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4 years ago

4. What is the volume of the cylinder? Express answer in terms of a (hold and

Mathematics

1 answer:

Vladimir [108]4 years ago

4 0

Given:

Base area = 4π mm²

Height = 10 mm

To find:

The volume of the cylinder.

Solution:

Base of the cylinder is circle.

Area of the base = πr²

πr² = 4π

Volume of the cylinder = πr²h

Substitute 4π in place of πr².

= 4π × 10

= 40π mm³

The volume of the cylinder is 40π mm³.

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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 144 millimeters,

valentinak56 [21]

Answer:

The probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The information provided is:

μ = 144 mm

σ = 7 mm

n = 50.

Since n = 50 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample mean.

$\bar X\sim N(\mu_{\bar x}=144, \sigma_{\bar x}^{2}=0.98)$

Compute the probability that the sample mean would differ from the population mean by more than 2.6 mm as follows:

$P(\bar X-\mu_{\bar x}>2.6)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}} >\frac{2.6}{\sqrt{0.98}})$

$=P(Z>2.63)\\=1-P(Z$

*Use a z-table for the probability.

Thus, the probability that the sample mean would differ from the population mean by more than 2.6 mm is 0.0043.

8 0

3 years ago

Carrie goes hiking every 8 days and swimming every 11 days. She did both kinds of exercise today. How many days from now will sh

Likurg_2 [28]

To get our answer, we just have to find the least common multiple (LCM) of 8 and 11. In this case, it's 88, because that's the smallest number that 8 and 11 are both factors of.

Hope this helped! :D

6 0

3 years ago

Find the exact value of sin(-15)

koban [17]

$1)\ \ \ sin(- \alpha )=-sin \alpha \\2)\ \ \ cos2 \alpha =1-2sin^2 \alpha \ \ \ \Rightarrow\ \ \ 2sin^2 \alpha =1-cos2 \alpha \\\\ \Rightarrow\ \ \ sin \alpha = \sqrt{\frac{\big{1-cos2 \alpha}}{\big{2}}} \\\\\\sin(-15^0)=-sin15^0=-\sqrt{\frac{\big{1-cos30^0}}{\big{2}}} =-\sqrt{\frac{\big{1- \frac{ \sqrt{3} }{2} }}{\big{2}}} =-\sqrt{\frac{\big{2- \sqrt{3}}}{\big{4}}} =\\\\ =- \frac{1}{2} \sqrt{2- \sqrt{3}}$