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3 years ago

A spinner has many equal sections of different colors. The probability that the spinner will not land on a

Mathematics

2 answers:

Nady [450]3 years ago

5 0

66 because 34% of it is blue

olchik [2.2K]3 years ago

3 0

Answer:

B 66%

Step-by-step explanation:

100% (total) - 34% (P(not landing on blue)) = 66%

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A 12-member jury is to be selected from 15 men and 13 women. Find the probability that this jury has 6 or 7 males.

Bas_tet [7]

Answer:

The right solution is "0.5545".

Step-by-step explanation:

According to the question,

The probability of having 6 or 7 males will be:

= $P(6 \ males)+ P(7 \ males)$

= $\frac{15_C_6\times 13_C_6}{28_C_{12}} + \frac{15_C_7\times 13_C_5}{28_C_{12}}$

= $\frac{5005\times 1716+6435\times 1287}{30421755}$

= $\frac{16870425}{30421755}$

= $0.5545$

8 0

3 years ago

Hey I need help just leave answer thx

Illusion [34]

Answer:

x = 61

Step-by-step explanation:

The angle above the line n adjacent to 2x - 6 is (x + 3) alternate angle.

Adjacent angles are supplementary, thus

2x - 6 + x + 3 = 180, that is

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61

4 0

3 years ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

tresset_1 [31]

Because I've gone ahead with trying to parameterize $S$ directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over $S$ straight away, let's close off the hemisphere with the disk $D$ of radius 9 centered at the origin and coincident with the plane $y=0$ . Then by the divergence theorem, since the region $S\cup D$ is closed, we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV$

where $R$ is the interior of $S\cup D$ . $\vec F$ has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z$

so the flux over the closed region is

$\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0$

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0$

$\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k$

with $0\le u\le9$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0$

$\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}$

8 0

3 years ago

The system of equations

cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

4 0

4 years ago

Triangle ABC is translated according to the rule (x, y) = (x+2y-S). If the coordinates of the pre-image of point B are

Liula [17]

The coordinates of b is 1.9

7 0

3 years ago