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2 years ago

Given that x = 6 and y = -4, evaluate the following expression.

Mathematics

1 answer:

mr_godi [17]2 years ago

8 0

Answer: -6.5a
Hopes this helps

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[25 POINTS] A cylinder has a volume of 400π cm3. Find the dimensions that minimize its surface area.

miss Akunina [59]

Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: $SA=2\pi rh+2\pi r^2$

Volume: $V=\pi r^2h$

Therefore, the height of a cylinder given its volume would be $h=\frac{V}{\pi r^2}$ , thus:

$SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2$

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

$\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r$

$0=-\frac{800}{r^2}+4\pi r$

$0=800\pi+4\pi r^3$

$-800\pi=4\pi r^3$

$-200=r^3$

$r\approx5.848$

If $0If [tex]r>5.848$ , then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is $r=5.848cm$ , making the minimum height $h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm$ .

In conclusion, the 2nd option is correct.

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2 years ago

A food scientist takes a random sample of 25 cereals in order to test the claim that the mean fiber content is less than 2.5 gra

Jlenok [28]

Answer:

Choice A: there is insufficient evidence to conclude that the mean for the fiber content is less than 2.5 gms.

Step-by-step explanation:

From the graphs given the more appropriate is one sample t- test

One sample t- test is used and the results are

Hypothesis Test Fiber

Sample Mean 2.62

Sample St. Dev 3.492

Degrees of Freedom 24

t- test statistic 0.1718

p- value 0.5675

the critical region for this test at ∝= 0.05 is t < -1.711

There is not enough evidence to reject the null hypothesis.

Since the calculated t= 0.1718 does not fall in the critical region the null hypothesis is accepted that the mean fiber content is not less than 2.5 grams.T

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Answer:

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Step-by-step explanation:

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