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FinnZ [79.3K]
2 years ago
11

Suppose that the halflife of a substance is 250 years . If there were ir 100 the substance , (a) give an exponential model for t

he situation, and (b) how much wil years?
can anyone answer this please:(
Mathematics
1 answer:
IgorLugansk [536]2 years ago
5 0
After 500 years one would have N nuclei of the original substance.

N = 100 * exp ( -ln(4) ) = 25

LOL.

I guess it is exp( - lamda * t)

Lamda, the decay constant is the ln(2) over the half life.

So we get exp( -ln(2)/250 * 500) or exp ( -ln(4) )
690 viewsView 1 Upvoter
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Answer:

a=4

Step-by-step explanation:

  • a^3=64

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The slipe of the line passing through the points (7, 5) and (21, 15) is
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The convex polygon below has 8 sides. Find the value of x ?
bulgar [2K]

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<h3>Sum of interior angles of convex polygon</h3>

The sum of interior angles of a convex polygon is calculated as follows;

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2 years ago
SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as
vovangra [49]

Answer:

a) P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

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b) P(400

P(-1

P(-1

c) z=-0.842

And if we solve for a we got

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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 SAT scores of a population, and for this case we know the distribution for X is given by:

X \sim N(500,100)  

Where \mu=500 and \sigma=100

We are interested on this probability

P(X>625)

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

z=\frac{x-\mu}{\sigma}

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

P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>1.25)=1-P(Z

Part b

We are interested on this probability

P(400

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

z=\frac{x-\mu}{\sigma}

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

P(400

And we can find this probability with this difference:

P(-1

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

P(-1

Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.8   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.842

And if we solve for a we got

a=500 -0.842*100=415.8

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.  

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strojnjashka [21]

Answer:

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Step-by-step explanation:

If interior angles are 3960 degrees then there are 24 sides. If polygon is regular, size of each exterior angle is 15 degrees.

A polygon has as many pairs of interior and exterior as number of its sides. Further each pair of exterior and interior add up to

180 degrees.

Sum of all the exterior angles of any polygon is

360 degrees

As sum of all the interior angles of the polygon is

3960 degrees

Sum of all pairs of exterior and interior angles is

3960 degrees + 360degrees = 4320 degrees

5 0
3 years ago
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