30 POINTS PLEASE HELP A teacher is assessing the correlation between the number of hours spent studying and the average score on a music test. The table shows the data:
Number of hours spent studying
(x)
0
0.5 1
1.5 2
2.5 3
3.5
4
Score on music test
(y)
60 62
64 66 68 70 72 74 76
Part A: Is there any correlation between the number of hours students spent studying and the score on the music test? Justify your answer (4 points)
Part B: Write a function that best fits the data (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)

a) For a constant increment in x-variable, there is a constant increment in y-variable, for example, for x = 0 to x = 0.5 (increment = 0.5) y-variable goes from 60 to 62 (increment = 2); the same is valid for any couple of (x,y) values. This behaviour is characteristic of linear equations.

b) slope:

m = (increment in y-variable)/(increment in x-variable) = 2/0.5 = 4

y-intercept:

y1 = m*x1 + h

60 = 4*0 + h

60 = h

equation: y = 4x + 60

where y represents scores and x represents hours spent studying

c) The slope indicates that you need to study 1 hour to increase your score in 4 points

The y-intercept indicates that you will get at least a score of 60, even though you hadn't studied

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.