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3 years ago

7

A miniature golf course recently provided its customers with 6 golf balls, of which 3 were blue. What is the experimental probab

ility that the next customer will receive a blue golf ball?

1 answer:

Schach [20]3 years ago

5 0

The next probable answer is 1:2

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Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

Find the unit rate.<br> 5/8 ounce per 1/4 pint

Katena32 [7]

Answer: 2.5 ounces/ pint

You can firstly turn your fractions into decimals 5/8 is equal to .625 and 1/4 is .25

Then you can divide .625 by .25 which is 2.5, So the unit rate is 2.5 ounces per pint.

4 0

3 years ago

ASAP HELP WILL GIVE BRAINLY

timurjin [86]

Answer:

$7x - 4y = -4\\(7x - 7x) - 4y = -7x - 4\\-4y = -7x - 4\\\frac{-4}{-4}y = \frac{-7x - 4}{-4}\\y = \frac{7}{4}x + 1\\m = \frac{7}{4}\\b = 1$

m = slope

b = y-intercept

Step-by-step explanation:

3 0

3 years ago

What is 9/10 divided by 3/5

Paha777 [63]

Answer:

1 /2 or 1.5

Step-by-step explanation:

Dividing fractions are relatively easy. One way to do it is multiplying the reciprocal of one of the fractions to the other. So 3/5 would become 5/3. Multiply, 9/10*5/3=45/30. Now that you have the answer you need to simplify which will end up into 1 1/2.

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3 years ago

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Is the following shape a right triangle? how do you know

maw [93]

Answer:

Yes, the following shape is a Right Triangle because it has a 90 Degree Angle!

3 0

2 years ago