On a class trip to the aquarium, there is 1 adult for every 7 students. If 44 students go on the field trip, how many adults are going on the field trip?

Answer:5326

Step-by-step explanation:

A=Pe^rt

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

Answer:

the answer is d. 4x²+x-6

Step-by-step explanation:

In order to combine the fractions, they need to have the same denominator.

So, multiply each of their numerators by the denominator they need to be equivalent.

This would look like this:

3x/x+3 --> 3x(x)/x(x+3)        ---simplify this as--> 3x²/x(x+3)

x-2/x  --> (x-2)(x+3)/x(x+3)  ---simplify this as --> x²+x - 6/x(x+3)

3x                    3x(x)                                     x-2                   (x-2)(x+3)

-----      --->        -----                 and             --------   --->           ---------

x+3                   x(x+3)                                    x                        x(x+3)

now that both fractions have the same denominator, we can add their numerators.

3x² + x²+x-6 = 4x²+x -6

This should now look like this:

4x²+x -6

-------------

x(x+3)

Answer:

44

Step-by-step explanation:

Find 10% of 80 = 8

Multiply by 5.5 because 10-4.5

get = 44

Answer:

45% less than, or 45% of 80 would be 36.

Step-by-step explanation:

pls mark brainliest

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.

Answer:

A buoyant girl ant

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:

1.                           2.

   -3, 4                      -3,  2

   -1,  2                       0,  1

   0, 1                         3,  0

   4, -3                      6,  -1

Step-by-step explanation:

Answer: 3x - 8

Hope it helps!

Answer:

9 + 6 + 4 − 2 + 1 − 1 5

9x+{\color{#c92786}{6}}+4x-2x+{\color{#c92786}{1}}{\color{#c92786}{-15}}

9x+6+4x−2x+1−15

9 − 8 + 4 − 2

Step-by-step explanation:

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:

c = 6+2x

Step-by-step explanation:

c = total cost, 6 = entrance fee, 2x = 2 dollars per food/drink item

Answer:

v = 0.416 m/s

Step-by-step explanation:

Give that,

Distance covered by a train, d = 50 m

Time taken, t = 120 s

We need to find the speed of a train. The formula for speed of an object is equal to the total distance covered divided by total time taken. It can be given by :

[tex]v=\dfrac{d}{t}\\\\v=\dfrac{50\ m}{120\ s}\\\\v=0.416\ m/s[/tex]

So, the speed of a train is 0.416 m/s.

Answer:

100 thousandths

Step-by-step explanation:

Answer:answer is an image

Answer:

B

Step-by-step explanation:

EDGE 2021

Answer: PLZ MARK BRAINLIEST

the answer is 80 words/minute

Step-by-step explanation:

Divide 2,320 by 29

Answer:

80 words per min

Step-by-step explanation:

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 :)

Answer:

1404

Step-by-step explanation:

Cross-multiplication

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:

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!

Two Answers: Angle 1, Angle 4

Adjacent angles share a common segment, line, or ray. Think of two adjacent rooms sharing a common wall.

Answer:

2a=-16

Step-by-step explanation:

all I could think of

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:

Answer:

b=10

Step-by-step explanation:

you need to simplify it

Answer:

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

Step-by-step explanation:

Answer:

16 per month

Step-by-step explanation:

you add the 10 and 6 together making it 16 total a month

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