In each of problems, determine intervals in which solutions are sure to exist.

1. y^(4) + 4y"' + 3y = t
2. ty"' + (sin t)y" + 3y = cos t
3. t(t - 1)y^(4) + e^ty" + 4t^2y = 0
4. y"' + ty" + t^2y' + t^3y = ln t
5. (x-1)y^(4) + (x + 1)y" + (tan x)y = 0
6. (x^2 - 4)y^(6) + x^2y"' + 9y = 0

Geometry: determine whether segment mn is parallel to segment kl. justify your answer. jm 6 mk 3 jn 8 nl 4

In a class, there are 12 girls. if the ratio of boys to girls is 5: 4 how many boys are there in the class

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?