solve the initial-value problem
y' = x^4 - \frac{1}{x}y, y(1) = 1.

The perimeter of a triangle is 69 cm. the first is 5 cm shorter than the second side. the third side is twice as long the first side. find the length of each side

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.

Suppose that sahil knows that 45 people with ages of 18 to 29 voted. without using a calculator, he quickly says then 135 people with ages of 30to 49 voted. is he correct? how might sohil have come up with his answer so quickly?