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3 years ago

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g A long-term study has revealed that a test for cancer in men is very effective. The study shows that 89% of the men for which

the test is positive actually have cancer. If a man selected at random tests positive for cancer with this test, what is the probability that he does not have cancer

1 answer:

VikaD [51]3 years ago

4 0

The answer is 89% because I had that Same question and it was 89%

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Question 3: Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she pa

Lera25 [3.4K]

Each bracelet was approximately 20.25

Here is my work:

67.50 - 27 = 40.5

40.5 divided by 2 = 20.25

Hope this helps!

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3 years ago

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Cylindrical hole of radius a is bored through a sphere of radius 2a. the surface of the hole passes through the center of the sp

r-ruslan [8.4K]

The amount of material removed is the volume of the region within the sphere bounded by the cylinder. Consider a sphere of radius $2a$ centered at the origin; this sphere has equation

$x^2+y^2+z^2=4a^2\iff z^2=4a^2-x^2-y^2$

The given cylinder has equation

$x^2+y^2=a^2$

The volume of the region of interest $\mathcal D$ is given by

$\displaystyle\iiint_{\mathcal D}\mathrm dV$

Converting to cylindrical coordinates, setting

$x=r\cos\theta$

$y=r\sin\theta$

$z=\zeta$

we have

$z^2=4a^2-r^2$

and

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\left|\dfrac{\partial(x,y,z)}{\partial(r,\theta,\zeta)}\right|\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$

$\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$

where $\dfrac{\partial(x,y,z)}{\partial(r,\theta,\zeta)}$ is the Jacobian of the transformation from $(x,y,z)$ to $(r,\theta,\zeta)$ . The region $\mathcal D$ is described by the set

$\left\{(r,\theta,\zeta)\,:\,0\le r\le a\land0\le\theta\le2\pi\land-\sqrt{4a^2-r^2}\le\zeta\le\sqrt{4a^2-r^2}\right\}$

The integral is then

$\displaystyle\iiint_{\mathcal D}\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=a}\int_{\zeta=-\sqrt{4a^2-r^2}}^{\zeta=\sqrt{4a^2-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

The integral with respect to $\zeta$ is symmetric about $\zeta=0$ , so we instead compute twice the integral from $\zeta=0$ to $\zeta=\sqrt{4a^2-r^2}$ , and we can immediately compute the integral with respect to $\theta$ :

$=\displaystyle4\pi\int_{r=0}^{r=a}r\sqrt{4a^2-r^2}\,\mathrm dr$

Now, let $s=4a^2-r^2$ , so that $\mathrm ds=-2r\,\mathrm dr$ :

$=\displaystyle-2\pi\int_{r=0}^{r=a}-2r\sqrt{4a^2-r^2}\,\mathrm dr=-2\pi\int_{s=4a^2}^{s=3a^2}\sqrt s\,\mathrm ds$

$=-2\pi\cdot\dfrac23s^{3/2}\bigg|_{s=4a^2}^{s=3a^2}$

$=\dfrac{4\pi}3\left((4a^2)^{3/2}-(3a^2)^{3/2}\right)$

$=\dfrac{4\pi(8-3^{3/2})a^3}3$

6 0

4 years ago

Help me with this :)))))))

lora16 [44]

Answer:

QR= 16

Step-by-step explanation:

HOPE THIS HELPS

3 0

3 years ago

Level 7 escape room 3

Sonja [21]

Answer:

A B E F

Step-by-step explanation:

-2 * -5 = 10

10 * 3 = 30

30 * -7 = -210

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3 years ago

What is the square root of 75643

JulsSmile [24]

The square root of 75,643 is 275.03.

Hope this helped :)

6 0

4 years ago

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