Math Answers

The CEO of a battery manufacturing company claimed that their batteries would last an average of 280 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested them. The tested batteries had a mean life span of 250 hours with a standard deviation of 40 hours. Do we have enough evidence to suggest that the claim of an average of 280 hours is false?

The CEO of a battery manufacturing company claimed that their batteries would last an average of 280 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested them. The tested batteries had a mean life span of 250 hours with a standard deviation of 40 hours. Do we have enough evidence to suggest that the claim of an average of 280 hours is false?

Nate is culturing bacteria that have a growth rate of 10% per hour. If the current population is 12,800 bacteria, how many bacteria will there be in 8 hours?

There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 4?

An association of City Mayors conducted a study to determine the average number of times

a family went to buy necessities in a week. They found that the mean is 4 times in a week. A

random sample of 20 families were asked and found a mean of 5 times in a week and a

standard deviation of 2. Use 5% significance level to test that the population mean is not

equal to 4. Assume that the population is normally distributed.

On average, four students visits the Mathematics and Statistics tutoring centre during a 5-minute period.  

(a) Calculate the probability that three students visit the center during a 5- minute period. 

(b) During a ten-minute period, what is the probability that at least 4 students visit the centre? 

two fair number cubes, labeled 1 through 6, are rolled and the results are recorded. how many outcomes are in the sample space?

find the derivative using chain rule.

1. y= (x³ + 3)⁵

2. y=(-3x⁵ + 1)³

3. y=(-5x³ - 3)³

4. y=(5x² + 3)⁴

5. f(x)=⁴√-3x⁴-2

6. f(x)= √-2x² + 1

Suppose that a particle moves along a line with position function s(t) =2t^2 +3t+1 where s is in meters and t is in seconds.

a. What is its initial position?

b. Where is it located after t = 2 seconds?

c. At what time is the particle at position s = 6?

A manufacturer of isopropyl alcohol claims that their product has a mean content of 480 mL. and a standard 

deviation of 21.5 mL. Assume that the variable is normally distributed.

a. If a sample is selected, what is the probability that the content will be less than 505 mL?

b. If a sample of 6 isopropyl alcohol is selected, what is the probability that the mean of the sample will be 

less than 505?