A family is planning to sell their home. If they want to be left with $116,100 after paying 10% of the selling price to a realtor as a commission, for how much must they sell the house?

9514 1404 393

Answer:

  tan(φ) = (x² -1)/(2x)

Step-by-step explanation:

In a right triangle, the tangent of one of the acute angles is the ratio of the opposite side to the adjacent side. Here, the length of the adjacent side is not given, but can be found from the Pythagorean theorem.

  adjacent side = √((x² +1)² -(x² -1)²) = √((x⁴ +2x² +1) -(x⁴ -2x²+1))

  adjacent side = √(4x²) = 2x

Then the tangent ratio is ...

  tan(φ) = (opposite side)/(adjacent side)

  tan(φ) = (x² -1)/(2x) . . . . . . for x > 0

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

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]

Answer:

B = 900 Libros

A = 2700 Libros

C = 1800 Libros

Step-by-step explanation:

A = 3B

2B = C

A + B + C = 5400

3B + B + 2B = 5400

6B = 5400

B = 5400 / 6

B = 900 Libros

A = 3B

A = 3(900)

A = 2700 Libros

C = 2B

C = 2(900)

C = 1800 Libros

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.  

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

Step-by-step explanation:

81/5=3x

x=81×1/5×3

x=81/15

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.

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.

Learn more about the Pythagoras Theorem at

https://brainly.com/question/231802

#SPJ2

Answer:

D. 56

Step-by-step explanation:

The general solution for the number of combinations with repetition is represented by the following expression:

[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)

Where:

[tex]n[/tex] - Total number of elements.

[tex]r[/tex] - Number of the sample.

If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:

[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]

[tex]x = 56[/tex]

Hence, correct answer is D.

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.

Learn more about tax on:

https://brainly.com/question/25783927

Answer:

imagine the upper triangle as the same as the lower one, but rotated by 180° around the corner point they share, and resized.

the base of the smaller triangle is resized by a factor of 3/4.5, or reduced: 1/1.5

we just take the length from the hypotenuse of the bigger triangle and resize it to, either by multiplying with 1/1.5 or by dividing by 1.5

personally, I find the latter easier.

x = 7.5/1.5 = 5

9514 1404 393

Answer:

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = LWH . . . . . the product of length, width, height

This rectangular prism has a volume of ...

  V = (12 ft)(6 ft)(4 ft) = 288 ft³ . . . . rectangular prism volume

__

The volume of a triangular prism is found from the formula ...

  V = Bh

where B is the area of the triangular base, and h is the height of the prism (distance between the triangular bases). The triangular base area is found from ...

  A = 1/2bh . . . . .where b is the base of the triangle, and h is its height.

Here, we have ...

  B = 1/2(6 ft)(4 ft) = 12 ft²

  V = Bh = (12 ft²)(6 ft) = 72 ft³ . . . . triangular prism volume

__

The total volume of the given geometry is the sum of the volumes of the parts:

  aquarium volume = 288 ft³ +72 ft³ = 360 ft³

Step-by-step explanation:

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:

-6/7

Step-by-step explanation:

If we have two points, we can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 4 - -2)/( -5 -2)

   = ( 4+2) /(-5-2)

    = 6/-7

   = -6/7

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:

NEGATIVE

Step-by-step explanation:

Answer:

positive

Step-by-step explanation:

positive

Answer:

65 miles

Step-by-step explanation:

costs = flat fee + cost per mile * miles

46 = 7+ .60m

Subtract 7 from each side

46-7 = 7+.6m-7

39 = .6m

Divide each side by .6

39/.6 = m

65 miles

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.

Step-by-step explanation:

domain = {-7, -3, 1}

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

Answer:

I am pretty sure that it's the second one

Answer:

2/7

Step-by-step explanation:

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:

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)

Answer:

question is not clear

specify the table

Answer:

y < -7.

Step-by-step explanation:

y - 6 < -13

Add 6 to both sides:

y - 6 + 6 < -13 + 6

y < -7.

Answer:

its legit 5

Step-by-step explanation:

Answer:

Very tricky question..

4 + 1 is 5 because you have written 4+1 not 4 1

so 5 is correct answer

Step-by-step explanation:

hope it helps