Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 techno songs, 2 country songs, and3 jazz songs on it. Mekala plans to listen to 270 songs. Complete the following statement with the best prediction.
Mekala will listen to...
Please choose from one of the following options.

a) Exactly 60 country songs
b) Close to 60 country songs but probably not exactly 60country songs
c)Exactly 210 country songs
d)Close to 210 country songs but probably not exactly 210 country songs

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.a city water tank holds 20 gallons of water. a technician empties 25% of the tank. how many more gallons of water must be removed from thetank so that it has 5 of the water that it started with: the technician must removemore gallons of water for the tank to have 5 of the water that it started with.

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0