<span>In general, the students increased their standardized math scores from 5th grade to 7th grade. The students might be more familiar with the exam and they have learned more in their math classes.</span>
For an inscribed quadrilateral, opposite angles add up to 180 degrees. In this case, if we are looking for the measure of angle D, we can use the fact that angles I & D add up to 180 degrees. Since angle I = 117:
117 + D = 180
D = 63 degrees
It would help if we represent the information in form of two-ways table as shown below
The number of students who are not on probation is 104 students
There are 23 students who are not on probation and is satisfied is 81 students
The probability of students not on probation and is satisfied is 81/104
Dy/dx = (ycos(x))/(1 + y²)
(1 + y²)/y dy = cos(x) dx
(1/y + y) dy = cos(x) dx
Integrating:
ln(y) + y²/2 = sin(x) + c
ln(1) + 1/2 = sin(0) + c
c = 1/2
Thus,
ln(y) + y²/2 = sin(x) + 1/2