Pierre Hugo is handling the estate of a prominent businesswoman. The will states that the surviving spouse is to receive 1/3 of the estate and the remaining 2/3 of the estate will be divided equally among 3 surviving children. What fraction of the estate does each child​ receive?

Using a trigonometric identity, it is found that the sine of the angle is given as follows:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

Considering an angle [tex]\theta[/tex], the identity is given as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the cosine is given as follows:

[tex]\cos{\theta} = \frac{3}{5}[/tex]

Hence the sine is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]

[tex]\sin^2{\theta} = \frac{16}{25}[/tex]

[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]

In quadrant IV, the sine is negative, hence:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

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Answer:

[tex]\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Increase the power by 1, then divide by the new power.

Given indefinite integral:

[tex]\displaystyle \int x \ln x \:\: \text{d}x[/tex]

To integrate the given integral, use Integration by Parts:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]

[tex]\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}[/tex]

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Answer:

294pi

Step-by-step explanation:

1/3*pi*r^2*h=V

1/3*pi*49*18=V

V=294pi

Answer:x=4

Step-by-step explanation:

tendrías que poner términos similares juntos, asegurándote de cambiar el signo de cualquier figura que cruce el igual al signo. luego restarías o sumarías, resolverías las ecuaciones de cada lado, ya que ahora están agrupadas. luego dividirás tu respuesta por el coeficiente que es 2 (2x). esto te dejaría con 4

4x - 2x = 1+7

4x-2x= 8

2x =8

divisir

x=8

Duplicate don't answer!

The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

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Answer:

y = (-4/5)x - 7/5

Step-by-step explanation:

The general equation of the line is slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".

y = mx + b                                   <----- Slope-intercept form

y = (-4/5)x + b                             <------ Plug -4/5 in "m"

-3 = (-4/5)(2) + b                         <----- Plug in "x" and "y" values from Point

-3 = -8/5 + b                               <------ Multiply -4/5 and 2

-15/5 = -8/5 + b                          <----- Assign common denominator

-7/5 = b                                      <----- Add 8/5 to both sides

Now that you have the slope and y-intercept, you can construct the equation.

y = (-4/5)x - 7/5

The product (a+b)(a-2b) is a^2 - ab - 2b^2

The product expression is given as:

(a+b)(a-2b)

Expand the bracket

a * a - a * 2b + b * a - b * 2b

Evaluate the product

a^2 - 2ab + ab - 2b^2

Evaluate the like terms

a^2 - ab - 2b^2

Hence, the product (a+b)(a-2b) is a^2 - ab - 2b^2

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The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

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Answer:

Step-by-step explanation:

|√2-y|=|y-√2|

√2-y=±(y-√2)

when √2-y=y-√2

y+y=√2+√2

2y=2√2

y=√2

when √2-y=-(y-√2)

√2-y=-y+√2

or 0=0

it gives no value of y.

so only possible value is y=√2

Answer:

D

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

To evaluate the function f(-4), we let x =4 in f(x) = [tex]2^{x}[/tex]

f(-4) = [tex]2^{-4}[/tex]

     = 1/[tex]2^{4}[/tex]

     =1/16

The amount you should put is 3846

The given parameters are:

Amount, A = 4000

Rate, r = 8%

Time = 0.5 year i.e. 6 months

The amount on simple interest is calculated as:

A = P(1 + RT)

This gives

4000 = P * (1 + 8% * 0.5)

Evaluate the product

4000 = P * (1 + 0.04)

Evaluate the sum

4000 = P * (1.04)

Divide both sides by 1.04

P= 3846

Hence, the amount you should put is 3846

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Answer:

0.25 or 1/4

Step-by-step explanation:

P(coin is flipped as head) = 0.5 or 1/2 (one of 2 sides)

P(coin is flipped as head twice) = P(coin is flipped as head) x P(coin is flipped as head)

= 0.5 x 0.5

= 0.25 or 1/4

Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

Here is conversion chart

1 day=24hr

so the equation to solve this would look like this

(24*11)+7

Therefore the answer is 271 hr

Answer:

endpoint or straight lines

Step-by-step explanation:

same

Explanation:

There are 7 ways to pick the first place position, then 6 ways for second place, 5 for third, and so on. We count down until we get to 1

7,6,5,4,3,2,1

Multiply out those values to get the final answer. On many calculators this can be done using the factorial button, indicated as an exclamation mark

7! = 7*6*5*4*3*2*1 = 5040

Hello,

    3y + 4 < 16

⇔ 3y < 16 - 4

⇔ 3y < 12

⇔ y < 12/3

⇔ y < 4

⇒ S = ] - ∞ ; 4 [

Answer:

6^4 * 6^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sqrt{- i} =\sqrt{(-1)i} =\sqrt{i^2i} =i\sqrt{i}[/tex]

Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U

When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.

From the given question, the following can be deduced:

RT ≅ US (given: opposite sides are equal)

and TS is a common side for the two triangles.

<TRS  ≅  <RSU (alternate angle property)

<RTS  ≅ <UST (right angle property)

<RTU  ≅  <SUT (alternate angle property)

Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R  ≅ <U.

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Answer:

Step-by-step explanation:

The magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

Ax = A cosθ

Ay = A sinθ

Ax = 7.7 x cos(27.8)

Ax = 6.81 m

Ay = 7.7 x sin(27.8)

Ay = 3.59 m

Bx = B cosθ

By = B sinθ

θ with respect to x - axis = 90 - 20 = 70⁰

Bx = 16.3 m x cos(70)

Bx = 5.575 m

By = 16.3 m x sin(70)

By = 15.32 m

Vx = Ax + Bx

Vx = 6.81 m + 5.575 m = 12.385 m

Vy = Ay + By

Vy = 3.59 m + 15.32 m = 18.91 m

V = √(Vy² + Vx²)

V = √(18.91² + 12.385²)

V = 22.6 m

tan θ = Vy/Vx

tan θ = (18.91)/(12.385)

tan θ = 1.527

θ = arc tan (1.527)

θ = 56.8⁰

Thus, the magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

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Answer:

6(q + 9)

Step-by-step explanation:

Answer:

d) -8 × 3 = -24

Step-by-step explanation:

a) -18 ÷ 6 = -3

b) 30 ÷ 3 = 10

c) -7 × -7 = 49

d) -8 × 3 = -24

Above from all, option d is done correctly.

Note: when negatives are multiplied together or divided they cancel out to being positive. For example: -1 × -1 = 1

Hello!

Let's solve to verify whether the equations are true.

⇒ -18 ÷ 6 = -3

⇒ Given answer : 3

⇒ Incorrect

⇒ 30 ÷ 3 = 10

⇒ Given answer : -10

⇒ Incorrect

⇒ -7 × -7 = 49

⇒ Given answer = -49

⇒ Incorrect

⇒ -8 × 3 = -24

⇒ Given answer = 24

⇒ Correct

∴ The equation which is correctly calculated is -8 × 3 = -24.

The express elevator will go 4 floors per seconds.

We have to find the rate of the express elevator before we can find how many floors one can go in one seconds.

time = 12 3 / 4  = 51 / 4 seconds

number of floor = 51 floors

rate = 51 / 51 / 4

rate = 51 × 4 / 51

rate = 4 floors per seconds

Therefore, the elevator will go 4 floors per seconds.

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Answer:

28n+24

Step-by-step explanation:

3 ( 7 n + 5 n + 8 ) - 8 n

combine 7n and 5n to get 12n

3 ( 12n + 8 ) - 8

distribute 3 to 12n +8

36n+24-8n

combine like terms

28n+24

since ypu cant simply any more it stays like thats

*by the way there is an app that helps with equation and explains the process, its Microsoft Math Solver. hope it helped

I assume you meant [tex]g(x)=4^x -1[/tex].

The graph is shown in the attached image.

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be written as 2 2 2 2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

The graph of the function is attached with the answer.

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The ice cube tray can make 200.96 cubic centimeters of ice.

For a sphere of radius R, the volume is:

[tex]V = \frac{4}{3}*3.14*R^3[/tex]

In this case, we have 6 spheres, each one with a radius of 2cm.

Then the total volume of ice that the ice cube tray can make at one time is:

[tex]volume = 6*V = 6*(\frac{4}{3} *3.14*(2cm)^3) = 200.96cm^3[/tex]

The ice cube tray can make 200.96 cubic centimeters of ice.

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Answer:

$33.915 for the cd

Step-by-step explanation:

70% of 19.95 = 13.965

19.95 + 13.965= 33.91

Answer:

1. Colouring Pencil 2. Notebook 3. Pencil Case

Step-by-step explanation: