All categories

3 years ago

Suppose that

Mathematics

1 answer:

Ganezh [65]3 years ago

8 0

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

You might be interested in

If Britt has 2 rings and gets one more how many rings does she have?

levacccp [35]

She will then have 3 rings

7 0

3 years ago

Read 2 more answers

Consider the probability distribution shown below. x 0 1 2 P(x) 0.15 0.80 0.05 Compute the expected value of the distribution. (

larisa [96]

Answer:

Expected value =0.9

Standard deviation = 0.4359

Step-by-step explanation:

Let's use the formula to find expected value or mean.

Expected value =Σ x *P(x)

x 0 1 2

P(x) ) .15 .8 .05

So, expected value = (0)(0.15) +1(0.8)+2(0.05)

= 0 +0.8 +0.1

=0.9

Expected value =0.9

Now, let's find standard deviation

x $(x- E(x))^{2}$ $(x-E(x))^{2} *p(x)$

0 $(0-0.9)^{2}$ $(0-0.9)^{2} *0.15$ =0.1215

1 $(1-0.9)^{2}$ $(1-0.9)^{2} *0.8$ =0.008

2 $(2-0.9)^{2}$ $(2-0.9)^{2} *0.05$ =0.0605

Now, add the last column together and then take square root to find standard deviation.

Standard deviation of the distribution = $\sqrt{0.1215+0.008+0.0605)}$

Simplify it, so standard deviation =0.4358898...

Round the answer to nearest four decimal places

Standard deviation = 0.4359

7 0

3 years ago

At a zoo in a butterfly enclosure, 5 drops of nectar is sufficient for 2 butterflies. How many butterflies could be fed with 59

Elan Coil [88]

Answer:

111 can i get brailyist for replying so fast.

8 0

3 years ago

Read 2 more answers

Is 3/4 and 3/8 equivalent fractions and why? Thanks

uranmaximum [27]

No, they are not equivalent. The numerators are equals, but the denominators are not, they are not equivalent. If the first one would be 6/8, they would be equivalent, because we can simplify the fractions by 2 and we got 3/4 again. Good luck !

4 0

3 years ago

Read 2 more answers

Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 4x2 + 9y2 = 36. cross-sect

Tasya [4]

$4x^2+9y^2=36\iff\dfrac{x^2}9+\dfrac{y^2}4=1$

defines an ellipse centered at $(0,0)$ with semi-major axis length 3 and semi-minor axis length 2. The semi-major axis lies on the $x$ -axis. So if cross sections are taken perpendicular to the $x$ -axis, any such triangular section will have a base that is determined by the vertical distance between the lower and upper halves of the ellipse. That is, any cross section taken at $x=x_0$ will have a base of length

$\dfrac{x^2}9+\dfrac{y^2}4=1\implies y=\pm\dfrac23\sqrt{9-x^2}$
$\implies \text{base}=\dfrac23\sqrt{9-{x_0}^2}-\left(-\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac43\sqrt{9-{x_0}^2}$

I've attached a graphic of what a sample section would look like.

Any such isosceles triangle will have a hypotenuse that occurs in a $\sqrt2:1$ ratio with either of the remaining legs. So if the hypotenuse is $\dfrac43\sqrt{9-{x_0}^2}$ , then either leg will have length $\dfrac4{3\sqrt2}\sqrt{9-{x_0}^2}$ .

Now the legs form a similar triangle with the height of the triangle, where the legs of the larger triangle section are the hypotenuses and the height is one of the legs. This means the height of the triangular section is $\dfrac4{3(\sqrt2)^2}\sqrt{9-{x_0}^2}=\dfrac23\sqrt{9-{x_0}^2}$ .

Finally, $x_0$ can be chosen from any value in $-3\le x_0\le3$ . We're now ready to set up the integral to find the volume of the solid. The volume is the sum of the infinitely many triangular sections' areas, which are

$\dfrac12\left(\dfrac43\sqrt{9-{x_0}^2}\right)\left(\dfrac23\sqrt{9-{x_0}^2}\right)=\dfrac49(9-{x_0}^2)$

and so the volume would be

$\displaystyle\int_{x=-3}^{x=3}\frac49(9-x^2)\,\mathrm dx$
$=\left(4x-\dfrac4{27}x^3\right)\bigg|_{x=-3}^{x=3}$
$=16$

6 0

3 years ago