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3 years ago

What is the mean of the following set of numbers? 32, 31, 37, 44 a. 13 b. 34 c. 36

Mathematics

1 answer:

ELEN [110]3 years ago

6 0

Mean is average

so we have 4 numbers
sum them then divide by 4

(32+31+37+44)=144
divide by 4
144/4=36

answer is C

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A right circular cone has a radius of 8 in. and a slant height of 12 in. These dimensions are multiplied by 6. By what factor is

Margarita [4]

Answer:

Factor: 36

Step-by-step explanation:

Ratio of sides

1 : 6

Ratio of areas

1² : 6²

1 : 36

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and

Nadusha1986 [10]

Call the surface $S$ ; then the area of $S$ is given by the surface integral

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

Parameterize the surface by

$\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}$

with $2\le u\le4$ and $0\le v\le2\pi$ . The surface element is given by

$\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$

So the area is

$\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8$

where $w=1+4u^2\implies\mathrm dw=8u\,\mathrm du$

$=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}$
$=\dfrac\pi6\left(65^{3/2}-17^{3/2}\right)\approx237.69$

8 0

3 years ago

Let X and Y be random variables with the following joint moment generating function: M_{X,Y}(s,t)=0.1+0.2e^s+0.3e^t+0.4e^{s+t}

MA_775_DIABLO [31]

We obtain the joint PMF directly from the joint MGF:

$M_{X,Y}(s,t)=0.1+0.2e^s+0.3e^t+0.4e^{s+t}$

$\implies\mathrm{Pr}[X=x,Y=y]=\begin{cases}0.1&\text{for }x=y=0\\0.2&\text{for }x=1,y=0\\0.3&\text{for }x=0,y=1\\0.4&\text{for }x=y=1\\0&\text{otherwise}\end{cases}$

Then

$\mathrm{Pr}[X=Y]=\mathrm{Pr}[X=Y=0]+\mathrm{Pr}[X=Y=1]=0.1+0.4=\boxed{0.5}$

8 0

3 years ago

Please help me with this question

vichka [17]

Write the ratio out.

Number of hands Betty won : Number of hands Adam won

5:20

Both can be simplified by the common factor of 5.

1:4 is the solution.

5 0

3 years ago