A gas company president for a particular city is interested in the proportion of all homes heated by gas. Historically, the proportion of all homes heated by gas has been 0.65. A sample of 75 homes was selected and it was found that 44 of them heated by gas. Perform the appropriate test of hypothesis to determine whether the proportion of homes heated by gas has changed. Test using alpha = 0.05. What the p-value and the decision for this test.

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.

The ratio of men to women working for a company is 4 to 5 . if there are 90 women working for the company, what is the total number of employees?

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.