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Makovka662 [10]
1 year ago
9

A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours,

55 mg of the substance remains. How many milligrams will remain after 26 hours
Mathematics
1 answer:
SpyIntel [72]1 year ago
4 0

Answer:

  44.7 mg

Step-by-step explanation:

The equation for exponential decay can be written in the form ...

  y = a·b^(t/p)

where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.

<h3>Setup</h3>

Using the above equation, we have ...

  a = initial value = 110 mg

  b = decay factor = 55/110 = 1/2 over time period p=20 hours

Then the equation is ...

  y = 110·(1/2)^(t/20) . . . . amount remaining after t hours

<h3>Solution</h3>

We want the amount remaining after 26 hours. That will be ...

  y = 110·(1/2)^(26/20) ≈ 44.67

About 44.7 milligrams will remain after 26 hours.

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Choose any positive integer. Powers of two here are not very interesting, so choose something else. If the number you have chose
Yakvenalex [24]

Answer:

Step-by-step explanation:

Let the integer be 6 for even and 7 for odd (say)

For 6, we divide by 2, now get 3.  Now we multiply by 3 and add 1 to get 10. Now since 10 is even divide by 5, now multiply by 3 and add 1 to get 16.  Now divide by 2 again by 2 again by 2 again by 2 till we get rid of even numbers.

The result is 1, so multiply by 3 and add 1 we get 4 now divide 2 times by 2 to get 1, thus this result now again repeats after 2 times.

Say if we select off number 3, multiply by 3 and add 1 to get 10 now divide by 5, now repeat the same process as above for 5 until we get 1 and it gets repeated every third time.

Thus whether odd or even after some processes, we get 1 and the process again and again returns to 1.

5 0
3 years ago
A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w
melamori03 [73]

Answer:

The hypothesis is:

<em>H₀</em>: p_{X}-p_{Y}=0.

<em>Hₐ</em>: p_{X}-p_{Y}.

Step-by-step explanation:

Let <em>X</em> = number of men who exercise regularly and <em>Y</em> = number of women who exercise regularly.

The information provided is:

n_{X}=150\\X=88\\n_{Y}=200\\Y=130

Compute the sample proportion of men and women who exercise regularly as follows:

\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587

\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and \hat p_{X}=0.587.

The random variable <em>Y</em> also follows a Binomial distribution with parameters <em>n</em> = 200 and \hat p_{Y}=0.65.

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\hat p=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}

So, the sampling distribution of the proportion of men and women who exercise regularly follows a Normal distribution.

A two proportion <em>z</em>-test cab be performed to determine whether the proportion of women is more than men who exercise regularly.

The hypothesis for this test cab be defined as:

<em>H₀</em>: The proportion of women is same as men who exercise regularly, i.e. p_{X}-p_{Y}=0.

<em>Hₐ</em>: The proportion of women is more than men who exercise regularly, i.e. p_{X}-p_{Y}.

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3 years ago
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How do you do this question?
tatyana61 [14]

Answer:

25

Step-by-step explanation:

The increments are 0.4, and the width of the interval is 10, so the number of increments (the number of times you need to use Euler's method) is:

10 / 0.4 = 25

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krok68 [10]

Answer:

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The answer would be B
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