Given and , find .  

To carry a 100-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a angle away from the vertical and the other makes a angle as shown in the figure below. Find each rope’s tension if the resultant force is vertical.Round your answer to two decimal places. ​ ​

Which case ruled with some exceptions, that officers must knock and announce their identity before entering a dwelling?

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

This United States Supreme Court Decision in 1857 included an opinion by Justice Roger Brooke Taney that stated that African Americans, at the time of the nation ‘s founding had ‘been regarded as… so far inferior that they had no rights which the white man was bound to respect.”

A random sample of 16 motels in Vacation City revealed that the mean room charge was $90 per day with a standard deviation of $8.  Assuming that the room charge per day has a normal distribution, give a 90% confidence interval estimate of the mean room charge. What is the sample size?

The total dollar value of all goods and services produced by all people within the boundaries of a country is called

EXTRA CREDIT: If you are dark-skinned and live at higher latitudes (e.g. in Canada), then there is likely a mismatch between your ________________ and UV light levels, and you may have health issues related to vitamin D _________________ if you do not eat a proper diet or seek medical attention.

The primarily physiological drive to find and eat food:

Identify the glycoprotein spike associated with the influenza virus that binds to respiratory mucosal receptors and triggers an inflammatory response: