Let $\omega$ be a complex number such that $\omega^7 = 1$ and $\omega \ne 1.$ Compute \[\omega^{16} + \omega^{18} + \omega^{20} + \dots + \omega^{54}.\]

Let w be a complex number such that w^7 = 1 and w does not = 1.
Compute w^16 + w^18 + w^20 + ... + w^54

Need ! discuss how to convert the standard form of the equation of a circle to the general form. 50 points

Astudy was interested in determining if eating milk chocolate lowered someone's cholesterol levels. ten people's cholesterol was measured. then, each of these individuals were told to eat 100g of milk chocolate every day and to eat as they normally did. after two weeks, their cholesterol levels were measured again. is there evidence to support that their cholesterol levels went down? how should we write the alternative hypothesis? (mud = the population mean difference= before - after)a. ha: mud = 0b. ha: mud > 0c. ha: mud < 0d. ha: mud does not equal 0

Complete the equation of the live through (-1,6) (7,-2)