Math Answers

There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 20% of the original amount increase in 20 years, how much will the population in the city after 40 years?

6 divides n^3 - n for n>=2

Prove by mathematical induction: 6 divides n^3 - n for n>=2

Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already 5 million of them. If the bacterial population follows a law of natural growth, how many bacteria should be present in the Petri dish after 5 minutes?

Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5 million pesos. After 2 years, the value decreased to 1.2 million pesos. If the amount of the car is directly proportional to the constant rate of decay in amount and such decrease in amount continues at the same rate, then how much is the estimated value of the car after 10 years?

Americans ate an average of 25.7 pounds of confectionery products each last year and

spent an average of $61.50 per person doing so. If the standard deviation of consumption is 3.75 pounds and the standard deviation of the amount spent is %5.89, find the following:

a. The probability that the sample mean confectionary consumption for a random sample

of 40 American consumers was greater than 27 pounds.

b. The probability that for a random sample of 50, the sample mean for confectionary

spending exceeded $60.00

The average per capita spending on health care in United States is $5274. If the standard

deviation is $600 and the distribution of health care spending is approximately normal, what is the probability that a randomly selected person spends more than $6000? Find the limits of the middle 50% of individual health care expenditures.

a company produces mosquito repellents that have a period of effectiveness that is approximately normally distributed with a mean of 300 hours and a standard deviation of 30 hours. A sample of 40 repellents was taken and the average period of effectiveness is computed as 290 hours. Test the hypothesis that µ = 300 against the alternative that µ ≠ 300