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1 year ago

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Mathematics

1 answer:

Elenna [48]1 year ago

6 0

a.) initial sample left : 794g

b.) Time taken to decay : 3.39

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

a.)

Substituting 25 for t in the expression, we get:

A(25)= $200e^{0.0541*25}$

$200e^{1.3525}$

Thus, after 25 years, there will be $200e^{1.3525}$ =2003.97=>794 g of the initial sample left in the sample.

794

b.)

We want to find t such that A(t)= $200e^{0.0541}$

=100.

Solving for t, we get:

= $200e^{0.0541}$ *t

=100

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541*t=ln(0.5)

Therefore, t= $\frac{ln(0.5)}{0.0541}$

=3.39 years.

To Learn More about Isotopes Decay follow link : brainly.com/question/16355768

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Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed w

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Complete Question

The complete question is shown on the first uploaded image

Answer:

The sales level that is the cut-off between quarters that are considers as "failure" and those that are not is evaluated as

$y = 6.3 \ million \ dollars$

Step-by-step explanation:

From the question we are told that the

Mean is $\mu = 8 \ million \ dollars$

Standard deviation is $\sigma = 1.3 \ million \ dollars$

Let Y be the random variable that denotes the sales made quarterly among health care information system

The normal distribution for this data is mathematically represented as

$Y$ ~ N $(\mu = 8 , \sigma^2 = 1.69)$

From the question we are told that a quarter is consider a failure by the company if the sales level that quarter in the bottom 10% of the of all quarterly sales

The the Probability of obtaining quarterly sales level that is equal to 10% of all quarterly sale (It is not below 10%) is mathematically represented as

$P[Y < y ] = 0.10$

This can be represented as a normal distribution in this manner

$P [ \frac{Y- \mu}{\sigma } < \frac{y -\mu}{\sigma} ] = 0.10$

Where $\frac{Y - \mu }{\sigma } = Z$ ~ $N(0 , 1)$

{This mean that this equal to the normal distribution between 0, 1 which is the generally range of every probability }

Therefor we have

$P[Z < \frac{y- 8}{1.3} ]$

The cumulative distribution function for a normal distribution of y is mathematically represented as

$\phi [\frac{y- 8}{1.3} ] = 0.10$

This is because a cumulative distribution function of a random value Y or a distribution of Y evaluated at y is the probability that Y will take will take a value that is less or equal to y

$\frac{y- 8}{1.3} = \phi ^{-1}(0.10)$

Calculating the inverse of the cumulative distribution function value of 0.10 which is negative the the critical value(Critical values determine what probability a particular variable will have when a sampling distribution is normal or close to normal.) of 0.01

$\phi ^{-1}(0.10) =- [1 - \frac{0.10}{2}]$