Please help !! Which are pairs of vertical angles?


< AOC and

Answer:

3/5 is the probability of drawing a blue card

Answer:

3/5

Step-by-step explanation:

total sum of probability is 1.

for the probability of drawing a red ball to be 2/5, then probability of drawing a blue ball is

1 - 2/5

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:

40m - 160m = 120m

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:

Step-by-step explanation:

Approximate rate of change:

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

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ2

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:

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

Step-by-step explanation:

Answer:

Step-by-step explanation:

Temperature change:

Change in 1 minute:

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

Step-by-step explanation:

r-5r-6s+8s-15

-4r+2s-15

= 2s-4r-15

The simplified form of the given expression is -4r+2s-15.

The given expression is r-5r-6s+8s-15.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be solved as follows:

r-5r-6s+8s-15

= -4r+2s-15

Therefore, the simplified form of the given expression is -4r+2s-15.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ2

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:

7 to 9

Step-by-step explanation:

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:

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

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:

Answer:42

Step-by-step explanation:

Answer:

−2.8 or - 2 8/10

Step-by-step explanation:

hope that helps

Answer:

23

Step-by-step explanation:

32=3x-4+x

32=4x-4

+4       +4

36=4x

/4   /4

9=x

Larger #= 3x-4

Larger #= 3(9)-4

Larger #= 27-4

larger #= 23

Answer:

Yes, no, no

Step-by-step explanation:

Answer:10 baskets yes

100 baskets yes

1000 baskets no

Step-by-step explanation:

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:

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:

n=7

Step-by-step explanation:

7 times 5 equals 35.

Answer:

n=7

Step-by-step explanation:

Give:5n = 35

To solve the n. we need to divide both side by 5.

5n/5=35/5

n=7

Answer:

4

Step-by-step explanation:

Because she gets 3 per multiple choice question, so 3 times 18

she gets 5 per response question, so 5 times 6

Jill total score on the test is 3 • 18 + 5 • 6. The correct option is 4.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given;

Jill scored 3 points for each of the 18 multiple choice questions she answered correctly.

That means,

use the multiplication operation,

3 x 18

And 5 points for each of the 6 short response questions she answered correctly.

That means,

5 x 6

To find the total score:

Add the scores,

3 x 18 + 5 x 6

or, 3 • 18 + 5 • 6

Therefore, 3 • 18 + 5 • 6 is the required expression.

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ2

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