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3 years ago

A cylinder closed tin of radius r cm is made from 600cm2 tin sheet of metal.

Mathematics

1 answer:

Zarrin [17]3 years ago

7 0

Answer:

Note: The expression "h =300- pi r /pi r" would equate to 299, as written. I find h = (300 - π $r^{2}$ )/πr to be the equation for height.

Step-by-step explanation:

The total surface area of a sylinder is 2πr(h+r) where h is the height and r is the radius. That consists of top and bottom disks, each with an area of π $r^{2}$ , for a total of 2π $r^{2}$ . The side is a continous sheet that has an area of 2πrh, where h is the height. 2πr is the circumference of the can, so the surface area of the side is 2πrh.

The total surace area of a closed cylinder is therefore 2π $r^{2}$ + 2πrh.

2π $r^{2}$ + 2πrh = 600

π $r^{2}$ + πrh = 300

πrh = 300 - π $r^{2}$

h = (300 - π $r^{2}$ )/πr

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The nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium. To determine if the

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We conclude that the sodium content is same as what the nutrition label states.

Step-by-step explanation:

We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.

The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.

Let $\mu$ = average sodium content.

So, Null Hypothesis, $H_0$ : $\mu$ = 1100 milligrams {means that the sodium content is same as what the nutrition label states}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 1100 milligrams {means that the sodium content is different from what the nutrition label states}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$ ~ $t_n_-_1$

where, $\bar X$ = sample average sodium content = 1088.64 milligrams

s = sample standard deviation = 234.12 milligrams

n = sample of packages of Oriental Spice Sauce = 40

So, test statistics = $\frac{1088.64-1100}{\frac{234.12}{\sqrt{40}}}$ ~ $t_3_9$

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The value of z test statistics is -0.307.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the sodium content is same as what the nutrition label states.

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