The table below shows the total number of hours Jessica Emily and Trina each studied after given a number of weeks

Trina's number of hours studied is proportional to number of weeks studied

Step-by-step explanation:

The ratio of each pair in any given table of values must be the same all through, for the relationship between two variables to be considered proportional.

In this case, we are looking at the relationship between number of weeks (x) and total number of hours studied (y).

The ratio for a pair is given as: y/x

If the ratio value for all pairs are the same in any of the given table, then it is proportional.

❌For Jessica's table of values, the first, second and third pair of values have a ratio of 2.5, however, the fourth pair has a different ratio of 4 (y/x = 40/10 = 4). So, this relationship is not proportional.

❌For Emily, the first, and second pair has a ratio of 2.5 while the third and fourth has different ratio. This also isn't a proportional relationship.

✅For Trina, the relationship between hours studied and the given number of weeks is proportional, because all pairs have the same ratio. That is: y/x = 5/2 = 10/4 = 20/8 = 25/10 = 2.5

✍️A proportional relationship can be written as .

Where,

y = total number of hours

x = number of weeks

k = constant of proportional = 2.5 (the ratio between y to x)

To generate an equation that represents the proportional relationship in the table of values for Trina, simply plug in the value of k in .

Thus, the equation would be:

✅.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)