Week 4 Assignment 1) Suppose the number of people who sign up for a band's mailing list is in proportion to how many people are at their show. One night

the band plays for 560 people and 37 sign up for their mailing list. The next night they play for 311 people. How many people does the band expect to sign up for their mailing list? Round your answer to the nearest person. 2) A conductor notes that the number of mistakes her orchestra makes one week before performance is proportional to the length of the piece. One piece is 12 minutes, 19 second long and the conductor notices 17 mistakes one week before performance. Their second piece is 21 minutes, 50 seconds long. How many mistakes does the conductor expect there to be in this second piece one week before performance? Round your answer to the nearest integer. 3) If you play a song at 128 beats per minute, it takes 3 minutes, 51 seconds to play. If you slow the tempo down to 112 beats per minute, how long does it take to play this song? Answer in terms of minutes and seconds, rounding to the nearest second. 4) One of the G-strings on a banjo plays a G4, which has a frequency of 392 Hz and is 26.25 inches long. The second fret on this string plays an A4, which has a frequency of 440 Hz. The tenth fret plays a F5, which has a frequency of 698.46 Hz. What is the distance between the second fret and the tenth fret on this banjo? Round your answer to the nearest 0.01 inch. Hint: there is no shortcut. First find the distance from the bridge to the second fret... 5) A singer earned a total of $950 at her first three gigs this month. Her fourth gig this month paid her $325, and her fifth gig this month paid her $455. Calculate her average earnings per gig at her first five gigs this month. 6) In April a band plays 8 shows and averages 260 people at each show. In May this band plays 5 shows and averages 185 people at each one. What is the average number of people at each show which this band played in these two months? Round to the nearest integer. 7) A mini-festival lasts a total of 5 hours, with exactly one performer on stage at all times (including set up and take down), and there are a total of 8 performers. The first 5 performers average 32 minutes each (including set up and take down) on the stage. What is the average time that each of the last 3 performers is on stage (including set up and take down)? Answer in terms of minutes and, if needed, seconds. 8) On July 1, the van's odometer reads 54,300 miles. The band which owns the van goes on tour. On December 1, the van's odometer reads 72,600 miles. What is the average number of miles which the van was driven each month during this period? y 6- 5 4 3 -6 -5 -4 -3 -2 -1 0 I 4 5 6 = 9) Find the curve's average slope between the two red dots, whose coordinates are integers