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3 years ago

11

Consider five circles with a radii of 1, 2, 4, 8, and 16 inches. Write your answer in terms of pi r square. Compare the areas an

d circumference of a circle when you double the radius? What happens to the area? What happens when you triple the radius.
The table lists the radius, circumference and area.

1 answer:

BartSMP [9]3 years ago

7 0

When you change the radius (multiply by k), a 1D size, the circumference is multiplied by k (1D), while the area is multiplied by $k^2$ (2D). I hope this helps on this problem and others.

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A ladder 13 feet long leans against a building. The bottom of the ladder is 5 feet away from the base of the building.How far up

seraphim [82]

Answer:

12 ft

Step-by-step explanation:

4 0

2 years ago

The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of

Karo-lina-s [1.5K]

Answer:

a) $P(\bar X$

b) $P(98$

c) $P(\bar X$

d) $P(93$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(99.9,30)$

Where $\mu=99.9$ and $\sigma=30$

We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:

$\bar X \sim N(\mu =99.9 , \frac{\sigma}{\sqrt{n}}= \frac{30}{\sqrt{38}}=4.87)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X$

$=P(Z$

Part b

For this case we want this probability:

$P(98$

$=P(\frac{98-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-0.39$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.39$

Part c

If we apply this formula to our probability we got this:

$P(\bar X$

$P(\bar X$

Part d

For this case we want this probability:

$P(93$

$=P(\frac{93-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-1.42$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.42$

3 0

3 years ago

Iodine-125 has a half-life of about 60 days.

Murljashka [212]

62.5 mg sample will remain after 240 days

Step-by-step explanation:

Given

Half-life = T = 60 days

The formula for calculating the quantity after n half lives is given by:

$N = N_0(\frac{1}{2})^n$

Here

N is the final amount

N_0 is the initial amount

n is the number of half lives passed

The number of half lives are calculated by dividing the time for which the remaining quantity has to be found by half life

The quantity has to be calculated for 240 days so,

$n = \frac{240}{60}\\n = 4$

Given

$N_0 = 1000\ mg$

Putting the values in the formula

$N = 1000 (\frac{1}{2})^4\\=1000 * \frac{1}{16}\\=\frac{1000}{16}\\=62.5\ mg$

Hence,

62.5 mg sample will remain after 240 days

Keywords: Half-life, sample

Learn more about half-life at:

#LearnwithBrainly

3 0

3 years ago

Use the coordinates grid below to draw a square

garik1379 [7]

Answer:

draw a square using only 16 squares representing the area, so 8 by 8 by 8 by 8

6 0

2 years ago

Collected 20 cans this week, 25 cans next week what is the percent of increase

BartSMP [9]

Hello!!

25 - 20 = 5

5/20 = 0.25

0.25 * 100 = 25%

Good luck :)

5 0

2 years ago