallons.
To know more about graph of straight line click on,
https://brainly.com/question/16934180
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can someone please help me ?? i’ll give brainliest
Answer:
ABE bc its the same degree angle
Step-by-step explanation:
Answer:
C) angle BEF
Step-by-step explanation:
Vertical angles are angles opposite each other where two lines cross. BEF is opposite of DEH