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2 years ago

11

You have 16 socks in your drawer. 4 are black, 6 are white, 4 are blue, and 2 are gray. Suppose you randomly choose a sock, repl

ace it, and randomly choose another. What is the probability that either the first sock is blue or the second sock is gray?

1 answer:

Alinara [238K]2 years ago

4 0

Answer:

11/32

Step-by-step explanation:

4/16 + 2/16 - 1/32

simplify and solve

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What is the equation of the line in slope-intercept form?

andreev551 [17]

Answer:

10x + 4y is the correct answer

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2 years ago

PLEASE ANSWER!!!!!! REALLY IMPORTANT

faust18 [17]

<u>Answer-</u>

<em>The height of the prism is</em><em> 6 units</em>

<u>Solution-</u>

As the base of the prism is a hexagon consisting of 2 congruent isosceles trapezoids.

So,

$V_{Prism}=Area_{Base}\times Height$

And,

$Area_{Base}=2\times \text{Area of the trapezoid}$

Also,

$\text{Area of the trapezoid}=\dfrac{1}{2}\times \text{Height}\times (\text{Sum of two parallel lines})$

$=\dfrac{1}{2}\times 3\times (5+8)\\\\=\dfrac{39}{2}$

Putting all the values,

$V_{Prism}=2\times \dfrac{39}{2}\times Height=39\times Height$

As the volume is given, so

$\Rightarrow 39\times Height=234$

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8 0

2 years ago

Read 2 more answers

I Need Help On This

disa [49]

Answer:

The first blank: not equal

The 2nd blank: not right triangle (it's acute triangle)

The 3rd blank: equal

The 4th blank: it's right triangle

Step-by-step explanation:

4^2 = 3^2 + 3^2

<=> 16 = 9 + 9

<=> 16 = 18 ( nonsense)

so triangle LKJ is not right triangle

5^2 = 4^2 + 3^2

<=> 25 = 16 + 9

<=> 25 = 25 ( make sense)

so triangle ABC is right triangle

Done!! :))

6 0

2 years ago

What is 2 15/16 Ian’s a decimal?

Arada [10]

Answer:

2.9375

Step-by-step explanation:

15 divided by 16 equals .9375 so 2 15/16 is 2.9375

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2 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

Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S$

Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by

$\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k$

with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is

d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

$\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}$

The surface element reduces to

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv$

so that it points toward the origin at any point on <em>S</em>.

Then the integral with respect to <em>u</em> and <em>v</em> is

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS$

$=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS$

$=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}$

4 0

3 years ago