Tell whether the angles are complementary or supplementary. Then find the value of x

Answer:

2a=-16

Step-by-step explanation:

all I could think of

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:

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

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:

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

Answer:

157 divided by 2 is 78.5 round that to get 70

108 divided by 5 is 21.6 round that to get 22

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.

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Answer:

1 /64

Decimal Form:

0.015625

Answer:

5, -7

Step-by-step explanation:

Answer:

5 and -7

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

120/4

Answer:

30

Step-by-step explanation:

Just divide 120 with 4

Hope this helps!!!!!!

Answer:

The discount is 20% off

hope this helps!

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:

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

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

Step-by-step explanation:

Answer:

24c

Step-by-step explanation:

First off, we know what in each case there are 24 bottles. So if we have c crates and want to know the water bottles inside them, we need to multiply 24 by c resulting in 24c or 24 x c.

Answer:

D. A line of credit backed by collateral.

Step-by-step explanation:

Answer:

D. A line of credit backed by collateral.

Step-by-step explanation:

did the quiz

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.

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Answer:11,356

Step-by-step explanation: that is the answer! I’m sure

Answer:11.355

Step-by-step explanation:

Answer:

(m-(1/3))(m^2+(1/3)m+(1/9)

Step-by-step explanation:

Just use the difference of cubes

Answer:

5.19

Step-by-step explanation:

first do 28.86 / 6 to find out how much each paid. then subtract that number (4.81) from 10

Answer - Every Person should get $5.19

Step-by-step explanation:

what i did is 6 x 10 = 60 then 60 - 28.86 = 31.14 / 6 = 5.19 Your welcome.

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:

True

Step-by-step explanation:

3:7 is girls to boys, and to find the total, do 7+3. After that, you'd get 10, and the ratio would be 3:10, so TRUE

Answer:

100 mm i think

Step-by-step explanation:

Given:

V'W'X'Y' has vertices V'(-3,2), W'(5,1), X'(0,4) and Y'(-2,0).

V'W'X'Y' is the image of VWXY rotated 90° around the origin.

To find:

The coordinates of VWXY (the pre-image).

Solution:

V'W'X'Y' is the image of VWXY rotated 90° around the origin. It means, the figure VWXY is rotated 90° counterclockwise around the origin.

So, if we rotate V'W'X'Y' 90° clockwise around the origin, then we get the original figure VWXY.

If a figure rotated 90° clockwise around the origin, then

[tex](x,y)\to (y,-x)[/tex]

[tex]V'(-3,2)\to V(2,3)[/tex]

[tex]W'(5,1)\to W(1,-5)[/tex]

[tex]X'(0,4)\to X(4,0)[/tex]

[tex]Y'(-2,0)\to Y(0,2)[/tex]

Therefore, the coordinates of preimage are V(2,3), W(1,-5), X(4,0) and Y(0,2).

Answer:

we conclude that the intervals in which the function P(t) is decreasing are:

Step-by-step explanation:

At x< 1, the function P(t) is decreasing

From the figure, it is clear that the function seems to be increasing

from (1, 3) and then 4 to onwards.

But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).

Therefore, we conclude that the intervals in which the function P(t) is decreasing are:

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

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

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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