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2 years ago

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As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1.11.

If the cans are currently 12 cm tall, 6 cm in diameter, and have a volume of 339.12 cm3, how much more will the new cans hold? Use 3.14 for π and round your answer to the nearest hundredth. 802.91 cm3 376.42 cm3 463.79 cm3 124.67 cm3

1 answer:

Elis [28]2 years ago

5 0

Answer:

124.67cm³

Step-by-step explanation:

==>Given:

Dimensions of current can:

Height (h) = 12cm

Diameter = 6cm (radius = 3cm)

Volume of current can (V1) = 339.12 cm³

Dimensions of future cans to be increased multiple of 1.11:

height = 12cm × 1.11 = 13.32 cm

radius = 3cm × 1.11 = 3.33 cm

Volume of future can (V2) = πr²h = 3.14*3.33²*13.32

= 3.14*11.0889*13.32 = 463.791025

V2 ≈ 463.79 cm³

==>Find how much more would new cans hold = Volume of new can - volume of current can

= 463.79 cm³ - 339.12 cm³

= 124.67cm³

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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$p$ represent the real population proportion of interest

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The population proportion have the following distribution

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Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

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And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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Part 2

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And rounded up we have that n=298

Part 3

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And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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Step-by-step explanation:

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