Na random sample of six microwave ovens, the mean repair cost was $65.00 and the standard deviation was $14.00. assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean mu. what is the margin of error of mu? interpret the results.

Explain step-by-step how to simplify -5(2x – 3y + 6z – 10).

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

If sin(x) = 0 and cos(x) = 1, what is tan(x)?