A symmetrical binomial distribution with large sample size can be approximated by a _________

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of $x^2+y^2\le1$ by

$x=\cos u$

$y=\sin u$

with $0\le u$ . Then $t(x,y)$ can be considered a function of $u$ alone:

$t(x,y)=t(\cos u,\sin u)=T(u)$

$T(u)=\cos^2u+3\sin^2u+13\cos u$

$T(u)=3+13\cos u-2\cos^2u$

$T(u)$ has critical points where $T'(u)=0$ :

$T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0$

$(1)\quad\sin u=0\implies u=0,u=\pi$

$(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4$

but $|\cos u|\le1$ for all $u$ , so this case yields nothing important.

At these critical points, we have temperatures of

$T(0)=14$

$T(\pi)=-12$

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0

2 years ago

You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have 765 words. Find the rate of change in words per m

alekssr [168]

You start at 4:04pm and end at 4:18pm. This means 14 minutes have passed

Now you had 275 word typed and now you have 765. To find the amount that were added simply subtract 765 by 275 and you'll get 490.

Finally, to find the average amount of words typed per minute, you'd divide 490 by 14 for each minute which is 35

Your answer is 35 words per minute

3 0

2 years ago

A survey of 132 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take

ddd [48]

Answer:

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 66/132 = 0.50

Number of samples n = 132

Confidence level = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

0.50 +/- 1.645√(0.50(1-0.50)/132)

0.50 +/- 1.645√(0.001893939393)

0.50 +/- 0.071589436011

0.50 +/- 0.072

(0.428, 0.572)

The 90% confidence level estimate of the true population proportion of students who responded "yes" is (0.428, 0.572)

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

7 0

2 years ago

ris is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 25 represents the number of flowers

olasank [31]

Answer:

A. f(s) = 2s + 34

B. Mole

C. f(s) = 2s + 54

Step-by-step explanation:

A. Its a prediction the 34 can be any number reasonably close to 25

B. Amount of substance - mole (mole)

c. f(s) = 2s + 54

3 0

2 years ago

Viruses and viral videos portfolio help

alexdok [17]

Care to elaborate, what I can say right now is just that a virus is a malicious program that invades your computer and multiplies itself across several programs and folders. a viral video is only similar because it becomes really popular across the internet and "spreads" throughout the internet by fame. hope that help... oh and id say this is more of a computers question.

6 0

2 years ago

A symmetrical binomial distribution with large sample size can be approximated by a __________