Find the value for the side marked below.
Round your answer to the nearest tenth.
47
у
74°
y = [?]

Answer:

[tex]Cov(X,Y) = -\frac{ 25}{9}[/tex]

Step-by-step explanation:

Given

[tex]Interval =[0,10][/tex]

[tex]X + Y < 10[/tex]

Required

[tex]Cov(X,Y)[/tex]

First, we calculate the joint distribution of X and Y

Plot [tex]X + Y < 10[/tex]

So, the joint pdf is:

[tex]f(X,Y) = \frac{1}{Area}[/tex] --- i.e. the area of the shaded region

The shaded area is a triangle that has: height = 10; width = 10

So, we have:

[tex]f(X,Y) = \frac{1}{0.5 * 10 * 10}[/tex]

[tex]f(X,Y) = \frac{1}{50}[/tex]

[tex]Cov(X,Y)[/tex] is calculated as:

[tex]Cov(X,Y) = E(XY) - E(X) \cdot E(Y)[/tex]

Calculate E(XY)

[tex]E(XY) =\int\limits^X_0 {\int\limits^Y_0 {\frac{XY}{50}} \, dY} \, dX[/tex]

[tex]X + Y < 10[/tex]

Make Y the subject

[tex]Y < 10 - X[/tex]

So, we have:

[tex]E(XY) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{XY}{50}} \, dY} \, dX[/tex]

Rewrite as:

[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {XY}} \, dY} \, dX[/tex]

Integrate Y

[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{XY^2}{2}}} }|\limits^{10 - X}_0 \, dX[/tex]

Expand

[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{X(10 - X)^2}{2} - \frac{X(0)^2}{2}}} }\ dX[/tex]

[tex]E(XY) =\frac{1}{50}\int\limits^{10}_0 {\frac{X(10 - X)^2}{2}}} }\ dX[/tex]

Rewrite as:

[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 X(10 - X)^2\ dX[/tex]

Expand

[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 X*(100 - 20X + X^2)\ dX[/tex]

[tex]E(XY) =\frac{1}{100}\int\limits^{10}_0 100X - 20X^2 + X^3\ dX[/tex]

Integrate

[tex]E(XY) =\frac{1}{100} [\frac{100X^2}{2} - \frac{20X^3}{3} + \frac{X^4}{4}]|\limits^{10}_0[/tex]

Expand

[tex]E(XY) =\frac{1}{100} ([\frac{100*10^2}{2} - \frac{20*10^3}{3} + \frac{10^4}{4}] - [\frac{100*0^2}{2} - \frac{20*0^3}{3} + \frac{0^4}{4}])[/tex]

[tex]E(XY) =\frac{1}{100} ([\frac{10000}{2} - \frac{20000}{3} + \frac{10000}{4}] - 0)[/tex]

[tex]E(XY) =\frac{1}{100} ([5000 - \frac{20000}{3} + 2500])[/tex]

[tex]E(XY) =50 - \frac{200}{3} + 25[/tex]

Take LCM

[tex]E(XY) = \frac{150-200+75}{3}[/tex]

[tex]E(XY) = \frac{25}{3}[/tex]

Calculate E(X)

[tex]E(X) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{X}{50}}} \, dY} \, dX[/tex]

Rewrite as:

[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {X}} \, dY} \, dX[/tex]

Integrate Y

[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 { (X*Y)|\limits^{10 - X}_0 \, dX[/tex]

Expand

[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)] - [X * 0])\ dX[/tex]

[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 ( [X*(10 - X)]\ dX[/tex]

[tex]E(X) =\frac{1}{50}\int\limits^{10}_0 10X - X^2\ dX[/tex]

Integrate

[tex]E(X) =\frac{1}{50}(5X^2 - \frac{1}{3}X^3)|\limits^{10}_0[/tex]

Expand

[tex]E(X) =\frac{1}{50}[(5*10^2 - \frac{1}{3}*10^3)-(5*0^2 - \frac{1}{3}*0^3)][/tex]

[tex]E(X) =\frac{1}{50}[5*100 - \frac{1}{3}*10^3][/tex]

[tex]E(X) =\frac{1}{50}[500 - \frac{1000}{3}][/tex]

[tex]E(X) = 10- \frac{20}{3}[/tex]

Take LCM

[tex]E(X) = \frac{30-20}{3}[/tex]

[tex]E(X) = \frac{10}{3}[/tex]

Calculate E(Y)

[tex]E(Y) =\int\limits^{10}_0 {\int\limits^{10 - X}_0 {\frac{Y}{50}}} \, dY} \, dX[/tex]

Rewrite as:

[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 {\int\limits^{10 - X}_0 {Y}} \, dY} \, dX[/tex]

Integrate Y

[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 { (\frac{Y^2}{2})|\limits^{10 - X}_0 \, dX[/tex]

Expand

[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] - [\frac{(0)^2}{2}])\ dX[/tex]

[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 ( [\frac{(10 - X)^2}{2}] )\ dX[/tex]

[tex]E(Y) =\frac{1}{50}\int\limits^{10}_0 [\frac{100 - 20X + X^2}{2}] \ dX[/tex]

Rewrite as:

[tex]E(Y) =\frac{1}{100}\int\limits^{10}_0 [100 - 20X + X^2] \ dX[/tex]

Integrate

[tex]E(Y) =\frac{1}{100}( [100X - 10X^2 + \frac{1}{3}X^3]|\limits^{10}_0)[/tex]

Expand

[tex]E(Y) =\frac{1}{100}( [100*10 - 10*10^2 + \frac{1}{3}*10^3] -[100*0 - 10*0^2 + \frac{1}{3}*0^3] )[/tex]

[tex]E(Y) =\frac{1}{100}[100*10 - 10*10^2 + \frac{1}{3}*10^3][/tex]

[tex]E(Y) =10 - 10 + \frac{1}{3}*10[/tex]

[tex]E(Y) =\frac{10}{3}[/tex]

Recall that:

[tex]Cov(X,Y) = E(XY) - E(X) \cdot E(Y)[/tex]

[tex]Cov(X,Y) = \frac{25}{3} - \frac{10}{3}*\frac{10}{3}[/tex]

[tex]Cov(X,Y) = \frac{25}{3} - \frac{100}{9}[/tex]

Take LCM

[tex]Cov(X,Y) = \frac{75- 100}{9}[/tex]

[tex]Cov(X,Y) = -\frac{ 25}{9}[/tex]

9514 1404 393

Answer:

  d.  $16.34

Step-by-step explanation:

Luce's income of 763 is between 760 and 780, so the third row of the table applies. Her allowances are 0, so the first column applies, indicating her federal tax withholding is $86.

Her state tax withholding is 19% of that amount, so is ...

  19% × $86 = $16.34 . . . . matches choice D

The amount in state tax that Lucy will contribute is D. $16.34.

Tax simply means a compulsory levy that's paid to the government by individuals and organizations.

In this case, the tax amount that will be paid will be:

= 19% × $86

= $16.34

In conclusion, the correct option is $16.34.

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Answer:

[tex]P = 288 * 3^{(\frac{t}{16}) }[/tex]

Step-by-step explanation:

According to the Question,

        [tex]P = 288 * 3^{(\frac{t}{16}) }[/tex] .  

Answer:

A

Step-by-step explanation:

Answer:

I think it’s 2 hope my answer was good have a nice day as well

Step-by-step explanation:

The period of the given function y = 5 sin (πx) + 4 is π.

We have given that,

y = 5 sin (πx) + 4

We have to determine the period

The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π.

Therefore the period of the given function is π.

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Answer:

787.50

Step-by-step explanation:

interest=principle*rate*time/100

interest=3500*7.5*3/100

interest=35*7.5*3

interest=787.50

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation: Different colours show different parts of africa and the general language spoken by individuals. From the map show, there are a lot of languages in Africa.

Answer:

-3.5, -3, -1, 3, 4.5

Step-by-step explanation:

Answer:

-3.5, -3, -1, 3, 4.5 because the higher the negative is, the lower the number.

Answer:

[tex]x = -6[/tex]

Step-by-step explanation:

[tex]18 = [(-2) + (-1)]x[/tex]

Required

Find x

Remove the inner brackets

[tex]18 = [-2-1]x[/tex]

[tex]18 = [-3]x[/tex]

Remove the square bracket

[tex]18 = -3x[/tex]

Divide both sides by -3

[tex]\frac{18}{-3} = x[/tex]

[tex]x = -6[/tex]

Answer:

Step-by-step explanation:

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}} [/tex]

FIND THE NUMBER THAT MAKE EQUIVALENT FRACTION.

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \red{solved} \\ \frac{4}{ \cancel{5}} = \frac{x}{ \cancel{40}^{ \: \: \: \tiny{8}} } \\ 8 \times 4 = x \\ 32 = x[/tex]

[tex] \blue{Part - 1} \\ \frac{4}{ \cancel{6}} = \frac{x}{ \cancel{24}^{ \: \: \: \tiny{4}} } \\ 4\times 4 = x \\ 16 = x[/tex]

[tex] \green{Part - 2} \\ \frac{1}{ 2} = \frac{6}{ x } \\ 6 \times 2 = x \\ 12 = x[/tex]

SOLVE LIKE THIS FOR ALL

PART - 3 --> 12

PART - 4--> 40

PART - 5 --> 6

PART - 6--> 4

PART - 7 --> 54

PART - 8 --> 12

PART - 9--> 36

PART - 10 --> 28

PART - 11--> 20

PART - 12 --> 28

PART - 13 --> 16

PART - 14 --> 20

PART - 15 --> 12

PART - 16 --> 6

PART - 17 --> 32

PART - 18--> 30

PART - 19 --> 27

PART - 20 --> 36

9514 1404 393

Answer:

  $2505.80

Step-by-step explanation:

After the first exchange, the tourist has ...

  $3000(12.90 R/$) = R38,700

After 7 days, she has ...

  R38,700 -7(R900) = R32,400

After the second exchange, she has ...

  R32,400 × ($1/R12.93) = $2505.80

She gets $2505.80 at the second exchange.

Explanation:

The sample space is simply the list of possible outcomes. We list all the hair colors possible in this class.

Answer:

NEGATIVE

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

positive

Answer:

r = 22.5

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

[tex]11411=\frac{4}{3} \pi r^{3}[/tex]

[tex]r^{3}=3(\frac{11411}{3})[/tex]

[tex]r^{3}=11411[/tex]

∛r³ = ∛11411

r = 22.5134076467

22.5134076467 rounded to the nearest tenth is 22.5

Answer:

its 14

Step-by-step explanation:

Answer:

1.03h

Step-by-step explanation:

S=vt

S= 15km/h*2h

S= 30km

Distance same, S=30km

v= 29km/h

t = 30/29

t = 1.03 h

Answer:

[tex]F = k\frac{m_1m_2}{r^2}[/tex]

Step-by-step explanation:

Direct proportional:

Multiplication

Inverse proportional:

Division

The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to the masses

This means that:

[tex]F = k\frac{m_1m_2}{}[/tex]

Inversely proportional to the square of the distance r between the objects.

Denominator is [tex]r^2[/tex]. Thus:

[tex]F = k\frac{m_1m_2}{r^2}[/tex]

so we'll go backwards.

emily ended with $6.00.

6×2 at the music store = $12

12×2 at the bakery = $24

24 × 2 at the grocery store = $48

she started with a total of $48.00

to check answer:

48 ÷ 2 = 24 at bakery

24 ÷ 2 = 12 at music

12 ÷ 2 =6 at lunch

Step-by-step explanation:

81/5=3x

x=81×1/5×3

x=81/15

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

Q1.

a. y = 3x + 0

b. y = 3x + 25

c. Plain is proportional because the y-intercept is zero.

d. It shows the cost of each coaster.

Q2

a. y = 4x + 0

b. It is proportional since the y-intercept is zero.

c. No the graph will never intersect because the equations in combination will result in parallel lines since there is a slight variation in the cost of EZ Coaters

Answer:

y = 8

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Identify

[Line] x = -3

Point (1, 8)

Step 2: Find Perpendicular Line

A vertical line's slope is undefined.

The negative reciprocal of an undefined slope is 0.

Given point (1, 8), our y-value is equal to 8.

∴ the perpendicular line is y = 8.

Answer:

B. $580

Step-by-step explanation:

Value of the retirement fund after x years:

The value of the retirement fund after x years is given by the following function:

[tex]y(x) = 307.6(1.11)^x[/tex]

Which is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made?

This is y(6). So

[tex]y(6) = 307.6(1.11)^6 = 575.34[/tex]

Close to $580, and thus, the correct answer is given by option B.

Answer:

B. $580 is best estimate for the value of the retirement fund after 6 years, if no additional deposits or withdrawals are made.

Thus it is little close to answer because actual answer is $575.34.

Step-by-step explanation:

domain = {-7, -3, 1}

range ={-8, -5, 7, 8}

Answer:

y = -8x - 1

Step-by-step explanation:

y = mx + b

7 = -8 (-1) + b   Substitute in points for x and y. Substitute -8 for m (parallel)

7 = 8 + b

-1 = b

Answer:

The number of selections is 49.

Step-by-step explanation:

drama = 7

horror films = 16

Select 3 movies at least two dramas

For 2 drama and 1 horror film

(3 C 2) x (16  C 1) = 48

For 3 drama

(3 C 3) = 1

So, total number of selections is 48 + 1 = 49.  

x = 65

Step-by-step explanation:

cos theta = 25/x

cos theta = x/169

25/x = x/169

x² = 169 x 25

x = 65

The missing length x = 65, using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

In the question, we are asked to find the value of x.

In the right triangle ABC, by Pythagoras' Theorem,

AC² + BC² = AB²,

or, x² + BC² = (144 + 25)²,

or, BC² = 169² - x² ... (i).

In the right triangle ACD, by Pythagoras Theorem,

AD² + DC² = AC²,

or, 25² + DC² = x²,

or, DC² = x² - 25² ... (ii).

In the right triangle BCD, by Pythagoras Theorem,

BD² + DC² = BC²,

or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},

or, x² + x² = 169² + 25² - 144² {Rearranging},

or, 2x² = 28561 + 625 - 20736,

or, 2x² = 8450,

or, x² = 4225,

or, x = √4225 = 65.

Thus, the missing length x = 65, using the Pythagoras Theorem.

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Answer:

BD = 29.3

Step-by-step explanation:

Each half of the rectangle is a right triangle.

The diagonal is the hypotenuse of each right triangle.

Let's focus on right triangle ABD

Reference angle = m<ABD = 35°

AB = CD = 24

Adjacent length = AB = 24

Diagonal = Hypotenuse = BD

To find BD, apply CAH:

Cos 35° = Adj/Hyp

Substitute

Cos 35° = 24/BD

BD × Cos 35° = 24

BD = 24/Cos 35°

BD = 29.3 (nearest tenth)