Answer:
$7.35
Step-by-step explanation:
Let cost of blanket be $x
10x + 1.50 ≤ 75
10x ≤ 73.50
x ≤ 7.35
therefore, maximum amount for each blanket is $7.35
Suppose that Y has density function
f(y) = ky(1 − y) if 0 ≤ y ≤ 1 0, elsewhere
A) Find the value of k that makes f (y) a probability density function.
B) Find P(Y ≤ .4|Y ≤ .8).
C) Find the .95-quantile, i.e., find a point φ.95 such that P(Y ≤ φ.95) = .95.
I'm assuming
[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]
(a) f(x) is a valid probability density function if its integral over the support is 1:
[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]
Compute the integral:
[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]
So we have
k / 6 = 1 → k = 6
(b) By definition of conditional probability,
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)
It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).
We have
[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]
Then
P(Y ≤ 0.4) = F (0.4) = 0.352
P(Y ≤ 0.8) = F (0.8) = 0.896
and so
P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393
(c) The 0.95 quantile is the value φ such that
P(Y ≤ φ) = 0.95
In terms of the integral definition of the CDF, we have solve for φ such that
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]
We have
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]
which reduces to the cubic
3φ² - 2φ³ = 0.95
Use a calculator to solve this and find that φ ≈ 0.865.
Using probability concepts, it is found that
a) The value is k = 6.
b) P(Y ≤ .4|Y ≤ .8) = 0.554.
c) The 95th percentile is x = 0.86465.
The density function is:
[tex]f(y) = ky(1 - y)[/tex]
Item a:
The condition that makes it a probability density function is:
[tex]\int_0^1 f(y) dy = 1[/tex]
Thus:
[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]
Then
[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]
[tex]k(\frac{3-2}{6}) = 1[/tex]
[tex]k = 6[/tex]
The value is k = 6.
Item b:
This probability is:
[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]
Then
[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]
[tex]p = 0.554[/tex]
Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.
Item c:
This is x for which:
[tex]\int_0^x f(y) dy = 0.95[/tex]
Thus:
[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]
[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]
Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.
A similar problem is given at https://brainly.com/question/22223588
If the simple interest on $3000 for 3 years is $720 , then what is the interest rate?
Answer:
8%
Step-by-step explanation:
Starting Principal: $
3,000.00
Years:
3
Annual Interest Rate:
8
%
Results
Future Value, using...
Simple Interest: $
3,720.00
Annually Compounded Interest: $
3,779.14
2. I earned $9. I bought 4 candy bars for $0.85 each. How much money do I
have left? *
A. $5.60
B. $8.15
C. $9.85
D. $12.40
Answer:
A
Step-by-step explanation:
4 x $0.85= $3.40
$9-$3.40= $5.60
Answer:
A. $5.60
Step-by-step explanation:
4x0.85 =3.4 and 9 -3.4 = 5.6
The GCF of 15 and 27
5. Which of the following is always true about
the graph of a horizontal line?
A. The graph will have a positive y-intercept.
B. The graph will have a negative y-intercept.
C. The slope of the graph will be undefined.
D. The slope of the graph will be zero.
Answer:
D. The slope of the graph will be zero.
Step-by-step explanation:
Slope of a line is given as [tex] \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1} [/tex].
For a horizontal line, the rise is always equal to zero since the line doesn't rise vertically. This means, [tex] y_2 - y_1 = 0 [/tex].
No matter the value of the run, [tex] x_2 - x_1 [/tex], when we divide zero by the value of the run, we would always have 0.
Therefore, the slope of an horizontal line would always be zero.
Sarah was given an exit slip with the problem: "45 is 75% of what?" Below is how she set up the equation with equivalent ratios.
Was she correct ? Or is there an error that can be corrected?
1.yes,she is correct
2.no, she should have set it up x/45 = 100/45
3.no,she should have set it up 45/x =75/100
The answer should be 60 if im correct.
You can tell if the value of a function for a certain interval is positive just by 2 points looking at its graph. If the value is positive that part of the graph will:
a: be to the right of the y-axis
b: be above the x-axis
c: intersect the x-axis
d: be below the x-axis
PLEASE IM BEGGING YOU please answer i’ll do anything i need in 10 minutes please
Answer:
1. 2.
-3, 4 -3, 2
-1, 2 0, 1
0, 1 3, 0
4, -3 6, -1
Step-by-step explanation:
Can someone help me find the area of the triangle
please!!!
Answer:
18
Step-by-step explanation:
which is the equation of a line in point slope form that passes through the point 2,5 and has a slope of 1/2
Answer:
see below
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y - 2 = 4(x- -1)
y - 2 = 4(x+1)
slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 4x+b
Substituting the point in
2 = 4(-1)+b
2 = -4+b
6 =b
y = 4x+6
standard form
Ax +by = c where A is a positive integer and b and c are integers
y = 4x+6
Subtract 4x from each side
-4x+y = 6
Multiply by -1
4x -y = 6
can you please help me with this question
Answer:
[tex]3\frac{4}{7} *(-6\frac{4}{7}), -7\frac{1}{7} *(-2\frac{1}{4}), 5\frac{1}{7} *5\frac{1}{7}[/tex]
Step-by-step explanation:
Answer: (For the first One)
1 1
5 ---- . 5 -----
7 7
36 36 1296 22 5
----- . ------- = ----------- = 26 ---------- = 2 ----------
7 7 49 49 49
Step-by-step explanation:
First you want to change you mixed numbers into improper fractions. Once done so, cross multiply if possible. Then, multiply across. Last, simplify.
help plz i need help
Answer:
it is 20 pairs count them 1 Collin and its 20
Adam is climbing up the stairs in a building. At a certain point, Adam starts counting the steps and when he reaches the last step, he has counted 56 steps. If he knows that there are a total of 100 steps in the building, how many steps did he climb before he started counting the steps?
Answer:
He climed 3 steps before he started counting the steps.
Step-by-step explanation:
pls mark me as a branliest
Answer:
The answer is he climbed 44 steps. Hope this helped :D
Step-by-step explanation:
help :((
Provide a small explanation if possible!!
Answer:
r = 24
Step-by-step explanation:
Just reverse everything,
3 x 16 = 48,
48 ÷ 2 = 24,
to double-check,
if you plug in 24 for r then you have,
2(24)/3 = 16
48/3 = 16
16 = 16
What are all of the possible classifications for a 3 × 3 system? Check all of the boxes that apply.
consistent and dependent
consistent and independent
inconsistent and dependent
inconsistent and independent
Answer:
consistent and dependent
consistent and independent
inconsistent and independent
Step-by-step explanation:
Answer:
1
2
4
Step-by-step explanation:
has nice day
50 POINTS PLS HELP!!!!
Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH?
A: A segment that passes through the center of dilation in the pre-image continues to pass through the center of dilation in the image.
B: A segment that does not pass through the center of dilation in the pre-image is parallel to its corresponding segment in the image.
C: A segment in the image has the same length as its corresponding segment in the pre-image.
D: A segment that does not pass through the center of dilation in the pre-image is perpendicular to its corresponding segment in the image.
Answer:
Answer choice C.
Step-by-step explanation:
11. Use matrices to solve the system of equations below. Be sure to show [A] and [B].
(3a + 2b + c = 15
a-b4c = 23
4b – 2c = -16
Answer:
2a=-16
Step-by-step explanation:
all I could think of
how do you find the distance between two negative fractions
Answer:
Use the number line and split the whole numbers into fractions
Step-by-step explanation:
Example: If a number line goes from -10 all the way to +10, and you are trying to find the distance between -2 1/4 and -7 3/4. You would split the number line into fourths and then locate -7 3/4. You would then count up to -2 1/4 to get 4 3/4.
Hopefully this makes sense!
it given that f (x) =xsquared 2+3x+2 find f(0) the value of x for which f (x)=0 help me to solve the question pls
Answer:
f(x) = 0 on x= -1 and x = -2
Step-by-step explanation:
Given function is:
[tex]f(x) = x^2+3x+2[/tex]
In order to find the value of x on which the function will have value zero we have to factorize the function and find zeroes of the function. The method used will be factorization of polynomial as the function is in polynomial form.
So,
[tex]x^2+3x+2\\=x^2+2x+x+2\\=x(x+2)+1(x+2)\\=(x+1)(x+2)[/tex]
To find the zeroes, putting the function = 0
[tex]f(x) = 0\\(x+1)(x+2) = 0\\x+1 = 0\\x = -1\\x+2 = 0\\x= -2[/tex]
Hence,
f(x) = 0 on x= -1 and x = -2
I WILL GIVE BRIANLEIST PLZ SOLVE I WILL ALSO GIVE 800 robux slove for line ad BC = 6 cm
Answer:
20 to 25 cm. Hope this helps. Tell me if i'm right or wrong. Can I have brainliest if I am right?
Step-by-step explanation:
Answer:
20 to 25 cm give that robux boi
Step-by-step explanation:
Can someone please help me
Jaylin has $50 in her fun account she deposit $ 10 per month into the account but $ 6 per month is deducted to pay for a streaming service
Answer:
16 per month
Step-by-step explanation:
you add the 10 and 6 together making it 16 total a month
Compare the degree of a polynomial and its depressed polynomial.
Answer:
The degree of a polynomial is one more than the degree of its depressed polynomial.
Step-by-step explanation:
if you answer correctly ill give you brainiest!
Answer:
What is the question?
Step-by-step explanation:
Step-by-step explanation:
theres no question kikashi
3) There are 1.000 meters in 1 kilometer. Convert 5,000 meters to kilometers. А) 0.5 km B) 5 km C) 50 km D 500 km. help this is timed
plss
Answer:
×_×°•○●□■♤♡◇♧☆▪︎¤《》₩¥£€
The average body temperature of all healthy adults is 98.6 F. A doctor takes a random sample of 100 healthy adults and records the temperature of each. The average temperature of these 100 adults is 98.2 F and the standard deviation is 6.9 F. Identify the values of the statistic and the parameter(s).
Answer:
Explained below.
Step-by-step explanation:
A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.
The parameter of interest is the average body temperature of all healthy adults, μ = 98.6°F.While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.
A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.
The statistic is the average body temperature of 100 randoly selected healthy adults, [tex]\bar x=98.2^{o}F[/tex].9. Solve the equation.
4(6 – x) + 4 = 2 (3x + 1) – 6
Answer:
x=3.2
Step-by-step explanation:
4(6 – x) + 4 = 2 (3x + 1) – 6
24 - 4x + 4 = 6x + 2 - 6
28 - 4x = 6x -4
-4x - 6x = - 4 - 28
-10x = - 32
divide both sides
x = 16/5 or x = 3.2
hope this helps :)
inequality of -3x - 6 < 50
Answer:
0
Step-by-step explanation:
look it up on google :)
please answer it I'll give all my points
Answer:
b=10
Step-by-step explanation:
you need to simplify it
An ant can travel at a constant speed of 780 inches every 5 minutes. How far can he travel in 9 minutes
Answer:
1404
Step-by-step explanation:
Cross-multiplication