All categories

3 years ago

Sullivan’s boss has 5 eyes total. Three of his eyes are smaller than the other two. What percentage of his eyes are larger?

Mathematics

1 answer:

il63 [147K]3 years ago

7 0

Answer:

40%

Step-by-step explanation:

3/5 are small so we have to find 2/5 which is 40%

2/5=x/100

cross multiply

you'll get: 5x=200

divide and thats how u get 40 %

You might be interested in

What is 1.1 to the 10th power

gulaghasi [49]

The answer would be 2.59374246 hope this helps

8 0

3 years ago

Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫

Pavel [41]

The area of the ellipse $E$ is given by

$\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy$

To use Green's theorem, which says

$\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy$

( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

$\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

and then we would simply compute the line integral. As the hint suggests, we can pick

$\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1$

The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

$\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}$

with $0\le t\le2\pi$ . Then the integral is

$\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt$

$=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi$

###

Notice that $x^{2/3}+y^{2/3}=4^{2/3}$ kind of resembles the equation for a circle with radius 4, $x^2+y^2=4^2$ . We can change coordinates to what you might call "pseudo-polar":

$\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}$

which gives

$x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}$

as needed. Then with $0\le t\le2\pi$ , we compute the area via Green's theorem using the same setup as before:

$\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt$

$=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt$

$=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt$

$=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi$

3 0

3 years ago

Show that 0.27 and 3.6 are multiplicative inverse

klasskru [66]

0.27*3.6
I hope is correct

3 0

3 years ago

Read 2 more answers

Which is the graph of x^2/16 + y^2/ 9 =1

jeka94

Answer:

Step-by-step explanation:

you can figure this out by replace the x and y with any one of the x, y positions and if the answer is 1 it's correct.

I tried 0^2/16+3^2/9 and I got 1.

I tried this with the first two but they didn't work.

6 0

3 years ago

A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random samp

motikmotik

Answer:

There is no statistical evidence at 1% level to accept that the mean net contents exceeds 12 oz.

Step-by-step explanation:

Given that a random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.

We find mean = 11.015

Sample std deviation = 3.157

a) $H_0: \bar x= 12 oz\\H_a: \bar x >12$

(Right tailed test)

Mean difference /std error = test statistic

$\frac{11.015-12}{\frac{3.157}{\sqrt{10} } } \\=-0.99$

p value =0.174

Since p >0.01, our alpha, fail to reject H0

Conclusion:

There is no statistical evidence at 1% level to accept that the mean net contents exceeds 12 oz.

3 0

3 years ago