Suppose you write each letter of the alphabet on a different slip of paper and put the slips into a hat. What is the probability of drawing one slip of paper from the hat at random and getting a vowel?

By the divergence theorem, the flux of [tex]\vec F[/tex] across S is equal to the volume integral of [tex]\mathrm{div}(\vec F)[/tex] over the interior of S.

We have

[tex]\vec F(x,y,z) = (x^3+y^3)\,\vec\imath + (y^3+z^3)\,\vec\jmath + (z^3+x^3)\,\vec k \\\\ \implies \mathrm{div}(\vec F) = \dfrac{\partial(x^3+y^3)}{\partial x} + \dfrac{\partial(y^3+z^3)}{\partial y} + \dfrac{\partial(z^3+x^3)}{\partial z} = 3(x^2+y^2+z^2)[/tex]

so that

[tex]\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \iiint_T \mathrm{div}(\vec F)\,\mathrm dV = 3 \iiint\limits_{x^2+y^2+z^2\le3} (x^2+y^2+z^2)\,\mathrm dx\,\mathrm dy\,\mathrm dz[/tex]

To compute the volume integral, convert to spherical coordinates with

x = ρ cos(θ) sin(ϕ)

y = ρ sin(θ) sin(ϕ)

z = ρ cos(ϕ)

so that

ρ ² = x ² + y ² + z ²

dx dy dz = ρ ² sin(ϕ) dρ dϕ dθ

The region T is the interior of the sphere S, given by the set

[tex]T = \left\{(\rho,\theta,\phi) \mid 0\le\rho\le3 \text{ and } 0\le\phi\le\pi \text{ and }0\le \theta\le2\pi\right\}[/tex]

So we have

[tex]\displaystyle 3 \int_0^{2\pi} \int_0^\pi \int_0^3 \rho^4 \sin(\phi) \,\mathrm d\rho \,\mathrm d\phi \,\mathrm d\theta \\\\ = 6\pi \left(\int_0^\pi \sin(\phi)\,\mathrm d\phi\right) \left(\int_0^3 \rho^4 \,\mathrm d\rho\right) = \boxed{\frac{2916\pi}5}[/tex]

The required surface integral S, and flux across F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]

Given that,

Function;[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},[/tex]

S is the sphere with center the origin and radius 3.

We have to determine,

Use the Divergence Theorem to calculate the surface integral S, F.dS that is, calculate the flux of F across S.

According to the question,

By the divergence theorem, the flux of [tex]\vec{F}[/tex]across S is equal to the volume integral of  [tex]div(\vec{f})[/tex] over the interior of S.

S is the sphere with center the origin and radius 3.

Therefore,

[tex]F(x, y, z) = (x^3 + y^3)\vec{i} + (y^3 + z^3)\vec{j} + (z^3 + x^3)\vec{k},\\\\= div\vec({F}) = \dfrac{d(x^3+y^3)}{dx} + \dfrac{d(y^3+z^3)}{dx} + \dfrac{d(z^3+x^3)}{dx} = 3(x^{2} + y^{2} + z^{2} )\\\\Then,\\\\\int \int_S \vec{F}(x, y, z) . \vec{ds} = \int \int \int _T div\vec{F}dV= 3 \int \int\int (x^{2} + y^{2} + z^{2} )dx.dy.dz[/tex]

To compute the volume integral, convert to spherical co-ordinate,

[tex]x = p\ cos\theta\ sin\phi\\\\y = p \ sin\theta \ sin\phi\\\\z = p\ cos\phi\\\\[/tex]

Therefore,

[tex]p^2 = x^{2} + y^{2} +z^{2} \\\\dx.dy.dz = x^{2} \ sin\phi \ dp\ d\phi \ d\theta[/tex]

The region T is the interior of the sphere S is given by the set,

[tex]T = {[ p,\theta,\phi}] | \ (0\leq p\leq 3 \ and \ \ 0\leq \phi \leq \pi \ and \ 0\leq 0\leq 2\pi )[/tex]

Then,

[tex]= 3 \int^2_0 \int^\pi _0 \int^3_0 p^4. sin(\phi). dp.d\phi .d\theta\\\\= 6\pi ( \int^\pi _0 sin(\phi).d\phi) (\int^3_0 p^4dp\\\\= \dfrac{2916\pi }{5}[/tex]

Hence, The required surface integral S, F·dS; that is [tex]\dfrac{2916\pi }{5}[/tex]

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Answer:

x=140⁰

Step-by-step explanation:

80+50=130

180-130=50

50+30=80

360-80=

280/2

=140

Answer:

If the diagram is 8 ovals with 4 squares each, and we know that this is a division,

then we have that an unknown number X is such that:

X/4 = 8 this is because we know that the division is by 4 (the number of squares in each oval) and the solution of the division is the number of ovals.

Then we can solve the equation for X. X/4 = 8

We multiply each side of the equality by 4 X= 4*8 = 32

then the diagram represents the division: 32/4 = 8 or " 32 divided by 4 = 8"

Answer:

Angle e = 35 degrees

Angle f = 180-35-109 = 36 degrees

Angle d = 109 degrees

Step-by-step explanation:

Step-by-step explanation:

Hi there!

Given;

The equation of straight line is 2y-3x+6 = 0.

a. Express in the form of y = mx + c.

2y-3x+6 = 0

2y = 3x-6

y = (3x-6)/2

y = (3/2)X - 3

Therefore, the required equation is : y = (3/2)x-3.

b.

The y-intercept of the equation is -3.

Hope it helps!

Answer:

y = c1 e^-x + c2 e^(3x)

Step-by-step explanation:

Review linear DE's

(D-3)(D+1)y = 0

Answer:

1/12

Step-by-step explanation:

multiply by three so 4x3 is 12 and that's 3 equal parts

Answer:

6 is the answer.

Answer:

89,892

Step-by-step explanation:

[tex]x+y[/tex]

[tex](38,221)+(51,671)[/tex]

[tex]89,892[/tex]

Answer:

Step-by-step explanation:

No because the sum of the two shorter legs does not equal the square of the hypotenuse.

3^2 =  9

6^2 =36

8^2 =64

9 and 36 do not equal 64

Answer:

11 degrees

Step-by-step explanation:

13-2=11.

The amount will Arundel need to pay preferred shareholders in 2021 if they wish to pay a dividend to common shareholders is 84,000

Using this formula

2021 preferred shareholders(per year)=Per dividend * Dividend rate

Let plug in the formula

2021 preferred shareholders(per year)=[(7,000*$100)*6%]

2021 preferred shareholders(per year)=($700,000*6%)*2

2021 preferred shareholders(per year)=42,000*2

2021 preferred shareholders(per year)=84,000

Inconclusion The amount will Arundel need to pay preferred shareholders in 2021 if they wish to pay a dividend to common shareholders is 84,000

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Answer is the third graph it was just an error..

Answer:

(-0.5, 1)- the midpoint, the distance is sqrt157

Step-by-step explanation:

The midpont is O

x0= (-6+5)/2= -0.5

yo= (4-2)/2=1

(-0.5, 1)

The distance is sqrt ((5-(-6))^2+(-2-4)^2)=sqrt 157

Answer:

Just 2 hours

Step-by-step explanation:

Since it takes 1 hour for 19, 19+19 is 38, so it takes 2 hours

Answer:

1. the smiley face, the top right corner.

2. top left corner again

3. rotation i think...

4.  e looks like the answer not sure.

Step-by-step explanation:

ez... maybe

Answer:

1st page-1

2nd page-b on the second line

3rd-b

4th-a

5th-c

Step-by-step explanation:

Answer:

Angle 1 is 129

Step-by-step explanation:

You do not need to solve the (3x+3) because you can see that these lines are parallel, so you can simply do 180-51 to get angle 1.

Answer:

4 hours

Step-by-step explanation:

After 4 hours, the north-bound truck will have traveled 232 miles and the south-bound truck will have traveled 256 miles.  232 + 256 = 488 miles.

Answer:

6

Step-by-step explanation:

The Volume is 4×6×9, which is 216

∛216

The cube root is 6.

I hope this helps!

pls ❤ and mark brainliest pls!

(0,2) is your answer

Explanation

Answer:

x=5

JK = 40 units

Step-by-step explanation:

JM=MK since the have the little red line which shows they are equal

7x+5 = 8x

Subtract 7x from each side

7x+5 -7x= 8x-7x

5 = x

JK = 7x+5 = 7(5)+5 = 35+5 = 40

Answer:

B. The way in which numbers are grouped to be added does not change the sum.

Answer:

(3, 5)

Step-by-step explanation:

The graph is is the standard y=|x| except the values tells you that x shifts 3 (within the absolute value or parentheses x does the opposite) to the right and the y value shifts 5 up (numbers outside parentheses affects y and does what it says). You can try using a table of values then graphing to check your answer.

What is 888 x - 666? = -591408

[tex]Hello[/tex] [tex]There![/tex]

Ummmmm... I could be wrong?

I think it is...

-591408

Hopefully, this helps you!!

[tex]AnimeVines[/tex]

Answer:

x=5/2 or 2.5

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

2.5 or 5/2

Step-by-step explanation:

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other - in other words, separated by the crossing point of the two lines, and not by the lines themselves.

that also means that they are equal.

and so,

8x + 15 = 4x + 25

4x = 10

x = 10/4 = 5/2 = 2.5

Answer:

answer is xy

Step-by-step explanation:

✓x-y=xy

y x=xy

Answer:

if m is the midpoint of AB

then,AM will be equal to MB

Therefore,

[tex]3x + 3 + 3x + 3 = 82 \\ 6x + 6 = 82 \\ 6x = 82 - 6 \\ 6x = 76 \\ x = \frac{76}{6} = \frac{38}{3} \\ \\ |am| = 3x + 3 \\ \: \: \: = 3( \frac{38}{3} ) + 3 \\ = 38 + 3 \\ = 41[/tex]

The equation of the graph after translation is y'' = √ ( x + 3 ) - 4

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

Let the equation of graph be represented as y

Now , the value of y is

y = √x

And , after a translation of graph by 3 units to the left , we get

y' = √ ( x + 3 )

Now , the translation of 4 units down is given by

y'' = y' - 4

y'' = √ ( x + 3 ) - 4

Hence , the translated equation is y'' = √ ( x + 3 ) - 4

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Answer:

[tex]a_1=\frac{39}{8}; \ d=-\frac{1}{4}.[/tex]

Step-by-step explanation:

1) if the first term is 'a₁', the difference of the sequence is 'd', then it is possible to write two equations for the sum of the first 20 terms and the next 20 terms;

2) for the first 20 terms: (a₁+a₂₀)*20/2=50;⇔ (a₁+a₁+19d)*10=50; ⇔2a₁+19d=5;

for the next 20 terms: (a₂₁+a₄₀)*20/2= -50;⇔ (a₁+20d+a₁+39d)*10=-50;⇔ 2a₁+59d= -5.

3) if to solve the system of two equations, then:

[tex]\left \{ {{2a_1+19d=5} \atop {2a_1+59d=-5}} \right. \ => \ \left \{ {{a_1=\frac{39}{8} } \atop {d=-\frac{1}{4} }} \right.[/tex]

4) finally: the first term is '39/8', the difference is '-1/4'.

Answer:

19

Step-by-step explanation:

There are 38 points total, each field goal is 2 points.

If we do 38/2 we get 19.

Image has work...

[tex]\frac{38}{2}[/tex]