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4 years ago

PLS HELP ASAP WILL LET U BE BRAINLIEST

Mathematics

1 answer:

ladessa [460]4 years ago

6 0

Hey there! :)

Area = length · width

The length MUST be 2x the width

Possible Combinations:

1 by 72 x
2 by 36 x
3 by 24 x
4 by 18 x
6 by 12 ✔
8 by 9 x

The only combination where the length is 2x the width is: 6 by 12

Width: 6
Length: 12

12 × 6 = 72

Hope this helps :)

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1. The cylindrical container is four-fifths full of powder. Show ALL work for the following.

Marizza181 [45]

By definition, the volume of a cylinder is given by:

$V = \pi r ^ 2h$

Where,

r: cylinder radius

h: cylinder height

Therefore, the total capacity of the container is:

$V = \pi (6) ^ 2 (18)$

Rewriting we have:

$V = 648 \pi$

Then, the amount of total dust is given by:

$V '= \frac{4}{5} V$

Where,

V: volume of the container

Substituting values:

$V '= \frac{4}{5} (648 \pi)$

Rewriting:

$V '= 518.4 \pi$

Answer:

The total capacity of the container in terms of π is:

$V = 648 \pi$

The volume of the powder in terms of π is:

$V '= 518.4 \pi$

5 0

3 years ago

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

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 $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: