You work 40 hours a week at a furniture store. You receive a $250 weekly salary, plus a 5% commission on sales over $2000. Assum
2 answers:
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<h2>Hello!</h2>
The answer is:
There will remain a total of 134 bacteria after 7 minutes.
<h2>Why?</h2>Exponential decay calculations are commonly used to find the decrease of amounts of populations, bacterias, and other situations when using proportional relationships. In order to find the problem, we must remember the equation used to calculate the exponential decay.
Where,
S, is the starting value/amount
r, is the rate (% to real number)
t, is the time elapsed.
We are given that the numbers of bacteria decrease by 50 after 5 minutes, starting with 200, and after 5 minutes the number of bacteria is 150
Calculating the rate of decrease, we have:
Therefore, the rate of decrease is 0.25 or 25% (after multiplying the number by 100)
Then, substituting the given information and the rate of decrease into the decay equation, we have:
Now, to calculate how many bacteria will remain after 7 minutes, we need to substitute it into the decay equation:
So, rounding to the nearest whole number, there will remain a total of 134 bacteria after 7 minutes.
Have a nice day!
Answer:
n=170
Step-by-step explanation:
1) Notation and definitions
random sample taken (variable of interest)
estimated proportion.
true population
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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 population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=170
And we are given that and want to find the value of x. Set f(x) to 16 and we get the equation:
Subtract both sides by 4
Divide both sides by 2
This is the answer. Let me know if you need any clarifications, thanks!