A recipe uses 2 eggs to make 24
cookies. How many cookies could
you make with 9 eggs?

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.

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[tex]\boxed{k = \frac{log_{e}(\frac{L +A }{A} )}{t} }[/tex]

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

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Answer:

Step-by-step explanation:

if the speed is 6 bracelets per hour then the table will go like this

2   12

5  30

7  42

11  66

16 and 2/3  hours is 100 bracelets

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!

Answer:

2a=-16

Step-by-step explanation:

all I could think of

Answer:

−2.8 or - 2 8/10

Step-by-step explanation:

hope that helps

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 :)

Step-by-step explanation:

b(a + c)

=-4(-3+2)

=12-8

=4

Answer:4

Step-by-step explanation:

Steps a (-3) add c (2) is -1

Then you have to times -1 by -4 which is 4 :D

Answer:

1.                           2.

   -3, 4                      -3,  2

   -1,  2                       0,  1

   0, 1                         3,  0

   4, -3                      6,  -1

Step-by-step explanation:

Answer:

The degree of a polynomial is one more than the degree of its depressed polynomial.

Step-by-step explanation:

Answer:

Yes, no, no

Step-by-step explanation:

Answer:10 baskets yes

100 baskets yes

1000 baskets no

Step-by-step explanation:

Answer:

7 to 9

Step-by-step explanation:

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:

Answer:

-5/2 is located on the left of -1

Step-by-step explanation:

Answer:

Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce

Answer:

12 ounces

Step-by-step explanation:

3.60 = .3x

divide by .3 on both sides

12 = x

Answer:

[tex]measure angle 1 = 62 ------> given\\measure angle 4 = 62 --------> vertical angle theorem[/tex]

Step-by-step explanation:

vertical angle theorem states that the angle vertical from another angle has to be congruent

p.s. i found it

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

Answer:

The student's GPA = 3.24

Step-by-step explanation:

To determine the student's GPA for the term,

First, we will determine the weighted grade points and then divide the result by the total credit.

The weighted grade point is the sum of the grade points in the courses.

Grade point for a course is calculated by multiplying the grade by the course credit.

For the Math course,

Grade point = 3.6 × 5 = 18.0

For the Music course,

Grade point = 2.5 × 2 = 5.0

For the Chemistry course,

Grade point = 3.0 × 5 = 15.0

For the Journalism course,

Grade point = 3.4 × 5 = 17.0

Hence,

The weighted grade point = 18.0 + 5.0 + 15.0 + 17.0

The weighted grade point = 55.0

Total credit = 5 + 2 + 5 + 5 = 17

∴ The student's GPA = 55.0 / 17 = 3.24

Hence, The student's GPA = 3.24

Answer:42

Step-by-step explanation:

Answer:

infinitely many solutions

Step-by-step explanation:

14x + 6 = 2(5+7x)-4

14x + 6 = 10 + 14x - 4

14x + 6 = 14x + 6

infinitely many solutions because both sides of the equation are equal

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.

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 number of marbles Peter had when he arrived home was 43 marbles

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of marbles Peter had on his way home = 171

The amount of marbles he lost on his way home = ( 3/4 ) th

Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home

The amount of marbles Peter have left = 1 - 3/4

                                                                = ( 1 / 4) th

So , The number of marbles Peter had left when he arrived home is =

Amount of marbles Peter have left x Number of marbles Peter had

The number of marbles Peter had left when he arrived home is = (1/4) x 171

= 171 / 4

= 42.75

≈ 43 marbles

Hence , the number of marbles Peter had left when he reached home is 43

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#SPJ2

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

Answer:

She will pay $28.4 for the additional gallons.

Step-by-step explanation:

First find the unit amount:

10.65/3 = 3.55

now multiply:

3.55 x 8 = 28.4

Answer:

Its statistical

Step-by-step explanation:

Answer: 5.4  or  5 2/5 Hope this helps have a GREAT night

Step-by-step explanation: