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Two Answers: Angle 1, Angle 4

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

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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Answer:

2a=-16

Step-by-step explanation:

all I could think of

Answer:  100f + 150e = 1250

Step-by-step explanation:

Subtract the 1st from the 2nd to solve for e:

50e = 250

e = 5 boxes (# of boxes of eight-once cups)

f + e = 10, so f = 5 boxes: (# of boxes of five-once cups)

6 boxes of 5-ounce cups and 4 boxes of 8-ounce cups could be bought.

Let x represent the number of box of 5-ounce cups and y represent the number of box of 8 ounce cups.

The room can only hold 10 more boxes, hence:

x + y ≤ 10   (1)

A maximum of $1200 is budgeted for yogurt cups. Hence:

100x + 150y ≤ 1200     (2)

Plotting the graph of the inequality, the solution is at (6, 4)

Therefore 6 boxes of 5-ounce cups and 4 boxes of 8-ounce cups could be bought.

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Answer:

You are going to try to eyeball it and if your not able to then another guess is to look for a 1/2 table spoon and use it twice

Step-by-step explanation:

Im worried if I a wrong

Answer:

You would divide 14/2 because there is a 2 cup measuring cup and you need 14 cup so 14 / 2 = 7 you need to use the measuring cup 7 times.

Step-by-step explanation:

Please mark brainliest

Have a great day!

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:

100 thousandths

Step-by-step explanation:

Answer:(3,-4) you just have to follow the equation.

Slope = change in y over change in x.

Slope = (-6 - -9) / (-6 - -2)

Slope = (-6 + 9) / (-6 + 2)

Slope = 3/-4

Slope = -3/4

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:5326

Step-by-step explanation:

A=Pe^rt

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:

96

Step-by-step explanation:

1200*92=110400/100=1104

1200-1104=96

Answer:

1152 students like rap just take the numbers n divide

Answer:

its a

Step-by-step explanation:

The phrase is Scale by a factor of 1 /r and rotate clockwise by θ.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number.

Given:

z=r(cos θ + i sin θ)

So, to divide a complex number the best phrase to describe is Scale by a factor of 1 /r and rotate clockwise by θ.

Learn more about complex number here:

https://brainly.com/question/28007020

#SPJ2

Answer:

below in bold

Step-by-step explanation:

f(x) = 2x - 7 - 3

~Combine like terms

f(x) = 2x - 10

When x = 2...

f(x) = 2(2) - 10

f(x) = 4 - 10

f(x) = -6

When x = 3...

f(x) = 2(3) - 10

f(x) = 6 - 10

f(x) = -4

When x = 4...

f(x) = 2(4) - 10

f(x) = 8 - 10

f(x) = -2

Best of Luck!

Answer:

y = 15

Add 18 to both sides to cancel out the negative next to the y

Answer:

y=15

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-18-(-3)=0

y-15 = 0  

Add  15  to both sides of the equation :  

                     y = 15

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:

5hours

Step-by-step explanation:

120÷2=60

60=1 hour

300÷60=5

5hours

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:

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:

b=10

Step-by-step explanation:

you need to simplify it

Answer:

7 pounds

Step-by-step explanation:

1 pound is $4 28/4 is 7

Answer:

c = 6+2x

Step-by-step explanation:

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

Answer:

A buoyant girl ant

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: