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3 years ago

A. What is the approximate perimeter of the concrete region?

Mathematics

1 answer:

Nastasia [14]3 years ago

7 0

You have a square with half circles along the sides.
The length of each side is 4ft, so the radius of the circles is 2ft

to calculate the perimeter you can calculate the circumference of 4 half circles = 2 complete circles
c=2r* $\pi$ =
2*2 $\pi$ =12.56
perimeter=2c=25.12=8 $\pi$

the area is the area of 2 circles+the area of the square
circle area= r^2* $\pi$ =2*2 $\pi$ =4 $\pi$
concrete area=circle area*2+square area
=4 $\pi$ *2+(4*4)
=8 $\pi$ +(4*4)
=8 $\pi$ +16ft
=41.12 ft^2

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A study investigating the relationship between age and annual medical expenses randomly samples 400 individuals in a city. It is

ICE Princess25 [194]

Answer:

The probability is 0.789

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\sigma = 16, n = 400, s = \frac{16}{\sqrt{400}} = 0.8$

Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.

Using $\mu = 30$ , this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So

X = 31

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{31 - 30}{0.8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 29

$Z = \frac{X - \mu}{s}$

$Z = \frac{29 - 30}{0.8}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

Rounded to three decimal places, 0.789

The probability is 0.789

4 0

3 years ago

Read 2 more answers

A computer chip has dimensions of 8mm x 8mm. the scale drawing shows 4cm by 4cm. the answer is 1cm represents 2mm but I don't kn

Andru [333]

$Change\ all\ dimensions\ to\ the\ same\ unit. \\ \\ \\ \\ 4cm==\textgreater\ 400\ mm$ $Work\ out\ the\ Scale\ factor, \\ \\ \\ \\ Scale\ factor= { \frac{Scaled\ dimension\ (same\ side)}{Actual\ dimension\ (same\ side)} } \\ \\ = { \frac{400}{8} } \\ \\ = 50$
$1\ mm\ on\ actual= 50\ mm\ on\ scaled. \\ \\ 2\ mm\ represents\ 1\ cm\ on\ scaled.$