Answer:
[tex]Mean = 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) =\left \{ {{\frac{c}{x^3} \ x\ge 2} \atop {0\ x<2}} \right.[/tex]
Required
The mean of x
Given that:
[tex]f(x) = \frac{c}{x^3}[/tex] [tex]x \ge 2[/tex]
First, solve for c using;
[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]
Substitute [tex]f(x) = \frac{c}{x^3}[/tex] and [tex]x \ge 2[/tex]
[tex]\int\limits^{\infty}_2 {\frac{c}{x^3}} \, dx = 1[/tex]
Isolate c
[tex]c\int\limits^{\infty}_2 {\frac{1}{x^3}} \, dx = 1[/tex]
Rewrite as:
[tex]c\int\limits^{\infty}_2 {x^{-3}} \, dx = 1[/tex]
[tex]c[\frac{x^{-3+1}}{-3 +1}]|\limits^{\infty}_2 = 1[/tex]
[tex]c[\frac{x^{-2}}{-2}]|\limits^{\infty}_2 = 1[/tex]
[tex]-\frac{c}{2} [x^{-2}]|\limits^{\infty}_2 = 1[/tex]
Expand
[tex]-\frac{c}{2} [{\infty}^{-2} - {2}^{-2}]= 1[/tex]
[tex]-\frac{c}{2} [0 - \frac{1}{4}]= 1[/tex]
[tex]-\frac{c}{2} *- \frac{1}{4}= 1[/tex]
[tex]\frac{c}{8}= 1[/tex]
Solve for c
[tex]x = 8 * 1[/tex]
[tex]x = 8[/tex]
So, we have:
[tex]f(x) = \frac{c}{x^3}[/tex] [tex]x \ge 2[/tex]
[tex]f(x) = \frac{8}{x^3}[/tex] [tex]x \ge 2[/tex]
So, the mean is calculated as:
[tex]Mean = \int\limits^a_b {x * f(x)} \, dx[/tex]
This gives;
[tex]Mean = \int\limits^{\infty}_2 {x * \frac{8}{x^3}} \, dx[/tex]
[tex]Mean = \int\limits^{\infty}_2 {\frac{8}{x^2}} \, dx[/tex]
[tex]Mean = 8\int\limits^{\infty}_2 {\frac{1}{x^2}} \, dx[/tex]
Rewrite as:
[tex]Mean = 8\int\limits^{\infty}_2 {x^{-2} \, dx[/tex]
Integrate
[tex]Mean = 8 {\frac{x^{-2+1}}{-2+1}|\limits^{\infty}_2[/tex]
[tex]Mean = 8 {\frac{x^{-1}}{-1}}|\limits^{\infty}_2[/tex]
[tex]Mean = -8x^{-1}|\limits^{\infty}_2[/tex]
Expand
[tex]Mean = -8[(\infty)^{-1} - 2^{-1}][/tex]
[tex]Mean = -8[0 - \frac{1}{2}][/tex]
[tex]Mean = -8* - \frac{1}{2}[/tex]
[tex]Mean = 8* \frac{1}{2}[/tex]
[tex]Mean = 4[/tex]
Can someone please answer?
Answer:
The answer is 24
Step-by-step explanation:
I need help PLZZZ!!!
Subtract
-5-(-6)=
Answer:
1 is the answer
Step-by-step explanation:
-5-(-6) = x
-5 + 6 = x
1 = x
Answer:
s1: -5-(-6)
s2: -5 + 6. multiply minus with minus first
s3: +1. simply arthmatic.
A certain computer microchip cannot be subjected to temperatures below 59° Fahrenheit. What is this in degrees Celsius?
Answer:
15°C
Step-by-step explanation:
Use the following formula to convert Fahrenheit to Celsius:
[tex]C=\frac{5}{9}(F-32)[/tex]
Substitute the value for the variable and solve for C.
[tex]C=\frac{5}{9}(59-32)\\C=\frac{5}{9}(27)\\C=15[/tex]
Therefore, 59°F is equivalent to 15°C.
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
radius = ? in.
length = ? in.
Answer:
radius r = 47/π in
length l = 23.5 in
Step-by-step explanation:
Let us recall that:
Volume of a cylinder = [tex]\pi r^2 h[/tex] --- (1)
The girth g = [tex]2 \pi r + h[/tex] ----- (2)
Given that:
height (h) + girth (g) = 141
Then g = 141 - h ----- (3)
Equating equation (2) and (3), we have:
141 - h = 2πr + h
2h = 141 - 2πr
h = 70.5 - πr ------ (4)
From, here now, we can now replace the value of h into equation (1)
i.e.
V = πr²(70.5 - πr)
V = 70.5πr² - π²r³
Taking the differential of the above equation with respect to r, we have:
[tex]\dfrac{dv}{dr} = 141 \pi r- 3\pi ^2 r^2[/tex]
By further differentiation:
[tex]\dfrac{d^2v}{dr^2} = 141 \pi - 6\pi ^2 r[/tex]
Let set [tex]\dfrac{dv}{dr}= 0[/tex], Then:
141πr - 3π²r² = 0
141πr = 3π²r²
Divide both sides by πr
141 = 3πr
r = 141/3π
r = 47/π in
Replacing the value of r = 47/π into equation (4), we have:
h = 70.5 - πr
h = 70.5 - π(47/π)
h = 70.5 - 47
h = 23.5 in
From equation (3);
h + g = 141
23.5 + g = 141
g = 141 - 23.5
g = 117.5 in
Volume = πr²h
V = π × (47/π )² × 23.5
V = 16523.94 in³
In 2016, there were approximately 4.46 x 10° people in Asia. On average, a person takes 8.4 x 106 breaths
per year. Using this data, what was the number of breaths of all the people in Asia in 2016? Expressing your answer
in scientific notation in the form a x 10what are the values of a and b?
What is the value of a?
What is the value of b?
ANSWER PRONTO NEEDA ASAP !!!
Answer:
3.75 x 10^7
a = 3.745 (rounded) or 3.7464 (exact)
b = 7
Step-by-step explanation:
Assuming you meant "a person takes 8.4 x 10^6 breaths
per year" we would multiply the number of people 4.46 x 10° by the number of breaths each person takes 8.4 x 10^6 and we get 37464000 and in scientific notation it would be 3.75 x 10^7
As an avid golfer, you want to estimate your average score for 18 holes of golf. Suppose you know that the standard deviation of your score is 16.425 strokes and you want to find a sample mean that is within 5.947 strokes of your true average for all rounds of golf with 90% confidence. How many rounds would you need to play to determine this
Answer:
21
Step-by-step explanation:
Given that
The holes of golf is 18
The standard deviation of the score is 16.425 strokes
The sample mean is 5.947
And, there is 90% confidence
We need to find out the number of rounds
So,
At 90% confidence interval, the critical value is +/- 1.645
Margin of error = 5.947
Z_0.05 × SD/sqrt (n) = 5.947
1.645 × 16.425/sqrt (n) = 5.947
sqrt(n) = 1.645 × 16.425 ÷ 5.947
sqrt(n) = 4.54
= 21
Sara
has
what
you can work out
she needs.
Saved & 75. This is 30% of
She needs. Explain how
Answer:
The question seems incomplete.
Step-by-step explanation:
Explain why sin(A)=sin(D)
I NEED HELP ASAP
becouse The size does not differ whether it is big or small, the degree remains the same
PLS HELP
What is the area of the triangle?
Answer:
B
Step-by-step explanation:
(base x height)/2 = (2.9 x 8.1)/2 = 11.7 cm^2
Answer:
B
Step-by-step explanation:
Which angles are supplementary to
∠4? Select all that apply.
∠2 ∠7
∠5 ∠6
∠1
Answer:
The supplementary angle are:
∠2
∠3
∠6
∠7
The sample survey showed that 67% of internet users said the internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends. (Round your answers to four decimal places.)
Answer:
The 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends is [tex](0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}, 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}})[/tex], in which n is the size of the sample.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
67% of internet users said the internet has generally strengthened their relationship with family and friends.
This means that [tex]\pi = 0.67[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}}[/tex]
The 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends is [tex](0.67 - 1.96\sqrt{\frac{0.67*0.33}{n}}, 0.67 + 1.96\sqrt{\frac{0.67*0.33}{n}})[/tex], in which n is the size of the sample.
Multiply: –c2(3c – 2)
Answer:
answer in picture
Step-by-step explanation:
pls help with this thxxu :))
The figure below shows a construction of a triangle,based on the steps and lengths shown,which type of triangle is it?
A- Equilateral
B- Isosceles
C- Scalene
D- Obtuse
Answer:
Scalene triangle (Option C)
Step-by-step explanation:
In a scalene triangle , all its sides have different lengths.
According to the figure given in question , lengths of all sides differ from each other. So , the triangle in the figure is a scalene triangle.
Referring to the picture below, which of these statements are true? Change in elevation from point A to B. The distance traveled from A to B along the straight line path is a state function. The distance traveled on the curved path from A to B is a state function. The change in elevation from point A to B (Δ) is a state function.
Answer:
Following are the responses to the given points:
Step-by-step explanation:
The State function is indeed a characteristic that does not depend upon on path to that specific significance.
In contrast, two route functions are called call path operations.
Throughout this case, only the state system includes them. Lift changes are dependent on a particular difference between two balancing states (pressure, temperature).
What are the algebraic properties of the logarithm function?
Answer:
344343234
Step-by-step explanation:
Jack Wilson bought a tool chest and tools on the installment plan for a total cost $1600. He paid $200 down and the rest in monthly installments of $56 each. How many months will it take Jack to pay for the tool chest and tools?
Answer:
25 months
Step-by-step explanation:
quick math
if a news paper costs 25p how much would 3 weeks . if the the paper is puplished six days each week
The best i could find out is 450p
Cube roots of 1 are +1 and -1 (true and false)
False cube root of 1 is plus 1 only.
Brayden saves $1,500 at a yearly simple interest rate of 2.5%. How many years
does it take for the amount he has saved to be double the original amount.
Answer:
40 years.
Step-by-step explanation:
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
Brayden saves $1,500 at a yearly simple interest rate of 2.5%.
This means that [tex]P = 1500, I = 0.025[/tex]
How many years does it take for the amount he has saved to be double the original amount?
This will happen when the earned money is the principal, that is, E = 1500. So
[tex]E = P*I*t[/tex]
[tex]1500 = 1500*(0.025)*t[/tex]
[tex]t = \frac{1}{0.025}[/tex]
[tex]t = 40[/tex]
40 years.
Answer:
Step-by-step explanation:
40 years.
Step-by-step explanation:
The simple interest formula is given by:
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
Brayden saves $1,500 at a yearly simple interest rate of 2.5%.
This means that
How many years does it take for the amount he has saved to be double the original amount?
This will happen when the earned money is the principal, that is, E = 1500. So
Find the distance from the point (1,4) to the line y = 1/3x - 3.
A) 4 units
B) 20 units
C) 4 units
OD) 20 units
Answer:
answer
is 6.325.............
Answer:
2√10
Step-by-step explanation:
I also got this question and it says I got it correct with this answer choice
The table shows the test scores and the sleep averages of several students. A) Write the least squares regression equation that models the data. Let x = the test score and y = average sleep. B) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. Show Your Work. ( Will Mark Brainliest but no Links or nonsense answers please). Answer A and Answer B.
Answer:
Approximately 92
Step-by-step explanation:
Using technology, the linear regression model obtained by fitting the data points is:
Y = 0.0914X1 - 0.3741
Where x = test score ; y = average sleep
Slope = 0.0914 ; intercept = - 0.3741
The test score of a student that sleeps 8 hours
y = 8
8 = 0.0914X1 - 0.3741
8 + 0.3741 = 0.0914X1
X = 8.3741 / 0.0914
X = 91.62
Carlos is interested in estimating the mean amount of time it takes players to complete a level of the game he's
designing. He recruits 7 players of varying skill levels and ages to play the level until they complete it (he's willing
to treat this as a random sample), and he times how long it takes each of them. They play separately from each
other, so Carlos is also willing to assume independence. Here are the data with summary statistics:
1
2
3
4
5
6
7
Player
Time (minutes)
48
46
40
34
49
40
37
Mean
T = 42 min
Standard deviation
8z = 5.7 min
Assume that all conditions for inference are met for this sample.
Which of the following is a 95% confidence interval for the mean time in minutes) it takes players to complete
this level?
Choose 1 answer:
1914
3 of 4 -
Answer:
42±5.3
Step-by-step explanation:
3x+y=15 create a word problem
Answer:
---
Step-by-step explanation:
3 adults and 1 child go to a park. The admission fee for adults is x, and the fee for children is y. They spent a total of 15 dollars. Solve for x and y.
---
hope it helps
sorry if it doesn't. I'm the person who solves the problems, not creates them
10 points! If correct you get brainliest.
Which one's apply?
Answer:
The answer is C and E
Step-by-step explanation:
The changes to a company's stock prices for five days are $1.25, -$0.75 , $1.25 -$0.75 and -$0.75 what is the mean change of the stock prices show your work (like fully show the steps por favor)
Answer: $0.05
Step-by-step explanation:
Mean of a given set of numbers simply means that one should find the average of the numbers. Therefore, the mean change of the stock prices will be:
= ($1.25 + -$0.75 + $1.25 + -$0.75 + -$0.75) / 5
= $0.25 / 5
= $0.05
Therefore, the mean change of the stock prices is $0.05.
choose the correct set up to solve for x
Answer:
I think c
but I am not sure
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Solve the given system of equations 4x+5y=10 -x-8=3y
Answer:
[tex]4x + 5y = 10 - - - (a) \\ - x - 8 = 3y \\ - x - 3y = 8 \\ x + 3y = - 8 - - - (b) \\ 4 \times (b) - (a) : \\ = > 0x + 7y = - 42 \\ y = - 6 \\ x - 21 = - 8 \\ x = 13 \\ { \boxed{x = 13}} \\ { \boxed{y = - 6}}[/tex]
Answer:(10,-6)
Step-by-step explanation:
https://app.edmentum.com/mimetex/mimetex?\fs3%5Cbegin%7Barray%7D%7BrclC30C30C30C30C30%7D%204x%20%5C%20+%20%5C%205y%20&=&%2010%20%5C%5C%20-4x%20%5C%20-%20%5C%2012y%20&=&%2032%5C%5C%20%5Chline%200%20%5C%20-%20%5C%207y%20&=&%2042%5C%5C%20y%20&=&%20-6%20%5Cend%7Barray%7D
https://app.edmentum.com/mimetex/mimetex?\fs3%5Cbegin%7Barray%7D%7BrclC30C30C30C30C30%7D%204x%5C%20+%20%5C%205y%20&=&10%20%5C%5C%204x%5C%20+%20%5C%205(-6)%20&=&10%20%5C%5C%204x%5C%20-%20%5C%2030%20&=&10%20%5C%5C%204x%20&=&%2040%20%5C%5C%20x%20&=&%2010%20%5Cend%7Barray%7D
Imani stopped at the post office to mail
three packages. The weight of each
package is given below. If the heaviest
package is removed, find the total weight of
the remaining two packages.
Answer:
24 packages
Step-by-step explanation:
what are the inputs of the function below
Please add an attachment/photo.
Answer:
There is no picture.
Graph: - 4x + 4y > 20 & 4x + 4y < -12
please help !!!!!