A quarter circle is attached to the side of a square as shown.

Mathematics

1 answer:

aleksklad [387]3 years ago

3 0

First you find the area of the square which is 8²=64 than you find the area of a circle using the formula πr² you get 201.06 and divide it by 4 because you only need the quarter and you get 50.26 the last step is to add the two areas together and you get 64+50.26=114.2

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If a certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms, what is

V125BC [204]

Answer:

The probability is $P(\= X < 40.4) = 0.84134$

Step-by-step explanation:

From the question we are told that

The mean is $\mu =40 \ \Omega$

The standard deviation is $\sigma = 2 \ \Omega$

The sample size is n = 25

The combined resistance is $\sum x_i = 1010 \ \Omega$

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i }{n}$

=> $\= x = \frac{1010 }{25}$

=> $\= x = 40.4 \ \Omega$

Generally the standard error of the mean is mathematically represented as

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

=> $\sigma_{x} = \frac{ 2 }{\sqrt{25} }$

=> $\sigma_{x} = 0.4$

Generally the probability that a random sample of 25 of these resistors will have a combined resistance of less than 1010 ohms is mathematically represented as

$P(\= X < 40.4) = P( \frac{\= X - \mu }{\sigma_{x }} < \frac{ 40.4 - 40 }{0.4} )$