Ethan hunt : )

a cable company had 595 subscribers. the ratio of regular subscribers to premium subscribers was 8: 9 how many regular subscribers did they have
use a tape diagram

john was looking at his streaming music stats. the ratio of song he liked to disliked was 5: 2 if he listened to 91 songs total how many did he like
use a tape diagram

at the fair the ratio of male to females was 4: 5 if there are 180 at the fair how many males are there
use a tape diagram

Number of Total Subscribers = 595

In Figure 1, Red boxes represent "regular subscribers" which is 8 in number whereas Blue boxes represent "premium subscribers".

1 box contains = 595/17 = 35 subscribers. 

Regular subscribers = 35 * 8 = 280

In short, Your Final Answer would be: 280

B.) Total Number of Songs = 91

Red boxes represent number of songs, he liked i.e., 5
Blue represents, he dislikes, i.e., 2

Number of songs in each box = 91/7 = 13

Now, The number of songs, he liked: 13 * 5 = 65 

In short, Your Answer would be: 65 songs

C.) Total people = 180
Red represents the box of males, which is 4
Blue for females.

Number of people for each box = 180/9 = 20

So, Number of males = 20 * 4 = 80

In short, Your Answer would be: 80 males

Hope this helps!

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.